Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

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skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Tue Oct 19, 2021 12:29 am
skierincolorado wrote: Tue Oct 19, 2021 12:17 am
comeinvest wrote: Tue Oct 19, 2021 12:10 am
skierincolorado wrote: Mon Oct 18, 2021 11:48 pm I would still trust the rates published in a research paper using the actual CTD security over back of the envelope calculations.
I wouldn't disagree, but also consider what I said in my other post: "Although at the end of the day, the comparisons to the Vanguard funds might be more meaningful to the investor for purpose of calculating all-in cost of leverage, as those are real investable alternatives to using futures. The rates of cash treasuries of the exact same tenor as the available futures contracts (especially the deliverable CTD itself) might be artificially "pushed down" by investors' demand for the futures and the futures/cash treasuries cash-and-carry arbitrage." Demand for long futures positions should translate to demand for the CTD by the hedging counterparties.
But there isn't a single tenor for futures contract, but rather a basket. If one tenor is pushed down, a different tenor would become CTD. I could see how this could be the case though if CTD clusters around a few tenors.
Hard to reverse-engineer the market forces for me as a layman. All I'm saying is the the comparison to the Vanguard funds might be meaningful for purpose of estimating an "all-in" cost of leverage, as in comparing to alternative methods of leverage like equity futures or options box spreads.
Figure 37 shows that interest rate deviations in the CTD have historically not been a problem, but briefly spiked slightly in March 2020:

https://www.financialresearch.gov/worki ... onnect.pdf



Regarding funds, I think what we want to do is calculate the fees of funds and the financing of futures independently. If they end up being about the same, then funds could be used interchangeably in backtests for deciding on a strategy. That appears to be the case based on the OFR research, and based on my calculation for ZN, which show financing of around 0.2% very similar to the the fees on VFITX. The calculation for ZF is a bit higher though, but we might be doing it wrong.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Tue Oct 19, 2021 12:02 am Here's ZB:

Sep 30 2011 -> Sep 30 2021 per SPGlobal:
320.97 -> 455.74 = 3.56% CAGR

VGLT average duration is 17.9 years

ZB CTD duration is currently 11.6 years.

Am I doing the duration wrong? VGLT is much longer duration than ZB.
It's UB. I corrected my post with the calcs and the one with the slippage per unit or duration. UB should have almost the same maturity as VGLT.
Topic Author
skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Tue Oct 19, 2021 12:41 am
skierincolorado wrote: Tue Oct 19, 2021 12:02 am Here's ZB:

Sep 30 2011 -> Sep 30 2021 per SPGlobal:
320.97 -> 455.74 = 3.56% CAGR

VGLT average duration is 17.9 years

ZB CTD duration is currently 11.6 years.

Am I doing the duration wrong? VGLT is much longer duration than ZB.
It's UB. I'm correcting my post with the calcs. UB should have almost the same maturity as VGLT.
For UB:

Sep 30 2011 -> Sep 30 2021 per SPGlobal:
137.78 -> 202.11 = 3.91% CAGR

VGLT had 4.29% CAGR

So .38% difference, plus .05% ER = .43% financing cost (.38% higher than the VGLT fee)

Could be that longer durations have higher financing which makes sense given they are less liquid. Could be that the duration of the CTD was different historically. Or the duration of VGLT could have changed.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Tue Oct 19, 2021 12:31 am
comeinvest wrote: Tue Oct 19, 2021 12:29 am
skierincolorado wrote: Tue Oct 19, 2021 12:17 am
comeinvest wrote: Tue Oct 19, 2021 12:10 am
skierincolorado wrote: Mon Oct 18, 2021 11:48 pm I would still trust the rates published in a research paper using the actual CTD security over back of the envelope calculations.
I wouldn't disagree, but also consider what I said in my other post: "Although at the end of the day, the comparisons to the Vanguard funds might be more meaningful to the investor for purpose of calculating all-in cost of leverage, as those are real investable alternatives to using futures. The rates of cash treasuries of the exact same tenor as the available futures contracts (especially the deliverable CTD itself) might be artificially "pushed down" by investors' demand for the futures and the futures/cash treasuries cash-and-carry arbitrage." Demand for long futures positions should translate to demand for the CTD by the hedging counterparties.
But there isn't a single tenor for futures contract, but rather a basket. If one tenor is pushed down, a different tenor would become CTD. I could see how this could be the case though if CTD clusters around a few tenors.
Hard to reverse-engineer the market forces for me as a layman. All I'm saying is the the comparison to the Vanguard funds might be meaningful for purpose of estimating an "all-in" cost of leverage, as in comparing to alternative methods of leverage like equity futures or options box spreads.
Figure 37 shows that interest rate deviations in the CTD have historically not been a problem, but briefly spiked slightly in March 2020:

https://www.financialresearch.gov/worki ... onnect.pdf



Regarding funds, I think what we want to do is calculate the fees of funds and the financing of futures independently. If they end up being about the same, then funds could be used interchangeably in backtests for deciding on a strategy. That appears to be the case based on the OFR research, and based on my calculation for ZN, which show financing of around 0.2% very similar to the the fees on VFITX. The calculation for ZF is a bit higher though, but we might be doing it wrong.
Not sure why VFITX has 0.2%, when VGSH and VGLT have 0.05% fees. Some folks on this forum also invest directly in treasuries. To answer your question, I think we can obtain a more meaningful estimate of "all-in" cost of leverage by comparing the performance of the futures to the performance of Vanguard funds, not just the performance of futures to e.g. cash treasuries of one tenor or a single cash treasury, then adding back ETF fees. Whether it matters or not, the calcs will show us. At the end of the day, performance per risk of an investable product is what matters.
Last edited by comeinvest on Tue Oct 19, 2021 2:56 am, edited 2 times in total.
Topic Author
skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

Might as well do TN while I'm at it.

Jane 30 2016 - Sep 30 2021
101.64 -> 118.13 = 2.69% CAGR

IEF
2.68% CAGR

-.01% difference + .15% IEF fee = .14% financing cost (.01% less than IEF fee)

Note TN is 8.8 while IEF is 8.03 duration.

Using 92% IEF / 8% VUSTX, I get 2.83% CAGR, which would be a .14% difference + .14% fee = .28% financing cost (.14% higher than IEF fee)

This one is fairly consistent with the OFR paper which finds ~.25% financing costs during this period.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Tue Oct 19, 2021 12:50 am
comeinvest wrote: Tue Oct 19, 2021 12:41 am
skierincolorado wrote: Tue Oct 19, 2021 12:02 am Here's ZB:

Sep 30 2011 -> Sep 30 2021 per SPGlobal:
320.97 -> 455.74 = 3.56% CAGR

VGLT average duration is 17.9 years

ZB CTD duration is currently 11.6 years.

Am I doing the duration wrong? VGLT is much longer duration than ZB.
It's UB. I'm correcting my post with the calcs. UB should have almost the same maturity as VGLT.
For UB:

Sep 30 2011 -> Sep 30 2021 per SPGlobal:
137.78 -> 202.11 = 3.91% CAGR

VGLT had 4.29% CAGR

So .38% difference, plus .05% ER = .43% financing cost (.38% higher than the VGLT fee)

Could be that longer durations have higher financing which makes sense given they are less liquid. Could be that the duration of the CTD was different historically. Or the duration of VGLT could have changed.
I would think it's because of higher (interest rate) risk to the counterparty, not liquidity. My understanding is that counterparties that hold the short treasury futures are constrained by regulations with respect to their total risk exposure. They basically have a certain bucket that they can fill with quasi-arbitrage positions (for example cash-and-carry arbitrage), and they optimize their exposure to hedge the products that they can generate the highest arbitrage return with. EDIT: They are probably perfectly hedged with respect to interest rates, but still have a limit on total exposure in case of catastrophic events or, for example, when the cash-and-carry fails like in Spring 2020.
Last edited by comeinvest on Tue Oct 19, 2021 1:11 am, edited 1 time in total.
Topic Author
skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Tue Oct 19, 2021 12:54 am
skierincolorado wrote: Tue Oct 19, 2021 12:31 am
comeinvest wrote: Tue Oct 19, 2021 12:29 am
skierincolorado wrote: Tue Oct 19, 2021 12:17 am
comeinvest wrote: Tue Oct 19, 2021 12:10 am

I wouldn't disagree, but also consider what I said in my other post: "Although at the end of the day, the comparisons to the Vanguard funds might be more meaningful to the investor for purpose of calculating all-in cost of leverage, as those are real investable alternatives to using futures. The rates of cash treasuries of the exact same tenor as the available futures contracts (especially the deliverable CTD itself) might be artificially "pushed down" by investors' demand for the futures and the futures/cash treasuries cash-and-carry arbitrage." Demand for long futures positions should translate to demand for the CTD by the hedging counterparties.
But there isn't a single tenor for futures contract, but rather a basket. If one tenor is pushed down, a different tenor would become CTD. I could see how this could be the case though if CTD clusters around a few tenors.
Hard to reverse-engineer the market forces for me as a layman. All I'm saying is the the comparison to the Vanguard funds might be meaningful for purpose of estimating an "all-in" cost of leverage, as in comparing to alternative methods of leverage like equity futures or options box spreads.
Figure 37 shows that interest rate deviations in the CTD have historically not been a problem, but briefly spiked slightly in March 2020:

https://www.financialresearch.gov/worki ... onnect.pdf



Regarding funds, I think what we want to do is calculate the fees of funds and the financing of futures independently. If they end up being about the same, then funds could be used interchangeably in backtests for deciding on a strategy. That appears to be the case based on the OFR research, and based on my calculation for ZN, which show financing of around 0.2% very similar to the the fees on VFITX. The calculation for ZF is a bit higher though, but we might be doing it wrong.
Not sure why VFITS has 0.2%, when VGSH and VGLT have 0.05% fees. Some folks on this forum also invest directly in treasuries. To answer your question, I think we can obtain a more meaningful estimate of "all-in" cost of leverage by comparing the performance of the futures to the performance of Vanguard funds, not just the performance of futures to e.g. cash treasuries of one tenor or a single cash treasury, then adding back ETF fees. Whether it matters or not, the calcs will show us. At the end of the day, performance per risk of an investable product is what matters.
Yes in this case we could simply state the cost of futures is xyz% higher than the cost of vanguard funds. For ZN and TN I am finding them to be quite similar to VFITX (which has .2% fees). This is useful for deciding what product to invest in.

But when deciding on what duration to invest in, we need useful backtests. And to create those backtests we need the actual financing cost and then to simulate that financing cost through the use of funds with fees similar to the financing cost (like VFITX) above cash, or shorting some duration that approximates the financing cost. So far financing costs of .2-.3% are consistent with the backtests using VFITX (fees of .2%) showing it to be superior to longer durations. I also wonder if the funds used in backtests used to have higher fees, which would impact leverage and optimal duration. Leveraging a high fee on a shorter duration won't look so good.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Tue Oct 19, 2021 12:50 am
comeinvest wrote: Tue Oct 19, 2021 12:41 am
skierincolorado wrote: Tue Oct 19, 2021 12:02 am Here's ZB:

Sep 30 2011 -> Sep 30 2021 per SPGlobal:
320.97 -> 455.74 = 3.56% CAGR

VGLT average duration is 17.9 years

ZB CTD duration is currently 11.6 years.

Am I doing the duration wrong? VGLT is much longer duration than ZB.
It's UB. I'm correcting my post with the calcs. UB should have almost the same maturity as VGLT.
For UB:

Sep 30 2011 -> Sep 30 2021 per SPGlobal:
137.78 -> 202.11 = 3.91% CAGR

VGLT had 4.29% CAGR

So .38% difference, plus .05% ER = .43% financing cost (.38% higher than the VGLT fee)

Could be that longer durations have higher financing which makes sense given they are less liquid. Could be that the duration of the CTD was different historically. Or the duration of VGLT could have changed.
Why the difference to my calcs? (hint: it's NOT the accuracy of my exponent 1/9.85)
I had: Nov 30 2011 - Sep 23 2021
per S&P total return chart 136.26 -> 206.43 => total return 1.515 => CAGR: 1.515 ^ (1/9.85) -> 4.3%
VGLT per IB performance chart: 55.83 -> 89.97 => total return 1.61 => CAGR: 1.61 ^ (1/9.85) -> 4.95%
Are we using different definitions of "return"?
Something wrong with using the IB performance charts?


I think you used Oct 1 instead of Sep 30 for the UB S&P end date. Using the correct data for your dates I get:
Sep 30 2011 -> Sep 30 2021 per SPGlobal: 137.78 -> 200.08 -> total return 1.452 -> CAGR 3.8%
VGLT per portfoliovisualizer.com : CAGR 4.29%
=> difference: 0.49% => (0.05% ER) slippage: 0.53%

We have to be careful with the dates, as there is a relatively high sensitivity of results to market fluctuations of single dates.

I'm still struggling with finding a cash comparison to ZB. skierincolorado?
Last edited by comeinvest on Tue Oct 19, 2021 4:39 am, edited 4 times in total.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Tue Oct 19, 2021 1:10 am
comeinvest wrote: Tue Oct 19, 2021 12:54 am
skierincolorado wrote: Tue Oct 19, 2021 12:31 am
comeinvest wrote: Tue Oct 19, 2021 12:29 am
skierincolorado wrote: Tue Oct 19, 2021 12:17 am

But there isn't a single tenor for futures contract, but rather a basket. If one tenor is pushed down, a different tenor would become CTD. I could see how this could be the case though if CTD clusters around a few tenors.
Hard to reverse-engineer the market forces for me as a layman. All I'm saying is the the comparison to the Vanguard funds might be meaningful for purpose of estimating an "all-in" cost of leverage, as in comparing to alternative methods of leverage like equity futures or options box spreads.
Figure 37 shows that interest rate deviations in the CTD have historically not been a problem, but briefly spiked slightly in March 2020:

https://www.financialresearch.gov/worki ... onnect.pdf



Regarding funds, I think what we want to do is calculate the fees of funds and the financing of futures independently. If they end up being about the same, then funds could be used interchangeably in backtests for deciding on a strategy. That appears to be the case based on the OFR research, and based on my calculation for ZN, which show financing of around 0.2% very similar to the the fees on VFITX. The calculation for ZF is a bit higher though, but we might be doing it wrong.
Not sure why VFITS has 0.2%, when VGSH and VGLT have 0.05% fees. Some folks on this forum also invest directly in treasuries. To answer your question, I think we can obtain a more meaningful estimate of "all-in" cost of leverage by comparing the performance of the futures to the performance of Vanguard funds, not just the performance of futures to e.g. cash treasuries of one tenor or a single cash treasury, then adding back ETF fees. Whether it matters or not, the calcs will show us. At the end of the day, performance per risk of an investable product is what matters.
Yes in this case we could simply state the cost of futures is xyz% higher than the cost of vanguard funds. For ZN and TN I am finding them to be quite similar to VFITX (which has .2% fees). This is useful for deciding what product to invest in.

But when deciding on what duration to invest in, we need useful backtests. And to create those backtests we need the actual financing cost and then to simulate that financing cost through the use of funds with fees similar to the financing cost (like VFITX) above cash, or shorting some duration that approximates the financing cost. So far financing costs of .2-.3% are consistent with the backtests using VFITX (fees of .2%) showing it to be superior to longer durations. I also wonder if the funds used in backtests used to have higher fees, which would impact leverage and optimal duration. Leveraging a high fee on a shorter duration won't look so good.
Regarding optimization objectives: It's a multivariate optimization problem. I personally am interested in (1) how does the cost of leverage differ for different treasury futures tenors; (2) based on (1) what is my "all-in" cost of leverage in comparison to a comparable, investable non-leveraged product (like a combo of Vanguard funds). This allows me to decide which method of leverage I use for my portfolio: treasury futures, equity futures, or options box spreads; the decision might depend on the tenor (maturity); (3) based on (1), what is the risk-adjusted return after cost of leverage of different treasury futures tenors in comparison with each other. This allows me to help decide my constant or dynamic positioning on the yield curve. I probably disagree with risk=duration, but I still have to figure that out. You could re-run your overall backtests using your assumption risk=duration i.e. constant units of duration, for example, as I think you did before, but subtracting from annual returns the difference between the cost of leverage slippage and the cost of whatever fund you used for your original calculation, as per (2), multiplied by the leverage factor of course. Maybe historic expense ratios can be found in old annual reports. I can't remember how you backtested the more distant decades?

Given the numbers in my rough "duration-adjusted slippage per tenor" calcs in my earlier post, it seems clear that the inclusion of financing cost slippage will tilt the calcs to some degree back in favor of longer tenors, if I'm not mistaken. It seems also clear that it will result in lower treasury allocations vs. equities, everything else being equal.

We might also consider using the most recent 5-year average implied financing cost instead of the 10-year average, because of documented regime changes.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

I compared the S&P cash-secured ultra T-Bond future with the S&P U.S. Treasury Bond 20+ Year Index.
The futures contract currently has a maturity of 25 years and 4 months. The treasury bond index currently has an average maturity of 26 years. I didn't verify this, but I think the carry with rolldown is usually pretty constant with respect to maturity in that maturity range.

On the spglobal page you can directly compare the charts and it shows you the 10-year annualized return for both.
As of today, the 10-year annualized returns are: ...
EDIT: Here are the data for all futures:

2-year futures index (currently 1.96 years maturity) vs. the treasury bond current 2-year index (1.92y average maturity):
10 years: 0.91% / 1.04% => slippage: 0.13%
5 years: 1.33% / 1.44% => slippage: 0.11%
3 years: 2.09% / 2.45% => slippage: 0.36%
1 year: -0.36% / -0.2% => slippage: 0.16%

3-year (Z3N) (introduced on July 13, 2020) futures index (currently 2 years 11.5 months maturity) vs. the treasury bond current 3-year index (2.88y average maturity):
10 years: ?% / 1.34% => slippage: ?%
5 years: ?% / 1.72% => slippage: ?%
3 years: ?% / 3.31% => slippage: ?%
1 year: ?% / -0.68% => slippage: ?%

5-year futures index (currently 4 years 4.5 months maturity) vs. S&P U.S. Treasury Bond Current 5-Year Index (currently 4.92 years average maturity):
10 years: 1.6% / 1.93% => slippage: 0.33%
5 years: 1.63% / 1.87% => slippage: 0.24%
3 years: 3.7% / 4.41% => slippage: 0.71%
1 year: -2.24 /-2.72% => excess gain: 0.48%

10-year note futures (currently 6 years 10 months maturity) vs. S&P U.S. Treasury Bond Current 7-Year Index (currently 6.92 years average maturity):
10 years: 2.39% / 2.78% => slippage: 0.33%
5 years: 2.01% / 2.34% => slippage: 0.33%
3 years: 5.06% / 5.51% => slippage: 0.45%
1 year: -3.81 /-4.1% => excess gain: 0.29%

S&P Ultra 10-Year U.S. Treasury Note Futures Index (currently 9 years 7 months maturity) vs. S&P U.S. Treasury Bond Current 10-Year Index (currently 9.88 years average maturity):
10 years: no data
5 years: 2.38% / 2.01% => excess gain: 0.33%
3 years: 6.39% / 6.33% => excess gain: 0.06%
1 year: -5.43 /-6.03% => excess gain: 0.6%

S&P U.S. Treasury Bond Futures Index (currently 15 years 7 months maturity) vs. (didn't find good match) S&P U.S. Treasury Bond 10-20 Year Index (currently 18.76 years average maturity):
10 years: 3.74% / 3.67% => excess gain: 0.07% (warning: didn't find good match)
5 years: 3.12% / 2.92% => excess gain: 0.2% (warning: didn't find good match)
3 years: 8.45% / 7.61% => excess gain: 0.84% (warning: didn't find good match)
1 year: -6.67 /-8.21% => excess gain: 1.54% (warning: didn't find good match)

S&P cash-secured ultra T-Bond future (25 years and 4 months) vs. the S&P U.S. Treasury Bond 20+ Year Index (26 years):
10 years: 4.3% (cash-secured futures index) / 5.04% (bond index) => slippage: 0.74%
5-year annualized returns: 3.61% (future) / 4.19% (bond index) => slippage: 0.58%
3-year: 9.99% / 10.72% => slippage: 0.73%
1-year: -8.44% / -8.35% => slippage: 0.09%


How about short UB vs. long ZB for a carry arbitrage after slippage?

We should also examine the slippage in rising vs. falling interest rates periods.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

@skierincolorado: What's your best way of quickly calculating current rolldown returns across the yield curve, or even better, do you know a source or a way to generate a chart that shows the current carry+rolldown yield by maturity?
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Mon Oct 18, 2021 10:56 pm
millennialmillions wrote: Mon Oct 18, 2021 9:55 pm
constructor wrote: Mon Oct 18, 2021 2:46 pm
millennialmillions wrote: Sun Oct 17, 2021 9:14 am Bentonkb linked to this CME paper, which describes how to calculate the Principal Invoice Price, a better representation of the market value.

"E.g., the conversion factor for delivery of the 2-3/8% T-note of Aug-24 vs. December 2017 10-year T-note futures is 0.8072. This suggests that a 2 3/8% security is approximately valued at 81% as much as a 6% security. Assuming a futures price of 125-08+/32nds (or 125.265625 expressed in decimal format), the principal invoice amount may be calculated as follows. Principal Invoice Price = 125.265625 x 0.8072 x $1,000 = $101,114.41 E.g., the conversion factor for delivery of the 1-7/8% T-note of Aug-24 vs. December 10-year T-note futures is 0.7807. This suggests that a 1-7/8% security is approximately valued at 78% as much as a 6% security. Assuming a futures price of 125-08+/32nds (or 125.265625), the principal invoice amount may be calculated as follows.
Principal Invoice Price
= 125.265625 x 0.7807 x $1,000
= $97,794.87
In order to arrive at the total invoice amount, one must of course further add any accrued interest since the last semi annual interest payment date to the principal invoice amount."

It looks like the current CTD underlying security has a conversion factor of 0.95. So I would calculate your current STT exposure as $109,245 * 0.95 CF * 2 (for $200,000 face value) * 4 contracts = $830,262.

Note it doesn't appear there is consensus on this calculation, but this seems to directly align with the CME paper, and I haven't seen a good reason to use any other number. Also, the conversion factor for STT is closer to 1 than ITT or LTT, so it doesn't have as much of an impact.
While I agree with you in terms understanding of the book/PDF in practice I found the conversion factor does not need to be taken account given these empirical observations. Let's use the most extreme example with UB which has a conversion factor of 0.6141 as per Treasury Analytics (https://www.cmegrou ... tics.html).

1. The volatility of UB is identical to TLT, and definitely not 0.6 times that of TLT. If the actual exposure is the "invoice price" which is 0.6 times the nominal value we would expect UB to be 0.6 times as volatile.
2. In the Treasury Analytics page there is DV01 for futures and DV01 for cash, and precisely Cash DV01 = 0.6 * Futures DV01. If the actual exposure is the invoice price then the DV01 would be identical.

Well basically these two points are the same point.

But I agree with you that it sounds like on delivery only 0.6 times the nominal amount of the underlying treasury would be delivered. Confusing... I wonder if I am understanding the delivery process incorrectly.

Edit: On page 12 it does say:
E .g ., if one held $10 million face value of the 2-3/8%-8/24 note, one might sell 81 December 2017 futures by reference to the conversion factor of 0 .8072 to execute a hedge .
So this confirms that the nominal value is correct, that one future contract hedges more than "one treasury", given the ration of (1 / conversion factor). Though my question remains how the delivery work, since this almost seems you might need to deliver fraction of a treasury, and what the invoice price really means in the delivery process.
Thank you for your reply. I'm amazed we haven't reached consensus on something so fundamental to this strategy...it should be important for everyone in this thread to have an answer to this.

I disagree with your reading of that section (page 9 of the CME PDF) and believe it actually confirms the opposite, that the futures price must be multiplied by the conversion factor to determine market value/market exposure. Look at this table:
Image

The cash price is the market value. Multiplying the futures price by the conversion factor gets us very close to this market value (and the difference is the basis, which is small enough to ignore for our purpose).

Ultimately, it doesn't matter that one futures contract hedges more than "one treasury". What matters is holding one futures contract gives you equivalent performance to investing $x directly in treasuries, or in a fund like TLT. This paper says that x ≈ futures price * CF.

The best way to settle this would be to use actual futures returns data compared against a fund to determine how much TLT is needed to replicate the results of 1 UB contract. Your point that "the volatility of UB is identical to TLT" doesn't answer this question of how much is needed.
Here is my understanding. I am not 100% confident in this, but am not overly concerned because the amounts are close enough for my purposes.

What is delivered is the 100k. What is paid is the invoice price. But because the invoice price is calculated as if the delivered bonds had a 6% yield, the invoice price changes reflect the price change of a basket of bonds with face value of 100k / CF. Thus the long position gets the return of the larger basket. The short position gets the referse of this return. If the short position wishes to hedge and collect the basis, they must own the larger basket.

Thus we get:

"E.g., if one were to buy the basis by buying $10 million
face value of the 2-3/8%-8/24 note, one might sell 81
December 2017 futures by reference to the conversion
factor of 0.8072."

Thus 81 ZN contracts have the same return as $10M of the CTD bond.

The higher number is the correct one (100k/CF)
Can somebody fill me in? I hope my exposure in the underlying (notional value?) is the current nominal futures price, adjusted for the financing cost and coupon payment between now and settlement date? Just like for equity index futures. So close enough what IB shows as "market value" in TWS. Correct?
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Mon Oct 18, 2021 4:32 pm
comeinvest wrote: Mon Oct 18, 2021 3:39 pm I looked at my portfolio today and saw that my UB futures went up big time, while most others went down, a trend that already manifested itself over the last few months and weeks. Those who read my previous posts know that I'm running a dynamic treasury futures strategy that is "diversified" across the yield curve.
I looked at the yield curve, and saw that it is almost flat between 20y and 30y.
Consequently I finally replaced my UB with 2 ZB today as part of my dynamic strategy. The yield curve shows ca. 1.9% at 17y (ZB maturity) vs 2.0% at 20y-30y. Unless the yield curve inverts on the far end, there is now little to no conceivable reason to have UB, therefore I deleted UB from my diversified treasury futures allocation, until there is again a measurable slope on the far end. Luckily, the DV01 of 2 ZB is almost equal to the DV01 of one UB, which made the switch easy.
I have to catch up with this message thread.

I am also in the process of deleting my short 2y ("hedge") position, locking in juicy gains, now that the carry is becoming equal or higher than that of the 5+ y futures. This part of my strategy was an overlay based on papers advocating a dynamic strategy based on current carry per duration.

EDIT: The maturity of ZB is only 15.5 years, with 1.75% yield. That makes my transition a little less convincing. I would prefer a 17y or 20y, but what can I do.
Congratulations, this has worked out very well so far for you. Of course it's not always so easy as positioning where there is slope. Often times slope on the far end could indicated that long-term interest rates are expected to rise. That didn't materialize in this case, but could in future cases. On other hand, maybe it was fairly predictable that long-term rates would fail to push above 2.1%. I don't feel confident that I can consistently make those predictions, and so like we've discussed I position where returns have historically been best - under 10 years. Having seriously considered a more dynamic market timing strategy, I'm certainly envious, but also looking forward to much better returns in the future as the roll yield and carry has nearly doubled for ZF and is now well over 2%. Of course rates probably will continue to rise so I don't expect to actually get over 2%, but the steepening of the middle part of the curve is a good thing in the long-run for ITT investors!

Also do consider that owning 2 ZB with 1.75% each (or 2 TN with 1.5% each) should provide a lot more return than 1 UB at 2%! There's only so much farther rates on those durations can rise before they also start pushing up the 20+ year rates. And that's not even factoring in the potential roll yield.
Maybe I'm the only one in this thread who also plays the Euro treasury curve and a bit off topic, but I'm also now unraveling my short positions in the "tub" of the green / orange curve (2-4 year area) that I established a while ago https://imgur.com/a/WG5UzFv Not sure if this was luck too, but I have a hard time understanding how such tubs can form, but glad to play them :) Is see another one in the 20 year area that I'm tempted to play against the 15y, but there's no future contract there...
zkn
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by zkn »

comeinvest wrote: Tue Oct 19, 2021 4:00 am I compared the S&P cash-secured ultra T-Bond future with the S&P U.S. Treasury Bond 20+ Year Index.
The futures contract currently has a maturity of 25 years and 4 months. The treasury bond index currently has an average maturity of 26 years. I didn't verify this, but I think the carry with rolldown is usually pretty constant with respect to maturity in that maturity range.

...
I have been closely reading this thread: thanks to all the posters for all the useful information.

I had a look at the spglobal page. To try to see if the comparisons are precise and to try to adjust for differences, I compared the risk (annualized monthly standard deviation) for each index pair, and the annualized risk-adjusted returns:

2-year futures index (currently 1.96 years maturity) vs. the treasury bond current 2-year index (1.92y average maturity):
10 years: risk .84% / .87% => risk-adj return 1.12% / 1.21% => slippage .09%
5 years: .98% / 1.08% => 1.40% / 1.36% => excess gain .04%
3 years: 1.09% / 1.20% => 2.02% / 2.12% = > slippage .1%

5-year futures index (currently 4 years 4.5 months maturity) vs. S&P U.S. Treasury Bond Current 5-Year Index (currently 4.92 years average maturity):
10 years: 2.60% / 3.07% => .64% / .64% => slippage .00%
5 years: 2.69% / 3.16% => .63% / .62% => excess gain .01%
3 years: 2.80% / 3.33% => 1.39% / 1.38% => excess gain .01%

10-year note futures (currently 6 years 10 months maturity) vs. S&P U.S. Treasury Bond Current 7-Year Index (currently 6.92 years average maturity):
10 years: 4.26% / 4.49% => .55% / .61% => slippage .06%
5 years: 4.36% / 4.55% => .46% / .52% = > slippage .06%
3 years: 4.56% / 4.85% => 1.13% / 1.16% => slippage .03%

S&P Ultra 10-Year U.S. Treasury Note Futures Index (currently 9 years 7 months maturity) vs. S&P U.S. Treasury Bond Current 10-Year Index (currently 9.88 years average maturity):
5 years: 6.07% / 6.28% => .37% / .30% => excess return .07%
3 years: 6.52% / 6.80% => .96% / .91% => excess return .05%

S&P U.S. Treasury Bond Futures Index (currently 15 years 7 months maturity) vs. (didn't find good match) S&P U.S. Treasury Bond 10-20 Year Index (currently 18.76 years average maturity):
10 years: 8.40% / 7.75% => .42% / .44% => excess return .02%
5 years: 8.80% / 8.60% => .29% / .30% => slippage .01%
3 years: 9.50% / 9.94% = > 82% / .71% = > excess return .11%

S&P cash-secured ultra T-Bond future (25 years and 4 months) vs. the S&P U.S. Treasury Bond 20+ Year Index (26 years):
10 years: 11.54% / 12.10% => .33% / .37% => slippage .04%
5 years: 12.33% / 12.36% => .22% / .27% => slippage .05%
3 years: 13.94% / 13.93% => .62% / .67% => slippage .05%

When comparing risk-adjusted return slippage, the difference is much closer than when comparing non-adjusted returns. The risk-adjusted return differences are always less than or equal to .11 in magnitude, and usually in the direction of a small slippage in the futures index. Some of the differences in the non-adjusted return may be reflecting differences in the maturity/duration that is reflected in the differences in the risk.
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skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Tue Oct 19, 2021 1:17 am
skierincolorado wrote: Tue Oct 19, 2021 12:50 am
comeinvest wrote: Tue Oct 19, 2021 12:41 am
skierincolorado wrote: Tue Oct 19, 2021 12:02 am Here's ZB:

Sep 30 2011 -> Sep 30 2021 per SPGlobal:
320.97 -> 455.74 = 3.56% CAGR

VGLT average duration is 17.9 years

ZB CTD duration is currently 11.6 years.

Am I doing the duration wrong? VGLT is much longer duration than ZB.
It's UB. I'm correcting my post with the calcs. UB should have almost the same maturity as VGLT.
For UB:

Sep 30 2011 -> Sep 30 2021 per SPGlobal:
137.78 -> 202.11 = 3.91% CAGR

VGLT had 4.29% CAGR

So .38% difference, plus .05% ER = .43% financing cost (.38% higher than the VGLT fee)

Could be that longer durations have higher financing which makes sense given they are less liquid. Could be that the duration of the CTD was different historically. Or the duration of VGLT could have changed.
Why the difference to my calcs? (hint: it's NOT the accuracy of my exponent 1/9.85)
I had: Nov 30 2011 - Sep 23 2021
per S&P total return chart 136.26 -> 206.43 => total return 1.515 => CAGR: 1.515 ^ (1/9.85) -> 4.3%
VGLT per IB performance chart: 55.83 -> 89.97 => total return 1.61 => CAGR: 1.61 ^ (1/9.85) -> 4.95%
Are we using different definitions of "return"?
Something wrong with using the IB performance charts?


I think you used Oct 1 instead of Sep 30 for the UB S&P end date. Using the correct data for your dates I get:
Sep 30 2011 -> Sep 30 2021 per SPGlobal: 137.78 -> 200.08 -> total return 1.452 -> CAGR 3.8%
VGLT per portfoliovisualizer.com : CAGR 4.29%
=> difference: 0.49% => (0.05% ER) slippage: 0.53%

We have to be careful with the dates, as there is a relatively high sensitivity of results to market fluctuations of single dates.

I'm still struggling with finding a cash comparison to ZB. skierincolorado?
Interesting, UB lost a full 1% in one day?
Topic Author
skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

zkn wrote: Tue Oct 19, 2021 8:10 am
comeinvest wrote: Tue Oct 19, 2021 4:00 am I compared the S&P cash-secured ultra T-Bond future with the S&P U.S. Treasury Bond 20+ Year Index.
The futures contract currently has a maturity of 25 years and 4 months. The treasury bond index currently has an average maturity of 26 years. I didn't verify this, but I think the carry with rolldown is usually pretty constant with respect to maturity in that maturity range.

...
I have been closely reading this thread: thanks to all the posters for all the useful information.

I had a look at the spglobal page. To try to see if the comparisons are precise and to try to adjust for differences, I compared the risk (annualized monthly standard deviation) for each index pair, and the annualized risk-adjusted returns:

2-year futures index (currently 1.96 years maturity) vs. the treasury bond current 2-year index (1.92y average maturity):
10 years: risk .84% / .87% => risk-adj return 1.12% / 1.21% => slippage .09%
5 years: .98% / 1.08% => 1.40% / 1.36% => excess gain .04%
3 years: 1.09% / 1.20% => 2.02% / 2.12% = > slippage .1%

5-year futures index (currently 4 years 4.5 months maturity) vs. S&P U.S. Treasury Bond Current 5-Year Index (currently 4.92 years average maturity):
10 years: 2.60% / 3.07% => .64% / .64% => slippage .00%
5 years: 2.69% / 3.16% => .63% / .62% => excess gain .01%
3 years: 2.80% / 3.33% => 1.39% / 1.38% => excess gain .01%

10-year note futures (currently 6 years 10 months maturity) vs. S&P U.S. Treasury Bond Current 7-Year Index (currently 6.92 years average maturity):
10 years: 4.26% / 4.49% => .55% / .61% => slippage .06%
5 years: 4.36% / 4.55% => .46% / .52% = > slippage .06%
3 years: 4.56% / 4.85% => 1.13% / 1.16% => slippage .03%

S&P Ultra 10-Year U.S. Treasury Note Futures Index (currently 9 years 7 months maturity) vs. S&P U.S. Treasury Bond Current 10-Year Index (currently 9.88 years average maturity):
5 years: 6.07% / 6.28% => .37% / .30% => excess return .07%
3 years: 6.52% / 6.80% => .96% / .91% => excess return .05%

S&P U.S. Treasury Bond Futures Index (currently 15 years 7 months maturity) vs. (didn't find good match) S&P U.S. Treasury Bond 10-20 Year Index (currently 18.76 years average maturity):
10 years: 8.40% / 7.75% => .42% / .44% => excess return .02%
5 years: 8.80% / 8.60% => .29% / .30% => slippage .01%
3 years: 9.50% / 9.94% = > 82% / .71% = > excess return .11%

S&P cash-secured ultra T-Bond future (25 years and 4 months) vs. the S&P U.S. Treasury Bond 20+ Year Index (26 years):
10 years: 11.54% / 12.10% => .33% / .37% => slippage .04%
5 years: 12.33% / 12.36% => .22% / .27% => slippage .05%
3 years: 13.94% / 13.93% => .62% / .67% => slippage .05%

When comparing risk-adjusted return slippage, the difference is much closer than when comparing non-adjusted returns. The risk-adjusted return differences are always less than or equal to .11 in magnitude, and usually in the direction of a small slippage in the futures index. Some of the differences in the non-adjusted return may be reflecting differences in the maturity/duration that is reflected in the differences in the risk.
This is genius thank you! I think that your calculations don’t reflect nominal financing costs - we would need to scale them for that. They are sharpe ratios. What is most important though is that we can see the futures continuous contracts generally had lower volatility than the corresponding indexes comeinvest and I were using indicating that the duration of the future was slightly shorter and explaining the lower return and higher implied financing costs.

I feel that we can safely rely on the financing costs in the OFR paper and that the expense ratio on vfitx is similar to the financing cost. Thus the optimization problems we have been analyzing are unaffected. ZF and ZN are still optimal durations and Treasury futures are an optimal choice for leverage.

LTCM - this whole discussion is an illustration of why I have never been comfortable with ZT. Financing costs do have some variability and they have gotten as high as .4% at times although they average more like .1-.2% over the last ten years, they have been a hair higher recently like .2%. ZT is just going to be overly sensitive to these assumptions. For ZF and ZN the financing cost could rise by .1% and it wouldn’t really matter.
zkn
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by zkn »

Right, my numbers are scaled by unit risk (differences in sharpe ratios). Interestingly, the differences are in the same ballpark across all durations. This suggests to me that we should not expect lower financing costs overall by having a smaller exposure via futures contracts with higher duration underlying treasuries vs a larger exposure via contracts with lower duration underlying treasuries. However, it does make sense that having a larger exposure to lower duration would be more sensitive to an absolute change in the financing costs, assuming that variability of financing costs does not scale with duration as well. Do we know that?
Topic Author
skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

zkn wrote: Tue Oct 19, 2021 10:45 am Right, my numbers are scaled by unit risk (differences in sharpe ratios). Interestingly, the differences are in the same ballpark across all durations. This suggests to me that we should not expect lower financing costs overall by having a smaller exposure via futures contracts with higher duration underlying treasuries vs a larger exposure via contracts with lower duration underlying treasuries. However, it does make sense that having a larger exposure to lower duration would be more sensitive to an absolute change in the financing costs, assuming that variability of financing costs does not scale with duration as well. Do we know that?
Based on the OFR papers, the variability does not really scale with duration. While the 5-yr has slightly higher financing costs on average over the last 5-10 years, the variability is similar. This suggests that changes in financing costs might be more of a risk to ZT than to ZF and ZN.

Fig 5
https://www.financialresearch.gov/brief ... Trades.pdf
Kbg
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Kbg »

Wonderful thread folks, appreciate the data dive and the analysis. If I might ask a summarizing question.

What do you feel is the max leverage for the overall port based on STT/ITT/LTT

IIRC correctly the optimal mixes are

STT 1:4 or 1:9
ITT 1:2.33 (e.g. 3:7) or 1:3
LTT ???

Hopefully I stated the above correctly. For example, would you lever up STT 1:9 to say x1.5 or would the 1:9 ratio be the max

(The instability of the STTs would seem to make them not a great choice)

Tks!
Last edited by Kbg on Tue Oct 19, 2021 11:31 am, edited 2 times in total.
hdas
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by hdas »

hhhhh
Last edited by hdas on Tue Oct 26, 2021 6:38 pm, edited 1 time in total.
....
Topic Author
skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

hdas wrote: Tue Oct 19, 2021 11:24 am
skierincolorado wrote: Tue Oct 19, 2021 9:16 am ZF and ZN are still optimal durations and Treasury futures are an optimal choice for leverage.
Still, if one assumes some level of normalization in interest rates, why do you want to be in the shorter maturities?. Have you look at the flattening that happens EVERY TIME there's a hike cycle?....

[Image
Because they have the highest risk adjusted returns both independently and when combined into a portfolio of stocks. Simple as that. We can try to disect why that is if you would like, and the various components of return, during various rate environments, or we can just accept that fact. There is a theoretical reason why shorter durations have better risk adjusted returns - beta seeking investors overprice longer duraitons.

You've posted the 30y - 5y yield chart. We can see that during hiking the spread gets quite low. The 5 year yield rises more than the 30 year yield during hiking. Conversely, it also falls more than the 30y during easing periods. So the rate on the 5y is a bit more volatile. But the duration is 1/6th so an equivalent interest rate move produes 1/6th the change in price. The volatility of the interest rate is not 6x greater. It's not even 2x greater. Ultimately, we end up with an asset with higher risk adjusted returns - primarily due to beta seeking investors overpricing long maturities.
Topic Author
skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

Kbg wrote: Tue Oct 19, 2021 11:23 am Wonderful thread folks, appreciate the data dive and the analysis. If I might ask a summarizing question.

What do you feel is the max leverage for the overall port based on STT/ITT/LTT

IIRC correctly the optimal mixes are

STT 1:4 or 1:9
ITT 1:2.33 (e.g. 3:7) or 1:3
LTT ???

Hopefully I stated the above correctly. For example, would you lever up STT 1:9 to say x1.5 or would the 1:9 ratio be the max

(The instability of the STTs would seem to make them not a great choice)

Tks!
There are different opinions and different ways we might calculate this.

We can look historically, or make future projections based on expected returns and risk. Looking historically it depends what period we use. If we look pre-1980, we will generally find lower bond allocations than if we only look post 1980. If we project future returns, we will generally find lower bond allocations because bonds have very low expected returns right now (although starting to creep up).

We can just look at sharpe ratios which only considers short-term variability, or we can look at variability in the 30+ year return as well. Looking at variability in 30+ year returns, we would find less allocation to bonds because bonds seem to have long interest rate cycles that can produce undesired variability in long-term returns.

Ultimately, I favor a combination of approaches. Ultimately for STT I would probably do 1:5 but I avoid STT because they are very sensitive to assumptions due to the high leverage ratio required. For ITT I prefer between 2:3. And for LTT I prefer something like 3:2. But again, LTT are not optimal because of the low risk-adjusted returns.

Thus I kind of see it as a pointless question for STT and LTT, because the only one I would consider investing in is ITT.

It also depends on the duration we define for each. For STT I would use just under 2 years. For ITT, 5.5 years. For LTT 15-18 years.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Tue Oct 19, 2021 5:27 am
skierincolorado wrote: Mon Oct 18, 2021 10:56 pm
millennialmillions wrote: Mon Oct 18, 2021 9:55 pm
constructor wrote: Mon Oct 18, 2021 2:46 pm
millennialmillions wrote: Sun Oct 17, 2021 9:14 am Bentonkb linked to this CME paper, which describes how to calculate the Principal Invoice Price, a better representation of the market value.

"E.g., the conversion factor for delivery of the 2-3/8% T-note of Aug-24 vs. December 2017 10-year T-note futures is 0.8072. This suggests that a 2 3/8% security is approximately valued at 81% as much as a 6% security. Assuming a futures price of 125-08+/32nds (or 125.265625 expressed in decimal format), the principal invoice amount may be calculated as follows. Principal Invoice Price = 125.265625 x 0.8072 x $1,000 = $101,114.41 E.g., the conversion factor for delivery of the 1-7/8% T-note of Aug-24 vs. December 10-year T-note futures is 0.7807. This suggests that a 1-7/8% security is approximately valued at 78% as much as a 6% security. Assuming a futures price of 125-08+/32nds (or 125.265625), the principal invoice amount may be calculated as follows.
Principal Invoice Price
= 125.265625 x 0.7807 x $1,000
= $97,794.87
In order to arrive at the total invoice amount, one must of course further add any accrued interest since the last semi annual interest payment date to the principal invoice amount."

It looks like the current CTD underlying security has a conversion factor of 0.95. So I would calculate your current STT exposure as $109,245 * 0.95 CF * 2 (for $200,000 face value) * 4 contracts = $830,262.

Note it doesn't appear there is consensus on this calculation, but this seems to directly align with the CME paper, and I haven't seen a good reason to use any other number. Also, the conversion factor for STT is closer to 1 than ITT or LTT, so it doesn't have as much of an impact.
While I agree with you in terms understanding of the book/PDF in practice I found the conversion factor does not need to be taken account given these empirical observations. Let's use the most extreme example with UB which has a conversion factor of 0.6141 as per Treasury Analytics (https://www.cmegrou ... tics.html).

1. The volatility of UB is identical to TLT, and definitely not 0.6 times that of TLT. If the actual exposure is the "invoice price" which is 0.6 times the nominal value we would expect UB to be 0.6 times as volatile.
2. In the Treasury Analytics page there is DV01 for futures and DV01 for cash, and precisely Cash DV01 = 0.6 * Futures DV01. If the actual exposure is the invoice price then the DV01 would be identical.

Well basically these two points are the same point.

But I agree with you that it sounds like on delivery only 0.6 times the nominal amount of the underlying treasury would be delivered. Confusing... I wonder if I am understanding the delivery process incorrectly.

Edit: On page 12 it does say:
E .g ., if one held $10 million face value of the 2-3/8%-8/24 note, one might sell 81 December 2017 futures by reference to the conversion factor of 0 .8072 to execute a hedge .
So this confirms that the nominal value is correct, that one future contract hedges more than "one treasury", given the ration of (1 / conversion factor). Though my question remains how the delivery work, since this almost seems you might need to deliver fraction of a treasury, and what the invoice price really means in the delivery process.
Thank you for your reply. I'm amazed we haven't reached consensus on something so fundamental to this strategy...it should be important for everyone in this thread to have an answer to this.

I disagree with your reading of that section (page 9 of the CME PDF) and believe it actually confirms the opposite, that the futures price must be multiplied by the conversion factor to determine market value/market exposure. Look at this table:
Image

The cash price is the market value. Multiplying the futures price by the conversion factor gets us very close to this market value (and the difference is the basis, which is small enough to ignore for our purpose).

Ultimately, it doesn't matter that one futures contract hedges more than "one treasury". What matters is holding one futures contract gives you equivalent performance to investing $x directly in treasuries, or in a fund like TLT. This paper says that x ≈ futures price * CF.

The best way to settle this would be to use actual futures returns data compared against a fund to determine how much TLT is needed to replicate the results of 1 UB contract. Your point that "the volatility of UB is identical to TLT" doesn't answer this question of how much is needed.
Here is my understanding. I am not 100% confident in this, but am not overly concerned because the amounts are close enough for my purposes.

What is delivered is the 100k. What is paid is the invoice price. But because the invoice price is calculated as if the delivered bonds had a 6% yield, the invoice price changes reflect the price change of a basket of bonds with face value of 100k / CF. Thus the long position gets the return of the larger basket. The short position gets the referse of this return. If the short position wishes to hedge and collect the basis, they must own the larger basket.

Thus we get:

"E.g., if one were to buy the basis by buying $10 million
face value of the 2-3/8%-8/24 note, one might sell 81
December 2017 futures by reference to the conversion
factor of 0.8072."

Thus 81 ZN contracts have the same return as $10M of the CTD bond.

The higher number is the correct one (100k/CF)
Can somebody fill me in? I hope my exposure in the underlying (notional value?) is the current nominal futures price, adjusted for the financing cost and coupon payment between now and settlement date? Just like for equity index futures. So close enough what IB shows as "market value" in TWS. Correct?
There has been some back and forth. Originally I was saying 100k/CF, but then there was some confusion with a couple people arguing that it is just the 100k because this is what is delivered. How can the exposure be different than what is delivered? I couldn't remember my reasoning, but re-reading the CME explanation I think I understand again. Hopefully putting it in writing will help me not forget.

Yes what is delivered is the 100k. But what is traded is a theoretical portfolio of 100k face value with 6% interest rates. This has a value of 100k/CF.

When the interest rate goes down, the value of 100k/CF moves like a larger ~125k bond.

Now we might say, OK but how did the invoice price change? The invoice price didn't change like a 125k bond because the invoice price is the futures price * the CF.

Here is what we were missing before. Not only did the futures price change, but the CF also changed. The CF got bigger. Thus the invoice price went up for two reasons. The futures price went up based on how ~125k in bonds would chance in price. If we multiplied by the old CF the invoice price would just change by the amount that ~100k in bonds would change in price. But we don't multiply by the old CF. We multiply by the new CF which is bigger. Thus the invoice price increased by the same nominal $ amount that the futures price increased by. Ta-da!

The mistake that some people were making was assuming that the CF does not change. BOTH the futures price AND the CF goes up when interest rates fall.

Thus we get CME's statement that:

"
"E.g., if one were to buy the basis by buying $10 million
face value of the 2-3/8%-8/24 note, one might sell 81
December 2017 futures by reference to the conversion
factor of 0.8072."

This is the statement we should rely upon and its interpretation is indisputable. 81M in futures contracts provides an exposure to 100M in bonds when the CF is .81.
Last edited by skierincolorado on Wed Oct 20, 2021 11:43 am, edited 1 time in total.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Tue Oct 19, 2021 9:16 am
zkn wrote: Tue Oct 19, 2021 8:10 am
comeinvest wrote: Tue Oct 19, 2021 4:00 am I compared the S&P cash-secured ultra T-Bond future with the S&P U.S. Treasury Bond 20+ Year Index.
The futures contract currently has a maturity of 25 years and 4 months. The treasury bond index currently has an average maturity of 26 years. I didn't verify this, but I think the carry with rolldown is usually pretty constant with respect to maturity in that maturity range.

...
I have been closely reading this thread: thanks to all the posters for all the useful information.

I had a look at the spglobal page. To try to see if the comparisons are precise and to try to adjust for differences, I compared the risk (annualized monthly standard deviation) for each index pair, and the annualized risk-adjusted returns:

2-year futures index (currently 1.96 years maturity) vs. the treasury bond current 2-year index (1.92y average maturity):
10 years: risk .84% / .87% => risk-adj return 1.12% / 1.21% => slippage .09%
5 years: .98% / 1.08% => 1.40% / 1.36% => excess gain .04%
3 years: 1.09% / 1.20% => 2.02% / 2.12% = > slippage .1%

5-year futures index (currently 4 years 4.5 months maturity) vs. S&P U.S. Treasury Bond Current 5-Year Index (currently 4.92 years average maturity):
10 years: 2.60% / 3.07% => .64% / .64% => slippage .00%
5 years: 2.69% / 3.16% => .63% / .62% => excess gain .01%
3 years: 2.80% / 3.33% => 1.39% / 1.38% => excess gain .01%

10-year note futures (currently 6 years 10 months maturity) vs. S&P U.S. Treasury Bond Current 7-Year Index (currently 6.92 years average maturity):
10 years: 4.26% / 4.49% => .55% / .61% => slippage .06%
5 years: 4.36% / 4.55% => .46% / .52% = > slippage .06%
3 years: 4.56% / 4.85% => 1.13% / 1.16% => slippage .03%

S&P Ultra 10-Year U.S. Treasury Note Futures Index (currently 9 years 7 months maturity) vs. S&P U.S. Treasury Bond Current 10-Year Index (currently 9.88 years average maturity):
5 years: 6.07% / 6.28% => .37% / .30% => excess return .07%
3 years: 6.52% / 6.80% => .96% / .91% => excess return .05%

S&P U.S. Treasury Bond Futures Index (currently 15 years 7 months maturity) vs. (didn't find good match) S&P U.S. Treasury Bond 10-20 Year Index (currently 18.76 years average maturity):
10 years: 8.40% / 7.75% => .42% / .44% => excess return .02%
5 years: 8.80% / 8.60% => .29% / .30% => slippage .01%
3 years: 9.50% / 9.94% = > 82% / .71% = > excess return .11%

S&P cash-secured ultra T-Bond future (25 years and 4 months) vs. the S&P U.S. Treasury Bond 20+ Year Index (26 years):
10 years: 11.54% / 12.10% => .33% / .37% => slippage .04%
5 years: 12.33% / 12.36% => .22% / .27% => slippage .05%
3 years: 13.94% / 13.93% => .62% / .67% => slippage .05%

When comparing risk-adjusted return slippage, the difference is much closer than when comparing non-adjusted returns. The risk-adjusted return differences are always less than or equal to .11 in magnitude, and usually in the direction of a small slippage in the futures index. Some of the differences in the non-adjusted return may be reflecting differences in the maturity/duration that is reflected in the differences in the risk.
This is genius thank you! I think that your calculations don’t reflect nominal financing costs - we would need to scale them for that. They are sharpe ratios. What is most important though is that we can see the futures continuous contracts generally had lower volatility than the corresponding indexes comeinvest and I were using indicating that the duration of the future was slightly shorter and explaining the lower return and higher implied financing costs.

I feel that we can safely rely on the financing costs in the OFR paper and that the expense ratio on vfitx is similar to the financing cost. Thus the optimization problems we have been analyzing are unaffected. ZF and ZN are still optimal durations and Treasury futures are an optimal choice for leverage.

LTCM - this whole discussion is an illustration of why I have never been comfortable with ZT. Financing costs do have some variability and they have gotten as high as .4% at times although they average more like .1-.2% over the last ten years, they have been a hair higher recently like .2%. ZT is just going to be overly sensitive to these assumptions. For ZF and ZN the financing cost could rise by .1% and it wouldn’t really matter.
I disagree.

1. What makes you believe that "Some of the differences in the non-adjusted return may be reflecting differences in the maturity/duration that is reflected in the differences in the risk." For both your data from equivalent Vanguard funds, and my data from equivalent bond indexes, we know the exact maturities and durations. Some are almost exactly that of the futures contract, and if not, we could do adjustments and I don't think it would explain the large slippages.

2. I never believed that (short-term) standard deviations, volatility, etc., are good measures of "risk" for long-term investors. My favorite measure is maximum drawdown. Because the futures are 100% sure to converge to the underlying CTD bond every 3 month, I would argue the risk of the future / futures strategy or the bond / bond strategy are exactly the same. The higher volatility of the bond wouldn't affect me a single bit if I were to invest in the bond. It might be due to the lower volume of the cash treasuries vs. the futures contracts. What do I care. Every 3 months I'm sure the two end up at the exact same point.

I still believe there is a real slippage. Proof: You and I start with $1mil. You buy futures and invest the cash in T-bills. I invest my $1mil in the underlying cash treasuries. At the end of some period, we will both end up with the exact same dollar amount with mathematical certainty, except I will be ahead of you by ca. 0.2%-0.7% p.a. as per our calcs. Please explain how I incurred more risk than you, that would allow you to buy more futures to keep up with my higher performance. I don't see it.
Topic Author
skierincolorado
Posts: 2377
Joined: Sat Mar 21, 2020 10:56 am

Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Tue Oct 19, 2021 12:28 pm
skierincolorado wrote: Tue Oct 19, 2021 9:16 am
zkn wrote: Tue Oct 19, 2021 8:10 am
comeinvest wrote: Tue Oct 19, 2021 4:00 am I compared the S&P cash-secured ultra T-Bond future with the S&P U.S. Treasury Bond 20+ Year Index.
The futures contract currently has a maturity of 25 years and 4 months. The treasury bond index currently has an average maturity of 26 years. I didn't verify this, but I think the carry with rolldown is usually pretty constant with respect to maturity in that maturity range.

...
I have been closely reading this thread: thanks to all the posters for all the useful information.

I had a look at the spglobal page. To try to see if the comparisons are precise and to try to adjust for differences, I compared the risk (annualized monthly standard deviation) for each index pair, and the annualized risk-adjusted returns:

2-year futures index (currently 1.96 years maturity) vs. the treasury bond current 2-year index (1.92y average maturity):
10 years: risk .84% / .87% => risk-adj return 1.12% / 1.21% => slippage .09%
5 years: .98% / 1.08% => 1.40% / 1.36% => excess gain .04%
3 years: 1.09% / 1.20% => 2.02% / 2.12% = > slippage .1%

5-year futures index (currently 4 years 4.5 months maturity) vs. S&P U.S. Treasury Bond Current 5-Year Index (currently 4.92 years average maturity):
10 years: 2.60% / 3.07% => .64% / .64% => slippage .00%
5 years: 2.69% / 3.16% => .63% / .62% => excess gain .01%
3 years: 2.80% / 3.33% => 1.39% / 1.38% => excess gain .01%

10-year note futures (currently 6 years 10 months maturity) vs. S&P U.S. Treasury Bond Current 7-Year Index (currently 6.92 years average maturity):
10 years: 4.26% / 4.49% => .55% / .61% => slippage .06%
5 years: 4.36% / 4.55% => .46% / .52% = > slippage .06%
3 years: 4.56% / 4.85% => 1.13% / 1.16% => slippage .03%

S&P Ultra 10-Year U.S. Treasury Note Futures Index (currently 9 years 7 months maturity) vs. S&P U.S. Treasury Bond Current 10-Year Index (currently 9.88 years average maturity):
5 years: 6.07% / 6.28% => .37% / .30% => excess return .07%
3 years: 6.52% / 6.80% => .96% / .91% => excess return .05%

S&P U.S. Treasury Bond Futures Index (currently 15 years 7 months maturity) vs. (didn't find good match) S&P U.S. Treasury Bond 10-20 Year Index (currently 18.76 years average maturity):
10 years: 8.40% / 7.75% => .42% / .44% => excess return .02%
5 years: 8.80% / 8.60% => .29% / .30% => slippage .01%
3 years: 9.50% / 9.94% = > 82% / .71% = > excess return .11%

S&P cash-secured ultra T-Bond future (25 years and 4 months) vs. the S&P U.S. Treasury Bond 20+ Year Index (26 years):
10 years: 11.54% / 12.10% => .33% / .37% => slippage .04%
5 years: 12.33% / 12.36% => .22% / .27% => slippage .05%
3 years: 13.94% / 13.93% => .62% / .67% => slippage .05%

When comparing risk-adjusted return slippage, the difference is much closer than when comparing non-adjusted returns. The risk-adjusted return differences are always less than or equal to .11 in magnitude, and usually in the direction of a small slippage in the futures index. Some of the differences in the non-adjusted return may be reflecting differences in the maturity/duration that is reflected in the differences in the risk.
This is genius thank you! I think that your calculations don’t reflect nominal financing costs - we would need to scale them for that. They are sharpe ratios. What is most important though is that we can see the futures continuous contracts generally had lower volatility than the corresponding indexes comeinvest and I were using indicating that the duration of the future was slightly shorter and explaining the lower return and higher implied financing costs.

I feel that we can safely rely on the financing costs in the OFR paper and that the expense ratio on vfitx is similar to the financing cost. Thus the optimization problems we have been analyzing are unaffected. ZF and ZN are still optimal durations and Treasury futures are an optimal choice for leverage.

LTCM - this whole discussion is an illustration of why I have never been comfortable with ZT. Financing costs do have some variability and they have gotten as high as .4% at times although they average more like .1-.2% over the last ten years, they have been a hair higher recently like .2%. ZT is just going to be overly sensitive to these assumptions. For ZF and ZN the financing cost could rise by .1% and it wouldn’t really matter.
I disagree.

1. What makes you believe that "Some of the differences in the non-adjusted return may be reflecting differences in the maturity/duration that is reflected in the differences in the risk." For both your data from equivalent Vanguard funds, and my data from equivalent bond indexes, we know the exact maturities and durations. Some are almost exactly that of the futures contract, and if not, we could do adjustments and I don't think it would explain the large slippages.

2. I never believed that (short-term) standard deviations, volatility, etc., are good measures of "risk" for long-term investors. My favorite measure is maximum drawdown. Because the futures are 100% sure to converge to the underlying CTD bond every 3 month, I would argue the risk of the future / futures strategy or the bond / bond strategy are exactly the same. The higher volatility of the bond wouldn't affect me a single bit if I were to invest in the bond. It might be due to the lower volume of the cash treasuries vs. the futures contracts. What do I care. Every 3 months I'm sure the two end up at the exact same point.

I still believe there is a real slippage. Proof: You and I start with $1mil. You buy futures and invest the cash in T-bills. I invest my $1mil in the underlying cash treasuries. At the end of some period, we will both end up with the exact same dollar amount with mathematical certainty, except I will be ahead of you by ca. 0.2%-0.7% p.a. as per our calcs. Please explain how I incurred more risk than you, that would allow you to buy more futures to keep up with my higher performance. I don't see it.
#2 is related to #1. I agree max-draw is a much better measure of risk, but both are directly related to duration, and the duration is likely different than what we realized in #1.

Regarding #1:

We don't know the exact maturities and durations. The duration of the CTD is constantly changing. Likewise, it's possible that the funds/indexes have used had some variation in their duration in the past.

The fact that the standard deviation of return for the futures contracts were substantially lower than the standard deviations of the cash position is strong evidence that it was of lower duration. It's also very likely that the max-draw would be lower as well. Perhaps zkn or one of us could calculate that? It would be an easy calculation.

This, combined with the fact that OFR finds somewhat lower financing costs than we do, I find to be compelling evidence that we are not comparing identical positions with identical maturities. It's also suspicious that we calculate much lower financing costs (aka a smaller difference in cost between futures and funds) for some durations, like .23% for ZN (or .05% more total cost more than the comparable funds used in the comparison), than for other durations.

For example you found excess gain on TN over the last 5 years to be .33% annualized .. I find that highly suspect. I think it might be because we should use the effective duration of the index not the average maturity. Also where do you see 9.2 as the duration of TN? I see 8.8.

The OFR data uses the actual CTD security. We should use that and then compare to the fees on funds. Or if we're going to compare futures to cash indexes/funds, we should definitely adjust for max-draw or stdev. Even then it is likely that the two positions are not identical, and one position may get lucky in some way especially over shorter time periods.
zkn
Posts: 67
Joined: Thu Oct 14, 2021 12:45 pm

Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by zkn »

We don't really need to assume that standard deviation is a good measure of the psychological experience of "risk". We can justify the exercise under weaker assumptions. We know that the futures and bond indices are not directly comparable. They differ in terms of mean effective duration, but also in how the effective duration changes over time and maybe even the distribution of effective durations within the index if more than one bond is tracked.

For example, looking at the mean effective duration of the S&P US Treasury Bond 10-20 Year Index on spglobal.com, it starts around 10 in 2016 and goes to 15 as of yesterday. Based on the description, it sounds like it might track a basket of bonds instead of just one bond in the case of futures. The mean effective duration of the S&P US Treasury Bond 5 Year Index zigs up and down about every month and goes from a low of 4.5 to a high of almost 5. Based on the description that it tracks the most recently issued 5-year US treasury note or bond, I am going to hazard a guess that the duration jumps up as new bonds are issued at durations closer to 5 and decays down in between new issues. I don't expect futures to have this pattern, but a different pattern as they track the CTD.

If we assume we can correct for these differences thru a linear transformation (assuming that bonds with different effective durations are approximately linearly related), then adjusting for standard deviation differences makes sense. Given the consistency of the results, it looks like it might work pretty well. I don't think it's perfect. For example, the 5-year shows no slippage risk-adjusted, but there is a pretty big difference between the futures and bond indices, so it is probably the approximation breaking down a bit.

Anyway, my take away is if we can get in the ballpark of the results in the OPR paper with a reasonable correction for differences between the indices, we haven't found evidence against the results in the paper. So I am inclined to agree with skierincolorado that the results in the OPR paper are probably trustworthy.
Topic Author
skierincolorado
Posts: 2377
Joined: Sat Mar 21, 2020 10:56 am

Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

zkn wrote: Tue Oct 19, 2021 3:03 pm We don't really need to assume that standard deviation is a good measure of the psychological experience of "risk". We can justify the exercise under weaker assumptions. We know that the futures and bond indices are not directly comparable. They differ in terms of mean effective duration, but also in how the effective duration changes over time and maybe even the distribution of effective durations within the index if more than one bond is tracked.

For example, looking at the mean effective duration of the S&P US Treasury Bond 10-20 Year Index on spglobal.com, it starts around 10 in 2016 and goes to 15 as of yesterday. Based on the description, it sounds like it might track a basket of bonds instead of just one bond in the case of futures. The mean effective duration of the S&P US Treasury Bond 5 Year Index zigs up and down about every month and goes from a low of 4.5 to a high of almost 5. Based on the description that it tracks the most recently issued 5-year US treasury note or bond, I am going to hazard a guess that the duration jumps up as new bonds are issued at durations closer to 5 and decays down in between new issues. I don't expect futures to have this pattern, but a different pattern as they track the CTD.

If we assume we can correct for these differences thru a linear transformation (assuming that bonds with different effective durations are approximately linearly related), then adjusting for standard deviation differences makes sense. Given the consistency of the results, it looks like it might work pretty well. I don't think it's perfect. For example, the 5-year shows no slippage risk-adjusted, but there is a pretty big difference between the futures and bond indices, so it is probably the approximation breaking down a bit.

Anyway, my take away is if we can get in the ballpark of the results in the OPR paper with a reasonable correction for differences between the indices, we haven't found evidence against the results in the paper. So I am inclined to agree with skierincolorado that the results in the OPR paper are probably trustworthy.
I also do take comeinvests point that if the returns of the cash indexes or etf funds are consistently better than the futures indexes, even after accounting for measures of risk such as max drawdown, then it doesn’t really matter if the difference is due to financing costs or because the cash indexes contain different securities. If we can get better risk adjusted returns by buying those securities then we should do that if possible. However as your analysis shows, the risk adjusted returns are not consistently better after accounting for stdev and (I’m assuming) max draw, other than a very small financing cost that we already knew about.
comeinvest
Posts: 2669
Joined: Mon Mar 12, 2012 6:57 pm

Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Tue Oct 19, 2021 12:04 pm
comeinvest wrote: Tue Oct 19, 2021 5:27 am
skierincolorado wrote: Mon Oct 18, 2021 10:56 pm
millennialmillions wrote: Mon Oct 18, 2021 9:55 pm
constructor wrote: Mon Oct 18, 2021 2:46 pm

While I agree with you in terms understanding of the book/PDF in practice I found the conversion factor does not need to be taken account given these empirical observations. Let's use the most extreme example with UB which has a conversion factor of 0.6141 as per Treasury Analytics (https://www.cmegrou ... tics.html).

1. The volatility of UB is identical to TLT, and definitely not 0.6 times that of TLT. If the actual exposure is the "invoice price" which is 0.6 times the nominal value we would expect UB to be 0.6 times as volatile.
2. In the Treasury Analytics page there is DV01 for futures and DV01 for cash, and precisely Cash DV01 = 0.6 * Futures DV01. If the actual exposure is the invoice price then the DV01 would be identical.

Well basically these two points are the same point.

But I agree with you that it sounds like on delivery only 0.6 times the nominal amount of the underlying treasury would be delivered. Confusing... I wonder if I am understanding the delivery process incorrectly.

Edit: On page 12 it does say:



So this confirms that the nominal value is correct, that one future contract hedges more than "one treasury", given the ration of (1 / conversion factor). Though my question remains how the delivery work, since this almost seems you might need to deliver fraction of a treasury, and what the invoice price really means in the delivery process.
Thank you for your reply. I'm amazed we haven't reached consensus on something so fundamental to this strategy...it should be important for everyone in this thread to have an answer to this.

I disagree with your reading of that section (page 9 of the CME PDF) and believe it actually confirms the opposite, that the futures price must be multiplied by the conversion factor to determine market value/market exposure. Look at this table:
Image

The cash price is the market value. Multiplying the futures price by the conversion factor gets us very close to this market value (and the difference is the basis, which is small enough to ignore for our purpose).

Ultimately, it doesn't matter that one futures contract hedges more than "one treasury". What matters is holding one futures contract gives you equivalent performance to investing $x directly in treasuries, or in a fund like TLT. This paper says that x ≈ futures price * CF.

The best way to settle this would be to use actual futures returns data compared against a fund to determine how much TLT is needed to replicate the results of 1 UB contract. Your point that "the volatility of UB is identical to TLT" doesn't answer this question of how much is needed.
Here is my understanding. I am not 100% confident in this, but am not overly concerned because the amounts are close enough for my purposes.

What is delivered is the 100k. What is paid is the invoice price. But because the invoice price is calculated as if the delivered bonds had a 6% yield, the invoice price changes reflect the price change of a basket of bonds with face value of 100k / CF. Thus the long position gets the return of the larger basket. The short position gets the referse of this return. If the short position wishes to hedge and collect the basis, they must own the larger basket.

Thus we get:

"E.g., if one were to buy the basis by buying $10 million
face value of the 2-3/8%-8/24 note, one might sell 81
December 2017 futures by reference to the conversion
factor of 0.8072."

Thus 81 ZN contracts have the same return as $10M of the CTD bond.

The higher number is the correct one (100k/CF)
Can somebody fill me in? I hope my exposure in the underlying (notional value?) is the current nominal futures price, adjusted for the financing cost and coupon payment between now and settlement date? Just like for equity index futures. So close enough what IB shows as "market value" in TWS. Correct?
There has been some back and forth. Originally I was saying 100k/CF, but then there was some confusion with a couple people arguing that it is just the 100k because this is what is delivered. How can the exposure be different than what is delivered? I couldn't remember my reasoning, but re-reading the CME explanation I think I understand again. Hopefully putting it in writing will help me not forget.

Yes what is delivered is the 100k. But what is traded is a theoretical portfolio of 100k face value with 6% interest rates. This has a value of 100k/CF.

When the interest rate goes down, the value of 100k/CF moves like a larger ~125k bond.

Now we might say, OK but how did the invoice price change? The invoice price didn't change like a 125k bond because the invoice price is the futures price * the invoice price.

Here is what we were missing before. Not only did the futures price change, but the CF also changed. The CF got bigger. Thus the invoice price went up for two reasons. The futures price went up based on how ~125k in bonds would chance in price. If we multiplied by the old CF the invoice price would just change by the amount that ~100k in bonds would change in price. But we don't multiply by the old CF. We multiply by the new CF which is bigger. Thus the invoice price increased by the same nominal $ amount that the futures price increased by. Ta-da!

The mistake that some people were making was assuming that the CF does not change. BOTH the futures price AND the CF goes up when interest rates fall.

Thus we get CME's statement that:

"
"E.g., if one were to buy the basis by buying $10 million
face value of the 2-3/8%-8/24 note, one might sell 81
December 2017 futures by reference to the conversion
factor of 0.8072."

This is the statement we should rely upon and its interpretation is indisputable. 81M in futures contracts provides an exposure to 100M in bonds when the CF is .81.
I never had time to dig into the nitty gritty of treasury futures delivery and always assumed what IB shows as market value is my exposure to the underlying minus expected coupons plus implied financing cost, and frankly I still didn't have time to study it. And was hoping I never have to, lol. Does everybody agree we have to apply the CF? How is it consistent with the observation that the volatility of the face values were similar that was made above? Where can I quickly find the current CF of the 5 different futures on any given day?
Topic Author
skierincolorado
Posts: 2377
Joined: Sat Mar 21, 2020 10:56 am

Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Tue Oct 19, 2021 5:03 pm
skierincolorado wrote: Tue Oct 19, 2021 12:04 pm
comeinvest wrote: Tue Oct 19, 2021 5:27 am
skierincolorado wrote: Mon Oct 18, 2021 10:56 pm
millennialmillions wrote: Mon Oct 18, 2021 9:55 pm

Thank you for your reply. I'm amazed we haven't reached consensus on something so fundamental to this strategy...it should be important for everyone in this thread to have an answer to this.

I disagree with your reading of that section (page 9 of the CME PDF) and believe it actually confirms the opposite, that the futures price must be multiplied by the conversion factor to determine market value/market exposure. Look at this table:
Image

The cash price is the market value. Multiplying the futures price by the conversion factor gets us very close to this market value (and the difference is the basis, which is small enough to ignore for our purpose).

Ultimately, it doesn't matter that one futures contract hedges more than "one treasury". What matters is holding one futures contract gives you equivalent performance to investing $x directly in treasuries, or in a fund like TLT. This paper says that x ≈ futures price * CF.

The best way to settle this would be to use actual futures returns data compared against a fund to determine how much TLT is needed to replicate the results of 1 UB contract. Your point that "the volatility of UB is identical to TLT" doesn't answer this question of how much is needed.
Here is my understanding. I am not 100% confident in this, but am not overly concerned because the amounts are close enough for my purposes.

What is delivered is the 100k. What is paid is the invoice price. But because the invoice price is calculated as if the delivered bonds had a 6% yield, the invoice price changes reflect the price change of a basket of bonds with face value of 100k / CF. Thus the long position gets the return of the larger basket. The short position gets the referse of this return. If the short position wishes to hedge and collect the basis, they must own the larger basket.

Thus we get:

"E.g., if one were to buy the basis by buying $10 million
face value of the 2-3/8%-8/24 note, one might sell 81
December 2017 futures by reference to the conversion
factor of 0.8072."

Thus 81 ZN contracts have the same return as $10M of the CTD bond.

The higher number is the correct one (100k/CF)
Can somebody fill me in? I hope my exposure in the underlying (notional value?) is the current nominal futures price, adjusted for the financing cost and coupon payment between now and settlement date? Just like for equity index futures. So close enough what IB shows as "market value" in TWS. Correct?
There has been some back and forth. Originally I was saying 100k/CF, but then there was some confusion with a couple people arguing that it is just the 100k because this is what is delivered. How can the exposure be different than what is delivered? I couldn't remember my reasoning, but re-reading the CME explanation I think I understand again. Hopefully putting it in writing will help me not forget.

Yes what is delivered is the 100k. But what is traded is a theoretical portfolio of 100k face value with 6% interest rates. This has a value of 100k/CF.

When the interest rate goes down, the value of 100k/CF moves like a larger ~125k bond.

Now we might say, OK but how did the invoice price change? The invoice price didn't change like a 125k bond because the invoice price is the futures price * the invoice price.

Here is what we were missing before. Not only did the futures price change, but the CF also changed. The CF got bigger. Thus the invoice price went up for two reasons. The futures price went up based on how ~125k in bonds would chance in price. If we multiplied by the old CF the invoice price would just change by the amount that ~100k in bonds would change in price. But we don't multiply by the old CF. We multiply by the new CF which is bigger. Thus the invoice price increased by the same nominal $ amount that the futures price increased by. Ta-da!

The mistake that some people were making was assuming that the CF does not change. BOTH the futures price AND the CF goes up when interest rates fall.

Thus we get CME's statement that:

"
"E.g., if one were to buy the basis by buying $10 million
face value of the 2-3/8%-8/24 note, one might sell 81
December 2017 futures by reference to the conversion
factor of 0.8072."

This is the statement we should rely upon and its interpretation is indisputable. 81M in futures contracts provides an exposure to 100M in bonds when the CF is .81.
I never had time to dig into the nitty gritty of treasury futures delivery and always assumed what IB shows as market value is my exposure to the underlying minus expected coupons plus implied financing cost, and frankly I still didn't have time to study it. And was hoping I never have to, lol. Does everybody agree we have to apply the CF? How is it consistent with the observation that the volatility of the face values were similar that was made above? Where can I quickly find the current CF of the 5 different futures on any given day?
Well you shouldn’t need the CF.. can just use the IB price which is like well over 100k for most contracts (100k/ cf) like 125 k for zf
zkn
Posts: 67
Joined: Thu Oct 14, 2021 12:45 pm

Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by zkn »

skierincolorado wrote: Tue Oct 19, 2021 3:42 pm
zkn wrote: Tue Oct 19, 2021 3:03 pm We don't really need to assume that standard deviation is a good measure of the psychological experience of "risk". We can justify the exercise under weaker assumptions. We know that the futures and bond indices are not directly comparable. They differ in terms of mean effective duration, but also in how the effective duration changes over time and maybe even the distribution of effective durations within the index if more than one bond is tracked.

For example, looking at the mean effective duration of the S&P US Treasury Bond 10-20 Year Index on spglobal.com, it starts around 10 in 2016 and goes to 15 as of yesterday. Based on the description, it sounds like it might track a basket of bonds instead of just one bond in the case of futures. The mean effective duration of the S&P US Treasury Bond 5 Year Index zigs up and down about every month and goes from a low of 4.5 to a high of almost 5. Based on the description that it tracks the most recently issued 5-year US treasury note or bond, I am going to hazard a guess that the duration jumps up as new bonds are issued at durations closer to 5 and decays down in between new issues. I don't expect futures to have this pattern, but a different pattern as they track the CTD.

If we assume we can correct for these differences thru a linear transformation (assuming that bonds with different effective durations are approximately linearly related), then adjusting for standard deviation differences makes sense. Given the consistency of the results, it looks like it might work pretty well. I don't think it's perfect. For example, the 5-year shows no slippage risk-adjusted, but there is a pretty big difference between the futures and bond indices, so it is probably the approximation breaking down a bit.

Anyway, my take away is if we can get in the ballpark of the results in the OPR paper with a reasonable correction for differences between the indices, we haven't found evidence against the results in the paper. So I am inclined to agree with skierincolorado that the results in the OPR paper are probably trustworthy.
I also do take comeinvests point that if the returns of the cash indexes or etf funds are consistently better than the futures indexes, even after accounting for measures of risk such as max drawdown, then it doesn’t really matter if the difference is due to financing costs or because the cash indexes contain different securities. If we can get better risk adjusted returns by buying those securities then we should do that if possible. However as your analysis shows, the risk adjusted returns are not consistently better after accounting for stdev and (I’m assuming) max draw, other than a very small financing cost that we already knew about.
I was thinking more abstractly in terms of correcting for differences in the indices to approximate the financing cost, but thinking about them as different products and just comparing them on typical statistics makes sense too.

So here is the max daily peak-to-tough for the index pairs. That is, the maximum difference between the price in any day minus the price in any following day. I also "leveraged" the futures index return by multiplying the return by the ratio of the max drawdowns, as if we had increased the futures position to match the max drawdown of the cash bond index with free leverage (free to make the analysis easier).

2-year futures index (currently 1.96 years maturity) vs. the treasury bond current 2-year index (1.92y average maturity):
.99% versus 1.10%; max drawdown 10.9% larger in cash bond index
.91% * 110.9% = 1.01% futures versus 1.04% cash bond; slippage .03%

5-year futures index (currently 4 years 4.5 months maturity) vs. S&P U.S. Treasury Bond Current 5-Year Index (currently 4.92 years average maturity):
4.50% versus 5.50%; max drawdown 22.0% larger in cash bond index
1.6% * 122.0% = 1.95% versus 1.93; excess gain .02%

10-year note futures (currently 6 years 10 months maturity) vs. S&P U.S. Treasury Bond Current 7-Year Index (currently 6.92 years average maturity):
7.4% versus 7.7%; max drawdown 4.2% larger in cash bond index
2.39% * 104.2% = 2.49% versus 2.78; slippage .29%

S&P Ultra 10-Year U.S. Treasury Note Futures Index (currently 9 years 7 months maturity) vs. S&P U.S. Treasury Bond Current 10-Year Index (currently 9.88 years average maturity):
10.0% versus 11.5%; max drawdown 15.2% larger in cash bond index
2.38% * 115.2% = 2.74% versus 2.01; excess gain .73%

S&P U.S. Treasury Bond Futures Index (currently 15 years 7 months maturity) vs. (didn't find good match) S&P U.S. Treasury Bond 10-20 Year Index (currently 18.76 years average maturity):
15.1% versus 17.8%; max drawdown 17.0% larger in cash bond index
3.74% * 117.0% = 4.38% versus 3.67%; excess gain .71%

S&P cash-secured ultra T-Bond future (25 years and 4 months) vs. the S&P U.S. Treasury Bond 20+ Year Index (26 years):
22.7% versus 21.3%; max drawdown 6.7% ***SMALLER*** in cash bond index
4.3% * 93.7% = 4.03% versus 5.04%; slippage 1.01%

We can see that most of the futures indices were safer than the paired cash bond indices according to max drawdown, with the exception of the final pairing. Comparing the results while matching position size on max drawdown is much more inconsistent across different durations than using Sharpe (or matching on SDs), however there is not a clear pattern to prefer cash bond or the futures. I suspect that max drawdown is a much more noisy measure of risk than SD in this context so I would not pay too much attention to the actual slippage/excess gain numbers as I don't think they are reliable. However, I think it does provide further support that the cash bond indices are more risky than the future bond indices that they were paired with, which made the future bond indices look like they had greater financing costs than they probably really do.
Last edited by zkn on Tue Oct 19, 2021 5:47 pm, edited 1 time in total.
comeinvest
Posts: 2669
Joined: Mon Mar 12, 2012 6:57 pm

Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Tue Oct 19, 2021 12:40 pm
comeinvest wrote: Tue Oct 19, 2021 12:28 pm
skierincolorado wrote: Tue Oct 19, 2021 9:16 am
zkn wrote: Tue Oct 19, 2021 8:10 am
comeinvest wrote: Tue Oct 19, 2021 4:00 am I compared the S&P cash-secured ultra T-Bond future with the S&P U.S. Treasury Bond 20+ Year Index.
The futures contract currently has a maturity of 25 years and 4 months. The treasury bond index currently has an average maturity of 26 years. I didn't verify this, but I think the carry with rolldown is usually pretty constant with respect to maturity in that maturity range.

...
I have been closely reading this thread: thanks to all the posters for all the useful information.

I had a look at the spglobal page. To try to see if the comparisons are precise and to try to adjust for differences, I compared the risk (annualized monthly standard deviation) for each index pair, and the annualized risk-adjusted returns:

2-year futures index (currently 1.96 years maturity) vs. the treasury bond current 2-year index (1.92y average maturity):
10 years: risk .84% / .87% => risk-adj return 1.12% / 1.21% => slippage .09%
5 years: .98% / 1.08% => 1.40% / 1.36% => excess gain .04%
3 years: 1.09% / 1.20% => 2.02% / 2.12% = > slippage .1%

5-year futures index (currently 4 years 4.5 months maturity) vs. S&P U.S. Treasury Bond Current 5-Year Index (currently 4.92 years average maturity):
10 years: 2.60% / 3.07% => .64% / .64% => slippage .00%
5 years: 2.69% / 3.16% => .63% / .62% => excess gain .01%
3 years: 2.80% / 3.33% => 1.39% / 1.38% => excess gain .01%

10-year note futures (currently 6 years 10 months maturity) vs. S&P U.S. Treasury Bond Current 7-Year Index (currently 6.92 years average maturity):
10 years: 4.26% / 4.49% => .55% / .61% => slippage .06%
5 years: 4.36% / 4.55% => .46% / .52% = > slippage .06%
3 years: 4.56% / 4.85% => 1.13% / 1.16% => slippage .03%

S&P Ultra 10-Year U.S. Treasury Note Futures Index (currently 9 years 7 months maturity) vs. S&P U.S. Treasury Bond Current 10-Year Index (currently 9.88 years average maturity):
5 years: 6.07% / 6.28% => .37% / .30% => excess return .07%
3 years: 6.52% / 6.80% => .96% / .91% => excess return .05%

S&P U.S. Treasury Bond Futures Index (currently 15 years 7 months maturity) vs. (didn't find good match) S&P U.S. Treasury Bond 10-20 Year Index (currently 18.76 years average maturity):
10 years: 8.40% / 7.75% => .42% / .44% => excess return .02%
5 years: 8.80% / 8.60% => .29% / .30% => slippage .01%
3 years: 9.50% / 9.94% = > 82% / .71% = > excess return .11%

S&P cash-secured ultra T-Bond future (25 years and 4 months) vs. the S&P U.S. Treasury Bond 20+ Year Index (26 years):
10 years: 11.54% / 12.10% => .33% / .37% => slippage .04%
5 years: 12.33% / 12.36% => .22% / .27% => slippage .05%
3 years: 13.94% / 13.93% => .62% / .67% => slippage .05%

When comparing risk-adjusted return slippage, the difference is much closer than when comparing non-adjusted returns. The risk-adjusted return differences are always less than or equal to .11 in magnitude, and usually in the direction of a small slippage in the futures index. Some of the differences in the non-adjusted return may be reflecting differences in the maturity/duration that is reflected in the differences in the risk.
This is genius thank you! I think that your calculations don’t reflect nominal financing costs - we would need to scale them for that. They are sharpe ratios. What is most important though is that we can see the futures continuous contracts generally had lower volatility than the corresponding indexes comeinvest and I were using indicating that the duration of the future was slightly shorter and explaining the lower return and higher implied financing costs.

I feel that we can safely rely on the financing costs in the OFR paper and that the expense ratio on vfitx is similar to the financing cost. Thus the optimization problems we have been analyzing are unaffected. ZF and ZN are still optimal durations and Treasury futures are an optimal choice for leverage.

LTCM - this whole discussion is an illustration of why I have never been comfortable with ZT. Financing costs do have some variability and they have gotten as high as .4% at times although they average more like .1-.2% over the last ten years, they have been a hair higher recently like .2%. ZT is just going to be overly sensitive to these assumptions. For ZF and ZN the financing cost could rise by .1% and it wouldn’t really matter.
I disagree.

1. What makes you believe that "Some of the differences in the non-adjusted return may be reflecting differences in the maturity/duration that is reflected in the differences in the risk." For both your data from equivalent Vanguard funds, and my data from equivalent bond indexes, we know the exact maturities and durations. Some are almost exactly that of the futures contract, and if not, we could do adjustments and I don't think it would explain the large slippages.

2. I never believed that (short-term) standard deviations, volatility, etc., are good measures of "risk" for long-term investors. My favorite measure is maximum drawdown. Because the futures are 100% sure to converge to the underlying CTD bond every 3 month, I would argue the risk of the future / futures strategy or the bond / bond strategy are exactly the same. The higher volatility of the bond wouldn't affect me a single bit if I were to invest in the bond. It might be due to the lower volume of the cash treasuries vs. the futures contracts. What do I care. Every 3 months I'm sure the two end up at the exact same point.

I still believe there is a real slippage. Proof: You and I start with $1mil. You buy futures and invest the cash in T-bills. I invest my $1mil in the underlying cash treasuries. At the end of some period, we will both end up with the exact same dollar amount with mathematical certainty, except I will be ahead of you by ca. 0.2%-0.7% p.a. as per our calcs. Please explain how I incurred more risk than you, that would allow you to buy more futures to keep up with my higher performance. I don't see it.
#2 is related to #1. I agree max-draw is a much better measure of risk, but both are directly related to duration, and the duration is likely different than what we realized in #1.

Regarding #1:

We don't know the exact maturities and durations. The duration of the CTD is constantly changing. Likewise, it's possible that the funds/indexes have used had some variation in their duration in the past.

The fact that the standard deviation of return for the futures contracts were substantially lower than the standard deviations of the cash position is strong evidence that it was of lower duration. It's also very likely that the max-draw would be lower as well. Perhaps zkn or one of us could calculate that? It would be an easy calculation.

This, combined with the fact that OFR finds somewhat lower financing costs than we do, I find to be compelling evidence that we are not comparing identical positions with identical maturities. It's also suspicious that we calculate much lower financing costs (aka a smaller difference in cost between futures and funds) for some durations, like .23% for ZN (or .05% more total cost more than the comparable funds used in the comparison), than for other durations.

For example you found excess gain on TN over the last 5 years to be .33% annualized .. I find that highly suspect. I think it might be because we should use the effective duration of the index not the average maturity. Also where do you see 9.2 as the duration of TN? I see 8.8.

The OFR data uses the actual CTD security. We should use that and then compare to the fees on funds. Or if we're going to compare futures to cash indexes/funds, we should definitely adjust for max-draw or stdev. Even then it is likely that the two positions are not identical, and one position may get lucky in some way especially over shorter time periods.
"The fact that the standard deviation of return for the futures contracts were substantially lower than the standard deviations of the cash position is strong evidence that it was of lower duration." - I don't believe so. But "believing" is religion and we are not in a church. Instead of believing, let's verify:
I got the futures maturities from the maturity dates of the CTD on the treasury analytics page, rounded to the nearest full month or half month. I don't see where I mentioned "9.2" in any of my posts, and I didn't look at durations yet. Let's look at the durations then. To be honest, I have not yet studied the concept of "modified duration" or "effective duration". So I'm just quoting those terms and numbers. (If someone could fill me in on MD in short words.) Let's start with TN as an example. TN CTD duration (D): 8.84; TN modified duration (MD): 8.77 S&P current 10-year bond index MD 9.22 / effective duration 9.22. If we assume that MD and not D is the meaningful number for purpose of risk, then we are talking about a 0.45 years shorter duration of the future compared to the cash security.
Now I think the slope in the 10-year area is typically no more than 1% per 10 years on average over history (please verify). But the rolldown yield typically decreases with maturity. Let's assume that the instant carry (yield to maturity plus rolldown yield) increases 0.5% per 10 y in the 10-year area on average. This assumption would translate to an adjustment of 0.5% / 10 * 0.45 = 0.0225%. That's less than the rounding errors in our data collection. So let's just say let's forget it.
S&P Ultra 10-Year U.S. Treasury Note Futures Index (currently 9 years 7 months maturity) vs. S&P U.S. Treasury Bond Current 10-Year Index (currently 9.88 years average maturity):
10 years: no data
5 years: 2.38% / 2.01% => excess gain: 0.33%
3 years: 6.39% / 6.33% => excess gain: 0.06%
1 year: -5.43 /-6.03% => excess gain: 0.6%

Modified duration comparisons:
Future / CTD MD / S&P bond index MD
ZT / 1.90 / 1.91
ZF / 4.29 / 4.81
ZN / 6.20 / 6.62
TN / 8.77 / 9.22
ZB / 11.56 / 14.99
UB / 18.3 / 19.2

"Likewise, it's possible that the funds/indexes have used had some variation in their duration in the past." - true, but we calculated a few dozen numbers over various time horizons including the recent 1-year time frame. Unlikely that almost all numbers are tilted to the same direction, and that the CTD and/or the composition of the bond index changed dramatically over the last 1 year, isn't it?

"The OFR data uses the actual CTD security. We should use that and then compare to the fees on funds." - For the reasons we discussed yesterday that the CTD securities may be in higher demand than treasuries of other but similar maturities, I would say if anything, comparing to e.g. the Vanguard funds is more meaningful to derive an "all-in" cost of leverage. Emphasis on "all-in", not theoretical. Vanguard funds are one example of a real investable asset that can be substituted with futures. Another example of a real investable asset is a ladder of cash treasuries with maturities similar to that of the futures. I don't know yet if CTD vs non-CTD makes a difference, I think you demonstrated yesterday that it doesn't; but if anything, to derive an "all-in" cost of leverage, we need to compare the investment alternatives that we have the choice to select, that are equivalent to the futures contract in our asset allocation. Also, I think you used Vanguard funds in your backtests, not CTDs.

"Or if we're going to compare futures to cash indexes/funds, we should definitely adjust for max-draw or stdev." - max draw down please, not stdev, at least not for me. Max draw down over an economic cycle, or over history. Not 1 month or something. We are studying futures for purpose of running a leveraged strategy. The amount of leverage is constrained by a max drawdown event over a long time frame. I don't think you can demonstrate that the cash treasuries have measurable higher drawdowns over an economic cycle, given that futures must converge to the cash treasuries every 3 months. What do I care about some fluctuations when I know my portfolio NAV will be mathematically exactly the same as yours every 3 months, plus annualized 0.2-0.7% that I pay to some bank or hedge fund to facilitate my leverage. I think the higher fluctuations may be a result of lower volume of the cash treasuries, as outlined in some papers. Please answer my thought experiment question above. You and I each have $1mil. Every 3 months your asset will converge to mine with mathematical precision. Please explain how you think you have less risk exposure.

I don't have an explanation currently for the excess gains for TN futures, but it is no factual evidence to invalidate our calculations that are very straightforward. Only if you can show me that there is a meaningful measure of risk where the futures and cash securities differ, can you convince me that there is no slippage as in a cost to me holding futures. The 0.2-0.7% is a real dollar cost to me that is the profit of some bank or hedge fund for facilitating my leverage. It's hard to talk that away.
Last edited by comeinvest on Tue Oct 19, 2021 6:22 pm, edited 1 time in total.
Topic Author
skierincolorado
Posts: 2377
Joined: Sat Mar 21, 2020 10:56 am

Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Tue Oct 19, 2021 5:47 pm
skierincolorado wrote: Tue Oct 19, 2021 12:40 pm
comeinvest wrote: Tue Oct 19, 2021 12:28 pm
skierincolorado wrote: Tue Oct 19, 2021 9:16 am
zkn wrote: Tue Oct 19, 2021 8:10 am

I have been closely reading this thread: thanks to all the posters for all the useful information.

I had a look at the spglobal page. To try to see if the comparisons are precise and to try to adjust for differences, I compared the risk (annualized monthly standard deviation) for each index pair, and the annualized risk-adjusted returns:

2-year futures index (currently 1.96 years maturity) vs. the treasury bond current 2-year index (1.92y average maturity):
10 years: risk .84% / .87% => risk-adj return 1.12% / 1.21% => slippage .09%
5 years: .98% / 1.08% => 1.40% / 1.36% => excess gain .04%
3 years: 1.09% / 1.20% => 2.02% / 2.12% = > slippage .1%

5-year futures index (currently 4 years 4.5 months maturity) vs. S&P U.S. Treasury Bond Current 5-Year Index (currently 4.92 years average maturity):
10 years: 2.60% / 3.07% => .64% / .64% => slippage .00%
5 years: 2.69% / 3.16% => .63% / .62% => excess gain .01%
3 years: 2.80% / 3.33% => 1.39% / 1.38% => excess gain .01%

10-year note futures (currently 6 years 10 months maturity) vs. S&P U.S. Treasury Bond Current 7-Year Index (currently 6.92 years average maturity):
10 years: 4.26% / 4.49% => .55% / .61% => slippage .06%
5 years: 4.36% / 4.55% => .46% / .52% = > slippage .06%
3 years: 4.56% / 4.85% => 1.13% / 1.16% => slippage .03%

S&P Ultra 10-Year U.S. Treasury Note Futures Index (currently 9 years 7 months maturity) vs. S&P U.S. Treasury Bond Current 10-Year Index (currently 9.88 years average maturity):
5 years: 6.07% / 6.28% => .37% / .30% => excess return .07%
3 years: 6.52% / 6.80% => .96% / .91% => excess return .05%

S&P U.S. Treasury Bond Futures Index (currently 15 years 7 months maturity) vs. (didn't find good match) S&P U.S. Treasury Bond 10-20 Year Index (currently 18.76 years average maturity):
10 years: 8.40% / 7.75% => .42% / .44% => excess return .02%
5 years: 8.80% / 8.60% => .29% / .30% => slippage .01%
3 years: 9.50% / 9.94% = > 82% / .71% = > excess return .11%

S&P cash-secured ultra T-Bond future (25 years and 4 months) vs. the S&P U.S. Treasury Bond 20+ Year Index (26 years):
10 years: 11.54% / 12.10% => .33% / .37% => slippage .04%
5 years: 12.33% / 12.36% => .22% / .27% => slippage .05%
3 years: 13.94% / 13.93% => .62% / .67% => slippage .05%

When comparing risk-adjusted return slippage, the difference is much closer than when comparing non-adjusted returns. The risk-adjusted return differences are always less than or equal to .11 in magnitude, and usually in the direction of a small slippage in the futures index. Some of the differences in the non-adjusted return may be reflecting differences in the maturity/duration that is reflected in the differences in the risk.
This is genius thank you! I think that your calculations don’t reflect nominal financing costs - we would need to scale them for that. They are sharpe ratios. What is most important though is that we can see the futures continuous contracts generally had lower volatility than the corresponding indexes comeinvest and I were using indicating that the duration of the future was slightly shorter and explaining the lower return and higher implied financing costs.

I feel that we can safely rely on the financing costs in the OFR paper and that the expense ratio on vfitx is similar to the financing cost. Thus the optimization problems we have been analyzing are unaffected. ZF and ZN are still optimal durations and Treasury futures are an optimal choice for leverage.

LTCM - this whole discussion is an illustration of why I have never been comfortable with ZT. Financing costs do have some variability and they have gotten as high as .4% at times although they average more like .1-.2% over the last ten years, they have been a hair higher recently like .2%. ZT is just going to be overly sensitive to these assumptions. For ZF and ZN the financing cost could rise by .1% and it wouldn’t really matter.
I disagree.

1. What makes you believe that "Some of the differences in the non-adjusted return may be reflecting differences in the maturity/duration that is reflected in the differences in the risk." For both your data from equivalent Vanguard funds, and my data from equivalent bond indexes, we know the exact maturities and durations. Some are almost exactly that of the futures contract, and if not, we could do adjustments and I don't think it would explain the large slippages.

2. I never believed that (short-term) standard deviations, volatility, etc., are good measures of "risk" for long-term investors. My favorite measure is maximum drawdown. Because the futures are 100% sure to converge to the underlying CTD bond every 3 month, I would argue the risk of the future / futures strategy or the bond / bond strategy are exactly the same. The higher volatility of the bond wouldn't affect me a single bit if I were to invest in the bond. It might be due to the lower volume of the cash treasuries vs. the futures contracts. What do I care. Every 3 months I'm sure the two end up at the exact same point.

I still believe there is a real slippage. Proof: You and I start with $1mil. You buy futures and invest the cash in T-bills. I invest my $1mil in the underlying cash treasuries. At the end of some period, we will both end up with the exact same dollar amount with mathematical certainty, except I will be ahead of you by ca. 0.2%-0.7% p.a. as per our calcs. Please explain how I incurred more risk than you, that would allow you to buy more futures to keep up with my higher performance. I don't see it.
#2 is related to #1. I agree max-draw is a much better measure of risk, but both are directly related to duration, and the duration is likely different than what we realized in #1.

Regarding #1:

We don't know the exact maturities and durations. The duration of the CTD is constantly changing. Likewise, it's possible that the funds/indexes have used had some variation in their duration in the past.

The fact that the standard deviation of return for the futures contracts were substantially lower than the standard deviations of the cash position is strong evidence that it was of lower duration. It's also very likely that the max-draw would be lower as well. Perhaps zkn or one of us could calculate that? It would be an easy calculation.

This, combined with the fact that OFR finds somewhat lower financing costs than we do, I find to be compelling evidence that we are not comparing identical positions with identical maturities. It's also suspicious that we calculate much lower financing costs (aka a smaller difference in cost between futures and funds) for some durations, like .23% for ZN (or .05% more total cost more than the comparable funds used in the comparison), than for other durations.

For example you found excess gain on TN over the last 5 years to be .33% annualized .. I find that highly suspect. I think it might be because we should use the effective duration of the index not the average maturity. Also where do you see 9.2 as the duration of TN? I see 8.8.

The OFR data uses the actual CTD security. We should use that and then compare to the fees on funds. Or if we're going to compare futures to cash indexes/funds, we should definitely adjust for max-draw or stdev. Even then it is likely that the two positions are not identical, and one position may get lucky in some way especially over shorter time periods.
"The fact that the standard deviation of return for the futures contracts were substantially lower than the standard deviations of the cash position is strong evidence that it was of lower duration." - I don't believe so. But "believing" is religion and we are not in a church. Instead of believing, let's verify:
I got the futures maturities from the maturity dates of the CTD on the treasury analytics page, rounded to the nearest full month or half month. I don't see where I mentioned "9.2" in any of my posts, and I didn't look at durations yet. Let's look at the durations then. To be honest, I have not yet studied the concept of "modified duration" or "effective duration". So I'm just quoting those terms and numbers. (If someone could fill me in on MD in short words.) Let's start with TN as an example. TN CTD duration (D): 8.84; TN modified duration (MD): 8.77 S&P current 10-year bond index MD 9.22 / effective duration 9.22. If we assume that MD and not D is the meaningful number for purpose of risk, then we are talking about a 0.45 years shorter duration of the future compared to the cash security.
Now I think the slope in the 10-year area is typically no more than 1% per 10 years on average over history (please verify). But the rolldown yield typically decreases with maturity. Let's assume that the instant carry (yield to maturity plus rolldown yield) increases 0.5% per 10 y in the 10-year area on average. This assumption would translate to an adjustment of 0.5% / 10 * 0.45 = 0.0225%. That's less than the rounding errors in our data collection. So let's just say let's forget it.
S&P Ultra 10-Year U.S. Treasury Note Futures Index (currently 9 years 7 months maturity) vs. S&P U.S. Treasury Bond Current 10-Year Index (currently 9.88 years average maturity):
10 years: no data
5 years: 2.38% / 2.01% => excess gain: 0.33%
3 years: 6.39% / 6.33% => excess gain: 0.06%
1 year: -5.43 /-6.03% => excess gain: 0.6%

"Likewise, it's possible that the funds/indexes have used had some variation in their duration in the past." - true, but we calculated a few dozen numbers over various time horizons including the recent 1-year time frame. Unlikely that almost all numbers are tilted to the same direction, and that the CTD and/or the composition of the bond index changed dramatically over the last 1 year, isn't it?

"The OFR data uses the actual CTD security. We should use that and then compare to the fees on funds." - For the reasons we discussed yesterday that the CTD securities may be in higher demand than treasuries of other but similar maturities, I would say if anything, comparing to e.g. the Vanguard funds is more meaningful to derive an "all-in" cost of leverage. Emphasis on "all-in", not theoretical. Vanguard funds are one example of a real investable asset that can be substituted with futures. Another example of a real investable asset is a ladder of cash treasuries with maturities similar to that of the futures. I don't know yet if CTD vs non-CTD makes a difference, I think you demonstrated yesterday that it doesn't; but if anything, to derive an "all-in" cost of leverage, we need to compare the investment alternatives that we have the choice to select, that are equivalent to the futures contract in our asset allocation. Also, I think you used Vanguard funds in your backtests, not CTDs.

"Or if we're going to compare futures to cash indexes/funds, we should definitely adjust for max-draw or stdev." - max draw down please, not stdev, at least not for me. Max draw down over an economic cycle, or over history. Not 1 month or 3 months. We are studying futures for purpose of running a leveraged strategy. The amount of leverage is constrained by a max drawdown event over a long time frame. I don't think you can demonstrate that the cash treasuries have measurable higher drawdowns over an economic cycle, given that futures must converge to the cash treasuries every 3 months. What do I care about some fluctuations when I know my portfolio NAV will be mathematically exactly the same as yours every 3 months, plus annualized 0.2-0.7% that I pay to some bank or hedge fund to facilitate my leverage. I think the higher fluctuations may be a result of lower volume of the cash treasuries, as outlined in some papers. Please answer my thought experiment question above. You and I each have $1mil. Every 3 months your asset will converge to mine with mathematical precision. Please explain how you think you have less risk exposure.

I don't have an explanation currently for the excess gains for TN futures, but it is no factual evidence to invalidate our calculations that are very straightforward. Only if you can show me that there is a meaningful measure of risk where the futures and cash securities differ, can you convince me that there is no slippage as in a cost to me holding futures.
You can't just compare two indexes (future vs cash) with the same maturity. If the coupons are different, the effective duration is different. And therefor the max-drawdown is different.

As zkn said above, the duration for the cash indices has considerble historical variation. And I'm quite certain that the futures indices do too - even moreso. It's going to be very difficult, possibly impossible, to properly match up durations. You would need the full history of effective duration for both indicies (cash and futures), and make appropriate adjustments to the entire return timeseries at every datapoint. We could approximate having the same duration by taking the average duration for the relevant period rather than simply the current duration. Or what we can still do is match up risk, as measured by stdev or max-draw. The two should be proportional anyways since the drawdown and variance of a bond are both directly proportional to duration.

And that's what zkn has done. We can still do it for max-draw, but I highly doubt the results will be consistently different than for stdev. One index may get lucky that its duration was shorter during a particular max-draw event, but that would not be repeatable going forward. And for that reason I might prefer stdev since it is likely more predictive of future max-draw, because it is a more comprehensive indirect measure of the duration of an index. Using max draw you might just get lucky that the futures index had shorter duration than the cash index during a particular major drawdown, which would make the futures index look better than it is. If the duration of the CTD subsequently increased, the next drawdown would be larger.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

I'm still suspicious of using standard deviations. Deviations may be the result of duration exposure, or, for example, fluctuations of demand and supply. The latter are not "risk" to me because the futures must converge to the CTD. Let me therefore calculate return per duration.

Modified duration comparisons:
Future / futures 5-y return / bond index 5-y return / CTD MD / S&P bond index MD / return per duration (CTD) / return per duration (bond index)
ZT / 1.33 / 1.44 / 1.90 / 1.91 / 0.7 / 0.75
ZF / 1.63% / 1.87% / 4.29 / 4.81 / 0.38 / 0.39
ZN / 2.01% / 2.34% / 6.20 / 6.62 / 0.324 / 0.353
TN / 2.38% / 2.01% / 8.77 / 9.22 / 0.271 / 0.218
ZB / 3.12% / 2.92% / 11.56 / 14.99 / 0.27 / 0.195
UB / 3.61% / 4.19% / 18.3 / 19.2 / 0.197 / 0.218


Striking it through because we don't know historic durations. But isn't it true that the CTD was always a bond with maturity close to the short end of the allowable range of deliverable bonds, since 10+ years ago when interest rates dropped below 6%?

I'm still not convinced of the standard deviation approach. Cash treasuries have lower volume than the futures market, right? If so, the fluctuations based on changes in liquidity - traders rushing to buy or sell on market turns, will be higher. Which would lead to higher standard deviations, but not to higher duration risk to me.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Tue Oct 19, 2021 11:41 am
hdas wrote: Tue Oct 19, 2021 11:24 am
skierincolorado wrote: Tue Oct 19, 2021 9:16 am ZF and ZN are still optimal durations and Treasury futures are an optimal choice for leverage.
Still, if one assumes some level of normalization in interest rates, why do you want to be in the shorter maturities?. Have you look at the flattening that happens EVERY TIME there's a hike cycle?....

[Image
Because they have the highest risk adjusted returns both independently and when combined into a portfolio of stocks. Simple as that. We can try to disect why that is if you would like, and the various components of return, during various rate environments, or we can just accept that fact. There is a theoretical reason why shorter durations have better risk adjusted returns - beta seeking investors overprice longer duraitons.

You've posted the 30y - 5y yield chart. We can see that during hiking the spread gets quite low. The 5 year yield rises more than the 30 year yield during hiking. Conversely, it also falls more than the 30y during easing periods. So the rate on the 5y is a bit more volatile. But the duration is 1/6th so an equivalent interest rate move produes 1/6th the change in price. The volatility of the interest rate is not 6x greater. It's not even 2x greater. Ultimately, we end up with an asset with higher risk adjusted returns - primarily due to beta seeking investors overpricing long maturities.
But I think hdas is basically playing with the idea of a dynamic allocation on the yield curve based on its current shape, particularly the current slope. Which according to some papers might generate excess returns. He says it's just a matter of time until the curve flattens, it has always flattened. So let's sit it out. It's not if, but when. Let's play the mean reversion. Let's tilt to longer maturities when there is some slope. Back to shorter when it's flat or inverts. Rinse and repeat.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Tue Oct 19, 2021 7:03 pm
skierincolorado wrote: Tue Oct 19, 2021 11:41 am
hdas wrote: Tue Oct 19, 2021 11:24 am
skierincolorado wrote: Tue Oct 19, 2021 9:16 am ZF and ZN are still optimal durations and Treasury futures are an optimal choice for leverage.
Still, if one assumes some level of normalization in interest rates, why do you want to be in the shorter maturities?. Have you look at the flattening that happens EVERY TIME there's a hike cycle?....

[Image
Because they have the highest risk adjusted returns both independently and when combined into a portfolio of stocks. Simple as that. We can try to disect why that is if you would like, and the various components of return, during various rate environments, or we can just accept that fact. There is a theoretical reason why shorter durations have better risk adjusted returns - beta seeking investors overprice longer duraitons.

You've posted the 30y - 5y yield chart. We can see that during hiking the spread gets quite low. The 5 year yield rises more than the 30 year yield during hiking. Conversely, it also falls more than the 30y during easing periods. So the rate on the 5y is a bit more volatile. But the duration is 1/6th so an equivalent interest rate move produes 1/6th the change in price. The volatility of the interest rate is not 6x greater. It's not even 2x greater. Ultimately, we end up with an asset with higher risk adjusted returns - primarily due to beta seeking investors overpricing long maturities.
But I think hdas is basically playing with the idea of a dynamic allocation on the yield curve based on its current shape, particularly the current slope. Which according to some papers might generate excess returns. He says it's just a matter of time until the curve flattens, it has always flattened. So let's sit it out. It's not if, but when. Let's play the mean reversion. Let's tilt to longer maturities when there is some slope. Back to shorter when it's flat or inverts. Rinse and repeat.
I’m not sure that’s what he’s saying, but either way I haven’t seen a rules based strategy that goes any farther than 10 years out on the curve. I have seen some rules based strategies that shift duration but never longer than 10 years. Such as a max carry (per duration ) strategy.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Tue Oct 19, 2021 6:40 pm I'm still suspicious of using standard deviations. Deviations may be the result of duration exposure, or, for example, fluctuations of demand and supply. The latter are not "risk" to me because the futures must converge to the CTD. Let me therefore calculate return per duration.

Modified duration comparisons:
Future / futures 5-y return / bond index 5-y return / CTD MD / S&P bond index MD / return per duration (CTD) / return per duration (bond index)
ZT / 1.33 / 1.44 / 1.90 / 1.91 / 0.7 / 0.75
ZF / 1.63% / 1.87% / 4.29 / 4.81 / 0.38 / 0.39
ZN / 2.01% / 2.34% / 6.20 / 6.62 / 0.324 / 0.353
TN / 2.38% / 2.01% / 8.77 / 9.22 / 0.271 / 0.218
ZB / 3.12% / 2.92% / 11.56 / 14.99 / 0.27 / 0.195
UB / 3.61% / 4.19% / 18.3 / 19.2 / 0.197 / 0.218


Striking it through because we don't know historic durations. But isn't it true that the CTD was always a bond with maturity close to the short end of the allowable range of deliverable bonds, since 10+ years ago when interest rates dropped below 6%?

I'm still not convinced of the standard deviation approach. Cash treasuries have lower volume than the futures market, right? If so, the fluctuations based on changes in liquidity - traders rushing to buy or sell on market turns, will be higher. Which would lead to higher standard deviations, but not to higher duration risk to me.
Yeah I considered that too, and it’s possible, but I think unlikely because per the ofr skowed the ctd is priced fairly relative to non-ctd, except for a very brief very slight deviation in March 2020 when bonds were going up in value anyways. But yeah testing with both shouldn’t be too difficult I’ll try to do it if zkn can’t .. sounded like they might have the data to do so already.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Tue Oct 19, 2021 11:49 am
Kbg wrote: Tue Oct 19, 2021 11:23 am Wonderful thread folks, appreciate the data dive and the analysis. If I might ask a summarizing question.

What do you feel is the max leverage for the overall port based on STT/ITT/LTT

IIRC correctly the optimal mixes are

STT 1:4 or 1:9
ITT 1:2.33 (e.g. 3:7) or 1:3
LTT ???

Hopefully I stated the above correctly. For example, would you lever up STT 1:9 to say x1.5 or would the 1:9 ratio be the max

(The instability of the STTs would seem to make them not a great choice)

Tks!
There are different opinions and different ways we might calculate this.

We can look historically, or make future projections based on expected returns and risk. Looking historically it depends what period we use. If we look pre-1980, we will generally find lower bond allocations than if we only look post 1980. If we project future returns, we will generally find lower bond allocations because bonds have very low expected returns right now (although starting to creep up).

We can just look at sharpe ratios which only considers short-term variability, or we can look at variability in the 30+ year return as well. Looking at variability in 30+ year returns, we would find less allocation to bonds because bonds seem to have long interest rate cycles that can produce undesired variability in long-term returns.

Ultimately, I favor a combination of approaches. Ultimately for STT I would probably do 1:5 but I avoid STT because they are very sensitive to assumptions due to the high leverage ratio required. For ITT I prefer between 2:3. And for LTT I prefer something like 3:2. But again, LTT are not optimal because of the low risk-adjusted returns.

Thus I kind of see it as a pointless question for STT and LTT, because the only one I would consider investing in is ITT.

It also depends on the duration we define for each. For STT I would use just under 2 years. For ITT, 5.5 years. For LTT 15-18 years.
I personally prefer to mentally, and in my spreadsheets, "normalize" duration exposure in different maturities to UB-equivalent exposure, as the optimal allocation to UB / LTT within a portfolio have been extensively studied in the HFEA thread. I have currently ca. 40% of NAV in UB-equivalent treasury exposure. I personally also will probably adjust my treasuries exposure over time in part on expected real returns and/or expected term premia. I don't think I would keep my allocation in a Spring 2020 low interest rate scenario, or when rates are negative if it ever happens. I think I will back up the truck when rates are measuably above expected inflation or above central bank inflation targets, or expected term premia are convincingly above zero. Unfortunately I haven't had time yet to write down a rules-based methodology.
Last edited by comeinvest on Tue Oct 19, 2021 7:24 pm, edited 4 times in total.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Tue Oct 19, 2021 7:14 pm
comeinvest wrote: Tue Oct 19, 2021 6:40 pm I'm still suspicious of using standard deviations. Deviations may be the result of duration exposure, or, for example, fluctuations of demand and supply. The latter are not "risk" to me because the futures must converge to the CTD. Let me therefore calculate return per duration.

Modified duration comparisons:
Future / futures 5-y return / bond index 5-y return / CTD MD / S&P bond index MD / return per duration (CTD) / return per duration (bond index)
ZT / 1.33 / 1.44 / 1.90 / 1.91 / 0.7 / 0.75
ZF / 1.63% / 1.87% / 4.29 / 4.81 / 0.38 / 0.39
ZN / 2.01% / 2.34% / 6.20 / 6.62 / 0.324 / 0.353
TN / 2.38% / 2.01% / 8.77 / 9.22 / 0.271 / 0.218
ZB / 3.12% / 2.92% / 11.56 / 14.99 / 0.27 / 0.195
UB / 3.61% / 4.19% / 18.3 / 19.2 / 0.197 / 0.218


Striking it through because we don't know historic durations. But isn't it true that the CTD was always a bond with maturity close to the short end of the allowable range of deliverable bonds, since 10+ years ago when interest rates dropped below 6%?

I'm still not convinced of the standard deviation approach. Cash treasuries have lower volume than the futures market, right? If so, the fluctuations based on changes in liquidity - traders rushing to buy or sell on market turns, will be higher. Which would lead to higher standard deviations, but not to higher duration risk to me.
Yeah I considered that too, and it’s possible, but I think unlikely because per the ofr skowed the ctd is priced fairly relative to non-ctd, except for a very brief very slight deviation in March 2020 when bonds were going up in value anyways. But yeah testing with both shouldn’t be too difficult I’ll try to do it if zkn can’t .. sounded like they might have the data to do so already.
I was not referring to CTD vs non-CTD, but to possibly higher market impact of changes in sentiment in the fixed income market on cash treasuries as a whole than on the futures market. Please someone test drawdowns over longer periods, if possible. Frankly I don't think we have shown much before we do that.
Last edited by comeinvest on Tue Oct 19, 2021 9:04 pm, edited 2 times in total.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Tue Oct 19, 2021 5:20 pm Well you shouldn’t need the CF.. can just use the IB price which is like well over 100k for most contracts (100k/ cf) like 125 k for zf
The application of the CF in the screenshot by millenialmilllions is wrong then? viewtopic.php?p=6276194#p6276194
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

Maybe I'm having some mental blockage, but taking a step back and trying to rationalize the math. Summary (UB as example):

Non-risk-adjusted slippage:
S&P cash-secured ultra T-Bond future (25 years and 4 months) vs. the S&P U.S. Treasury Bond 20+ Year Index (26 years):
10 years: 4.3% (cash-secured futures index) / 5.04% (bond index) => slippage: 0.74%
5-year annualized returns: 3.61% (future) / 4.19% (bond index) => slippage: 0.58%
3-year: 9.99% / 10.72% => slippage: 0.73%
1-year: -8.44% / -8.35% => slippage: 0.09%

Risk-adjusted slippage: ("I compared the risk (annualized monthly standard deviation) for each index pair, and the annualized risk-adjusted returns")
S&P cash-secured ultra T-Bond future (25 years and 4 months) vs. the S&P U.S. Treasury Bond 20+ Year Index (26 years):
10 years: 11.54% / 12.10% => .33% / .37% => slippage .04%
5 years: 12.33% / 12.36% => .22% / .27% => slippage .05%
3 years: 13.94% / 13.93% => .62% / .67% => slippage .05%

Current duration comparison:
Future / futures 5-y return / bond index 5-y return / CTD MD / S&P bond index MD / return per duration (CTD) / return per duration (bond index)
UB / 3.61% / 4.19% / 18.3 / 19.2 / 0.197 / 0.218

Can it be that a mere 0.9 year shorter duration (18.3 vs. 19.2) justifies sacrificing a 0.7% annual return, when the total nominal return is only what - like 2%? We are talking about 35% or more of the (nominal) return. I know we don't know the historical durations, but still.

Another question: This thread is about leverage, i.e. most of us don't invest the cash collateral in T-bills. Instead, we are adding an overlay of a treasury allocation via futures on an equities portfolio, and we pay the funding rate (short-term rate + slippage).
The return generated from that overlay is much smaller than the nominal returns from treasuries. Our incremental return from the overlay is just the difference between long-term and short-term rates (term premium). Let's say 0.5%. (I'm forgetting rebalancing effects for this discussion.)
Shouldn't a fair "risk-adjusted return" be based on the incremental return that we are generating from that incremental addition of leveraged futures (with the implied funding cost already subtracted), instead of on the nominal return of only the positive part of that addition (the treasury without the funding cost)?
Example: assume expected term premium is 0.5%. This is our expected additional return from adding treasury futures to our portfolio. Basically what I'm saying is, shouldn't we use this all-in net return as input to the "annualized risk-adjusted returns" in zkn's "risk-adjusted slippage"?
An intuitive thought experiment using my example to support my thought: term premium 0.5%, 10-year nominal slippage 0.74% p.a., would you prefer to be invested in a portfolio with 0.5% - 0.74% = -0.24% expected return, or in one with 0.5% expected return, even if the latter has slightly higher standard deviations? Shouldn't we put the total incremental risk in relation to the total incremental return, instead of just the positive part of it?
Last edited by comeinvest on Tue Oct 19, 2021 9:10 pm, edited 2 times in total.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by hdas »

hhhhh
Last edited by hdas on Tue Oct 26, 2021 6:39 pm, edited 1 time in total.
....
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by hdas »

comeinvest wrote: Tue Oct 19, 2021 7:03 pm But I think hdas is basically playing with the idea of a dynamic allocation on the yield curve based on its current shape, particularly the current slope. Which according to some papers might generate excess returns. He says it's just a matter of time until the curve flattens, it has always flattened. So let's sit it out. It's not if, but when. Let's play the mean reversion. Let's tilt to longer maturities when there is some slope. Back to shorter when it's flat or inverts. Rinse and repeat.
skierincolorado wrote: Tue Oct 19, 2021 7:10 pm I’m not sure that’s what he’s saying, but either way I haven’t seen a rules based strategy that goes any farther than 10 years out on the curve. I have seen some rules based strategies that shift duration but never longer than 10 years. Such as a max carry (per duration ) strategy.
h
Last edited by hdas on Tue Oct 26, 2021 6:39 pm, edited 1 time in total.
....
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by constructor »

millennialmillions wrote: Mon Oct 18, 2021 9:55 pm
constructor wrote: Mon Oct 18, 2021 2:46 pm
millennialmillions wrote: Sun Oct 17, 2021 9:14 am Bentonkb linked to this CME paper, which describes how to calculate the Principal Invoice Price, a better representation of the market value.

"E.g., the conversion factor for delivery of the 2-3/8% T-note of Aug-24 vs. December 2017 10-year T-note futures is 0.8072. This suggests that a 2 3/8% security is approximately valued at 81% as much as a 6% security. Assuming a futures price of 125-08+/32nds (or 125.265625 expressed in decimal format), the principal invoice amount may be calculated as follows. Principal Invoice Price = 125.265625 x 0.8072 x $1,000 = $101,114.41 E.g., the conversion factor for delivery of the 1-7/8% T-note of Aug-24 vs. December 10-year T-note futures is 0.7807. This suggests that a 1-7/8% security is approximately valued at 78% as much as a 6% security. Assuming a futures price of 125-08+/32nds (or 125.265625), the principal invoice amount may be calculated as follows.
Principal Invoice Price
= 125.265625 x 0.7807 x $1,000
= $97,794.87
In order to arrive at the total invoice amount, one must of course further add any accrued interest since the last semi annual interest payment date to the principal invoice amount."

It looks like the current CTD underlying security has a conversion factor of 0.95. So I would calculate your current STT exposure as $109,245 * 0.95 CF * 2 (for $200,000 face value) * 4 contracts = $830,262.

Note it doesn't appear there is consensus on this calculation, but this seems to directly align with the CME paper, and I haven't seen a good reason to use any other number. Also, the conversion factor for STT is closer to 1 than ITT or LTT, so it doesn't have as much of an impact.
While I agree with you in terms understanding of the book/PDF in practice I found the conversion factor does not need to be taken account given these empirical observations. Let's use the most extreme example with UB which has a conversion factor of 0.6141 as per Treasury Analytics (https://www.cmegrou ... tics.html).

1. The volatility of UB is identical to TLT, and definitely not 0.6 times that of TLT. If the actual exposure is the "invoice price" which is 0.6 times the nominal value we would expect UB to be 0.6 times as volatile.
2. In the Treasury Analytics page there is DV01 for futures and DV01 for cash, and precisely Cash DV01 = 0.6 * Futures DV01. If the actual exposure is the invoice price then the DV01 would be identical.

Well basically these two points are the same point.

But I agree with you that it sounds like on delivery only 0.6 times the nominal amount of the underlying treasury would be delivered. Confusing... I wonder if I am understanding the delivery process incorrectly.

Edit: On page 12 it does say:
E .g ., if one held $10 million face value of the 2-3/8%-8/24 note, one might sell 81 December 2017 futures by reference to the conversion factor of 0 .8072 to execute a hedge .
So this confirms that the nominal value is correct, that one future contract hedges more than "one treasury", given the ration of (1 / conversion factor). Though my question remains how the delivery work, since this almost seems you might need to deliver fraction of a treasury, and what the invoice price really means in the delivery process.
Thank you for your reply. I'm amazed we haven't reached consensus on something so fundamental to this strategy...it should be important for everyone in this thread to have an answer to this.

I disagree with your reading of that section (page 9 of the CME PDF) and believe it actually confirms the opposite, that the futures price must be multiplied by the conversion factor to determine market value/market exposure. Look at this table:
Image

The cash price is the market value. Multiplying the futures price by the conversion factor gets us very close to this market value (and the difference is the basis, which is small enough to ignore for our purpose).

Ultimately, it doesn't matter that one futures contract hedges more than "one treasury". What matters is holding one futures contract gives you equivalent performance to investing $x directly in treasuries, or in a fund like TLT. This paper says that x ≈ futures price * CF.

The best way to settle this would be to use actual futures returns data compared against a fund to determine how much TLT is needed to replicate the results of 1 UB contract. Your point that "the volatility of UB is identical to TLT" doesn't answer this question of how much is needed.
Does this chart of UB divided by TLT convince you for the last point? Gaps are due to different quarter futures. Within each quarter the line is flat, or at least does not differ by a factor of 0.6.

Image

As I said I still don't fully understand the delivery process and thus would love to see discussion here, but I am convinced that the conversion factor is irrelevant if we only care about replicating exposure and not delivery. Empirically I ran HFEA with UB and MES for a while and the return appeared identical to what I would get from UPRO and TMF. Then I switched to ZN and ZF and it's all messed up now.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by jarjarM »

comeinvest wrote: Tue Oct 19, 2021 7:03 pm But I think hdas is basically playing with the idea of a dynamic allocation on the yield curve based on its current shape, particularly the current slope. Which according to some papers might generate excess returns. He says it's just a matter of time until the curve flattens, it has always flattened. So let's sit it out. It's not if, but when. Let's play the mean reversion. Let's tilt to longer maturities when there is some slope. Back to shorter when it's flat or inverts. Rinse and repeat.
Interesting, thanks to hdas and comeinvest on providing some idea on how to play the hike cycle. :beer
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

jarjarM wrote: Tue Oct 19, 2021 9:44 pm
comeinvest wrote: Tue Oct 19, 2021 7:03 pm But I think hdas is basically playing with the idea of a dynamic allocation on the yield curve based on its current shape, particularly the current slope. Which according to some papers might generate excess returns. He says it's just a matter of time until the curve flattens, it has always flattened. So let's sit it out. It's not if, but when. Let's play the mean reversion. Let's tilt to longer maturities when there is some slope. Back to shorter when it's flat or inverts. Rinse and repeat.
Interesting, thanks to hdas and comeinvest on providing some idea on how to play the hike cycle. :beer
But be careful what you wish for. It's not that easy. A while ago I thought it's free money, until I did some more due diligence and discovered that the risk-adjusted returns might be similar to those of investing in an equity index (as it should be). You have to account for unexpected drawdowns when flattening or steepening goes against what you expected, and your possible profits per capital are much slimmer than for equities. Having that said, I would probably move all my treasury futures to the short end if and when the curve is almost or entirely flat or inverted, and to the long end when the slope is measurably above average. In scenarios when there is an apparent risk/reward mismatch. I haven't had time to do backtesting or risk analysis unfortunately. I shorted the ZT when the 2-year rates were around 0.15%, thinking downside is limited, but I was aware that rates might go negative. But the risk/reward potential seemed skewed to me.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by cometqq »

skierincolorado wrote: Tue Oct 19, 2021 5:20 pm
comeinvest wrote: Tue Oct 19, 2021 5:03 pm
skierincolorado wrote: Tue Oct 19, 2021 12:04 pm
comeinvest wrote: Tue Oct 19, 2021 5:27 am
skierincolorado wrote: Mon Oct 18, 2021 10:56 pm

Here is my understanding. I am not 100% confident in this, but am not overly concerned because the amounts are close enough for my purposes.

What is delivered is the 100k. What is paid is the invoice price. But because the invoice price is calculated as if the delivered bonds had a 6% yield, the invoice price changes reflect the price change of a basket of bonds with face value of 100k / CF. Thus the long position gets the return of the larger basket. The short position gets the referse of this return. If the short position wishes to hedge and collect the basis, they must own the larger basket.

Thus we get:

"E.g., if one were to buy the basis by buying $10 million
face value of the 2-3/8%-8/24 note, one might sell 81
December 2017 futures by reference to the conversion
factor of 0.8072."

Thus 81 ZN contracts have the same return as $10M of the CTD bond.

The higher number is the correct one (100k/CF)
Can somebody fill me in? I hope my exposure in the underlying (notional value?) is the current nominal futures price, adjusted for the financing cost and coupon payment between now and settlement date? Just like for equity index futures. So close enough what IB shows as "market value" in TWS. Correct?
There has been some back and forth. Originally I was saying 100k/CF, but then there was some confusion with a couple people arguing that it is just the 100k because this is what is delivered. How can the exposure be different than what is delivered? I couldn't remember my reasoning, but re-reading the CME explanation I think I understand again. Hopefully putting it in writing will help me not forget.

Yes what is delivered is the 100k. But what is traded is a theoretical portfolio of 100k face value with 6% interest rates. This has a value of 100k/CF.

When the interest rate goes down, the value of 100k/CF moves like a larger ~125k bond.

Now we might say, OK but how did the invoice price change? The invoice price didn't change like a 125k bond because the invoice price is the futures price * the invoice price.

Here is what we were missing before. Not only did the futures price change, but the CF also changed. The CF got bigger. Thus the invoice price went up for two reasons. The futures price went up based on how ~125k in bonds would chance in price. If we multiplied by the old CF the invoice price would just change by the amount that ~100k in bonds would change in price. But we don't multiply by the old CF. We multiply by the new CF which is bigger. Thus the invoice price increased by the same nominal $ amount that the futures price increased by. Ta-da!

The mistake that some people were making was assuming that the CF does not change. BOTH the futures price AND the CF goes up when interest rates fall.

Thus we get CME's statement that:

"
"E.g., if one were to buy the basis by buying $10 million
face value of the 2-3/8%-8/24 note, one might sell 81
December 2017 futures by reference to the conversion
factor of 0.8072."

This is the statement we should rely upon and its interpretation is indisputable. 81M in futures contracts provides an exposure to 100M in bonds when the CF is .81.
I never had time to dig into the nitty gritty of treasury futures delivery and always assumed what IB shows as market value is my exposure to the underlying minus expected coupons plus implied financing cost, and frankly I still didn't have time to study it. And was hoping I never have to, lol. Does everybody agree we have to apply the CF? How is it consistent with the observation that the volatility of the face values were similar that was made above? Where can I quickly find the current CF of the 5 different futures on any given day?
Well you shouldn’t need the CF.. can just use the IB price which is like well over 100k for most contracts (100k/ cf) like 125 k for zf
So two ZFs give you an exposure to 250k ITT not 200k ITT. To have an exposure to 200k ITT, you'd buy one ZF and 75k VGIT. Is this correct? I feel that whether one ZF is an exposure to 125k or 100k ITT is important. The difference is certainly not negligible.
Topic Author
skierincolorado
Posts: 2377
Joined: Sat Mar 21, 2020 10:56 am

Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

jarjarM wrote: Tue Oct 19, 2021 9:44 pm
comeinvest wrote: Tue Oct 19, 2021 7:03 pm But I think hdas is basically playing with the idea of a dynamic allocation on the yield curve based on its current shape, particularly the current slope. Which according to some papers might generate excess returns. He says it's just a matter of time until the curve flattens, it has always flattened. So let's sit it out. It's not if, but when. Let's play the mean reversion. Let's tilt to longer maturities when there is some slope. Back to shorter when it's flat or inverts. Rinse and repeat.
Interesting, thanks to hdas and comeinvest on providing some idea on how to play the hike cycle. :beer
Until we see a rules based backrest that significantly outperforms buy and hold ITT we should remain skeptical. It’s a market timing strategy which we should be inherently skeptical of given EMH. Even if such a backtest were provided, the rules are constantly changing and historical sources of alpha often do not persist. I would want to see it backtested over a very long period of 60+ years and that it has delivered alpha in each 20 year subset of the 60 years as well. I would probably also want a theoretical reason why the alpha has persisted (other than everybody else being to dumb to notice it).

Going long on the curve sounds like it makes sense when the curve is steep. But sometimes the steepness precedes a rise in rates across the whole curve. It would have been better to be in middle durations like 10 years in such a case where the carry and roll down is better.

Even when 10 y rates rise more than 30 y rates it will often have been better to be in the 10 y because the carry and roll is better. There are very few moments in history where it would have been better to be in the 30 y. The last few months happened to be one such case but in the big picture the benefit was minimal.

I’ve read a few papers on dynamic hedge fund strategies and none of them ever go farther than 10 years out on the curve. There’s a reason for this. The slope of the curve past ten years is pretty much always less steep.
Last edited by skierincolorado on Wed Oct 20, 2021 11:23 am, edited 1 time in total.
Topic Author
skierincolorado
Posts: 2377
Joined: Sat Mar 21, 2020 10:56 am

Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

cometqq wrote: Wed Oct 20, 2021 5:53 am
skierincolorado wrote: Tue Oct 19, 2021 5:20 pm
comeinvest wrote: Tue Oct 19, 2021 5:03 pm
skierincolorado wrote: Tue Oct 19, 2021 12:04 pm
comeinvest wrote: Tue Oct 19, 2021 5:27 am

Can somebody fill me in? I hope my exposure in the underlying (notional value?) is the current nominal futures price, adjusted for the financing cost and coupon payment between now and settlement date? Just like for equity index futures. So close enough what IB shows as "market value" in TWS. Correct?
There has been some back and forth. Originally I was saying 100k/CF, but then there was some confusion with a couple people arguing that it is just the 100k because this is what is delivered. How can the exposure be different than what is delivered? I couldn't remember my reasoning, but re-reading the CME explanation I think I understand again. Hopefully putting it in writing will help me not forget.

Yes what is delivered is the 100k. But what is traded is a theoretical portfolio of 100k face value with 6% interest rates. This has a value of 100k/CF.

When the interest rate goes down, the value of 100k/CF moves like a larger ~125k bond.

Now we might say, OK but how did the invoice price change? The invoice price didn't change like a 125k bond because the invoice price is the futures price * the invoice price.

Here is what we were missing before. Not only did the futures price change, but the CF also changed. The CF got bigger. Thus the invoice price went up for two reasons. The futures price went up based on how ~125k in bonds would chance in price. If we multiplied by the old CF the invoice price would just change by the amount that ~100k in bonds would change in price. But we don't multiply by the old CF. We multiply by the new CF which is bigger. Thus the invoice price increased by the same nominal $ amount that the futures price increased by. Ta-da!

The mistake that some people were making was assuming that the CF does not change. BOTH the futures price AND the CF goes up when interest rates fall.

Thus we get CME's statement that:

"
"E.g., if one were to buy the basis by buying $10 million
face value of the 2-3/8%-8/24 note, one might sell 81
December 2017 futures by reference to the conversion
factor of 0.8072."

This is the statement we should rely upon and its interpretation is indisputable. 81M in futures contracts provides an exposure to 100M in bonds when the CF is .81.
I never had time to dig into the nitty gritty of treasury futures delivery and always assumed what IB shows as market value is my exposure to the underlying minus expected coupons plus implied financing cost, and frankly I still didn't have time to study it. And was hoping I never have to, lol. Does everybody agree we have to apply the CF? How is it consistent with the observation that the volatility of the face values were similar that was made above? Where can I quickly find the current CF of the 5 different futures on any given day?
Well you shouldn’t need the CF.. can just use the IB price which is like well over 100k for most contracts (100k/ cf) like 125 k for zf
So two ZFs give you an exposure to 250k ITT not 200k ITT. To have an exposure to 200k ITT, you'd buy one ZF and 75k VGIT. Is this correct? I feel that whether one ZF is an exposure to 125k or 100k ITT is important. The difference is certainly not negligible.
Correct. The quote from Cme confirms this. 10m hedged by only 81 contracts.
Last edited by skierincolorado on Wed Oct 20, 2021 11:24 am, edited 1 time in total.
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