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 »

hdas wrote: Thu Oct 21, 2021 9:52 pm
comeinvest wrote: Thu Oct 21, 2021 9:35 pm
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)
ZF / 1.63% / 1.87% / 4.29 / 4.81 / 0.38 / 0.39

Seems like the duration adjustment explains the difference in my chart. This for the 5-year chart. But if your read all the comments of skier and zkn, they argued that standard deviations are more meaningful, as durations might have changed during the time frame.
2.5% in 2 years is too much. In any case, the main conclusion is that using VFITX as a backtest tool is very bad. Even worst when you compound with leverage 3x, and then only charge CASHX as the cost of the leverage.
As already proven, the returns of the futures contracts scaled for max-drawdown and/or stdev are very similar to or often greater than the cash index.
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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 »

constructor wrote: Thu Oct 21, 2021 8:16 pm
skierincolorado wrote: Wed Oct 20, 2021 5:45 pm
This explains the statement by CME and others that 10M in bonds is hedged by just 81 contracts when the CF is .81. Or taking the inverse, 81 contracts has equal exposure to 10M in bonds. Not 8.1M.

https://us.etrade.com/knowledge/library ... -to-market
The only puzzle in my whole understanding is: With CF = 0.81, and say I long 1 contract till expiration for actual delivery. This means I need to be delivered a face value of $100,000 / 0.81 = $123,456. But each treasury has face value of $1,000 right? How do I receive 123 and then 456/1000 treasuries? Can one own/deliver a fraction of a $1,000 treasury?
The delivery is just $100k face value in CTD bonds. Or futures price * CF in market value of the CTD.

That's the whole confusing part. If the delivery is just futures price * CF, how do my returns reflect the full futures price? It took me a while - but they do.
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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 »

hdas wrote: Thu Oct 21, 2021 9:26 pm
comeinvest wrote: Thu Oct 21, 2021 9:17 pm
hdas wrote: Thu Oct 21, 2021 8:41 pm While your point it's true, it just doesn't explain away the underperformance of futures. I added ZN funded, which has a duration of 6+ years and that also underperforms VFITX.
skier and zkn thought they explained it with duration discrepancies
Both the higher (ZN) and the lower (ZF) duration futures underperform VFITX, so that is not the factor. It must be the implied financing and the fact that you are not making anything in the funded position 3m T-bills. The difference is very significant, 2-2.5% in 2 years....Imagine the compound error of this on those imaginary 30y backtests of PV, total delusion.
You can't compare ZN or ZF to VFITX. They have different durations. Just because ZN has longer duration, doesn't mean it will return more. 6.5 year interest rates could have gone up or down in a different way the 5.5 year rates. The shape of the curve could change. You are comparing apples and bananas. 1.5 * banana does not equal apple.

I suggest rereading the entire conversation between zkn, cominvest and I. If you compare cash and futures indexes with very close durations, and then scale by max-daw or stdev, the returns are nearly identical with almost no slippage. When there is slippage, it is often less than the 0.2% fee on VFITX that I use in backtesting.
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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: Thu Oct 21, 2021 9:35 pm
hdas wrote: Thu Oct 21, 2021 9:26 pm
comeinvest wrote: Thu Oct 21, 2021 9:17 pm
hdas wrote: Thu Oct 21, 2021 8:41 pm While your point it's true, it just doesn't explain away the underperformance of futures. I added ZN funded, which has a duration of 6+ years and that also underperforms VFITX.
skier and zkn thought they explained it with duration discrepancies
Both the higher (ZN) and the lower (ZF) duration futures underperform VFITX, so that is not the factor. It must be the implied financing and the fact that you are not making anything in the funded position 3m T-bills. The difference is very significant, 2-2.5% in 2 years....Imagine the compound error of this on those imaginary 30y backtests of PV, total delusion.
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)
ZF / 1.63% / 1.87% / 4.29 / 4.81 / 0.38 / 0.39

Seems like the duration adjustment explains the difference in my chart. This is for the 5-year chart. But if you read all the comments of skier and zkn, they demonstrated that standard deviations are more meaningful, as durations might have changed during the time frame.

For your chart ZF vs. VFITX: VFITX currently has average duration of 5.2 years. ZF CTD has 4.29 modified duration. Per your chart, the performance is ca. 3% for ZF vs. 6% for VFITS over about 2 years. Adjusting 3% for the ratio of the different durations gives: 3 / 4.29 * 5.2 = 3.6%. Effective slippage would be 6 - 3.6 = 2.4, annualized ca. 1.2%. That is vs. VFITX that has the expense ratio already subtracted. You are right, something doesn't add up. Not sure if durations of either the future or the Vanguard fund changed dramatically during the last 2 years, I doubt. We may have to wait for skier or zkn.
Yeah so you've shown for the charts you posted the return per duration is pretty much identical.

For zkn's chart's we'll need both the exact data and methodology he is using.
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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 »

Providing and verifying methodologies is important in these kinds of discussions. Here is mine:

August 30 2019 to September 30 2021

ZF
581.56 -> 602.49 = 3.599% https://www.spglobal.com/spdji/en/indic ... ndex/#data

VFITX (I used August 31 start date which was a Saturday)
10,000 -> 10,508 = 5.08% https://www.portfoliovisualizer.com/bac ... ion1_1=100

ZF duration = 4.3 years currently
VFITX duration = 5.3 years currently

scaled ZF = 3.599 * 5.3 / 4.3 = 4.44%

ZF cost = 5.08-4.44 = 0.62% (before VFITX fees)

Annualized cost = 0.62% / 2.0416 years = 0.30% (before VFTIX fees) *** EDIT: originally incorrectly used 1.92 years

Total ZF cost = 0.30% + 0.2% VFITX fee = 0.50%

EDIT: See my next post for a continuation of this method


This 0.52% total annualized ZF cost above a fee-free cash return is *substantially* smaller than what hdas posted.

It is still on the higher side. There are a few problems with the calculation though.
1) the durations of 4.3 and 5.3 are only the current reported values. We don't know what the actual historical values were. I would prefer to scale by stdev, but I will need to get my hands on daily data for VFITX then. (EDIT: see my next post I scale by one month drawdown).
2) scaling a banana does not equal an apple. There is no way to scale the 4.3y treasury so that it is exactly the same as a 5.3y treasury
3) this is a short period to perform such a highly sensitive calculation. It would be better to perform it over a longer period, such as 5 years (as we have already done repeatedly)


I question the necessity of repeatedly performing these calculations since we have reported financing costs for each contract computed by OFR in published academic papers and we have verified those costs ourselves over quite a few contracts and time periods. The assumption at this point should be if the computed costs do not align with the OFR values, than an error has been made on our part - not OFR's.
Last edited by skierincolorado on Fri Oct 22, 2021 9:30 am, edited 4 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 »

skierincolorado wrote: Fri Oct 22, 2021 1:24 am Providing and verifying methodologies is important in these kinds of discussions. Here is mine:

August 30 2019 to September 30 2021

ZF
581.56 -> 602.49 = 3.599% https://www.spglobal.com/spdji/en/indic ... ndex/#data

VFITX (I used August 31 start date which was a Saturday)
10,000 -> 10,508 = 5.08% https://www.portfoliovisualizer.com/bac ... ion1_1=100

ZF duration = 4.3 years currently
VFITX duration = 5.3 years currently

scaled ZF = 3.599 * 5.3 / 4.3 = 4.44%

ZF cost = 5.08-4.44 = 0.62% (before VFITX fees)

Annualized cost = 0.62% / 2.0416 years = 0.30% (before VFTIX fees) EDIT: 2.01416 not 1.92 years

Total ZF cost = 0.30% + 0.2% VFITX fee = 0.50%


This 0.50% total annualized ZF cost above a fee-free cash return is *substantially* smaller than what hdas posted.

It is still on the higher side. However, I will note that the durations of 4.3 and 5.3 are only the current reported values. We don't know what the actual historical values were. I would prefer to scale by stdev, but I will need to get my hands on daily data for VFITX then.

I will note that this is a short period (less than 2 years), the cost of 0.52% is only slightly higher than I would expect, and that there are a number of possible explanations for the remaining difference. Generally I would prefer to perform such a calculation over a longer time period, like 5 years, so it is less dependent on small anomalies or errors.

I question the necessity of repeatedly performing these calculations since we have reported financing costs for each contract computed by OFR in published academic papers and we have verified those costs ourselves over quite a few contracts and time periods. The assumption at this point should be if the computed costs do not align with the OFR values, than an error has been made on our part - not OFR's.
Lazy man calculation of max draw.... Aug 30 2019 to Sep 30 2019

ZF
581.56 -> 578.51 = -0.53%

VFITX
10,000 -> 9930 = -0.7%

So we can see that in this one month drawdown, VFITX lost 0.7% while ZF only lost 0.53%.

Using this as our scaling ratio

3.599% * 0.7 / 0.53 = 4.75%

ZF cost = 5.08-4.75 = 0.33% (before VFITX fees)

Annualized cost = 0.33% / 2.0416 years = 0.16% (before VFTIX fees)

Total ZF cost = 0.17% + 0.2% VFITX fee = 0.36%


So now we are down to a 0.36% cost - which is pretty consistent with what OFR reported during this period. Figure 5: https://www.financialresearch.gov/brief ... Trades.pdf


And we still have all the aforementioned issues. Scaling a banana does not equal an apple. This is a short time period. We don't know the actual exact durations. OFR already calculated all of this for us. Etc.....
Last edited by skierincolorado on Fri Oct 22, 2021 9:32 am, edited 3 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: Fri Oct 22, 2021 1:24 am Providing and verifying methodologies is important in these kinds of discussions. Here is mine:

August 30 2019 to September 30 2021

ZF
581.56 -> 602.49 = 3.599% https://www.spglobal.com/spdji/en/indic ... ndex/#data

VFITX (I used August 31 start date which was a Saturday)
10,000 -> 10,508 = 5.08% https://www.portfoliovisualizer.com/bac ... ion1_1=100

ZF duration = 4.3 years currently
VFITX duration = 5.3 years currently

scaled ZF = 3.599 * 5.3 / 4.3 = 4.44%

ZF cost = 5.08-4.44 = 0.62% (before VFITX fees)

Annualized cost = 0.62% / 1.92 years = 0.32% (before VFTIX fees)

Total ZF cost = 0.32% + 0.2% VFITX fee = 0.52%


This 0.52% total annualized ZF cost above a fee-free cash return is *substantially* smaller than what hdas posted.

It is still on the higher side. However, I will note that the durations of 4.3 and 5.3 are only the current reported values. We don't know what the actual historical values were. I would prefer to scale by stdev, but I will need to get my hands on daily data for VFITX then.

I will note that this is a short period (less than 2 years), the cost of 0.52% is only slightly higher than I would expect, and that there are a number of possible explanations for the remaining difference. Generally I would prefer to perform such a calculation over a longer time period, like 5 years, so it is less dependent on small anomalies or errors.

I question the necessity of repeatedly performing these calculations since we have reported financing costs for each contract computed by OFR in published academic papers and we have verified those costs ourselves over quite a few contracts and time periods. The assumption at this point should be if the computed costs do not align with the OFR values, than an error has been made on our part - not OFR's.
I have learned more about treasury futures just in the last few days than in my entire life before, and I personally think it doesn't hurt to spend some time on validating and cross-checking the methodology and math from a variety of angles and a variety of comparison data points, for a strategy that is not well documented elsewhere and that I hope to let run for decades.

Having that said, I tried to check the plausibility of "other possible explanations". First, the possibility that we are comparing "apples to bananas" referring to your post above. Let's see how slightly higher durations performed during this period.
Per S&P charts: Aug 30 -> Sep 30 2021 (2.083 years)
5-year bond index: 110.1 -> 114.78 => performance 1.0425
7-year bond index: 113.67 -> 118.47 => performance 1.0422
I'm not even finishing the per-unit-of-duration calc, as I can see that the 5-year performed better than slightly higher maturities/durations during this period. So "apples to bananas" is unlikely to explain the underperformance of the ZF vs. VFITX.

But I'm noticing that you used 1.92 years. Aren't we looking at exactly 25 months = 2.083 years? If so,
Annualized cost = 0.62% / 2.083 years = 0.30% (before VFTIX fees)
Total ZF cost = 0.30% + 0.2% VFITX fee = 0.5%

So we still have something to explain.

I think you can find free daily stock and ETF data on the internet. Seems like it's also possible to download data from IB via the API, if you have a market data subscription for stocks/ETF.

EDIT: You just beat me with your max draw post.
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: Fri Oct 22, 2021 1:37 am
What I'm still confused about is, if the performance is so dependent on duration rather than maturity, why can I find yield curves per maturity all over the place, but no yield curves by duration?
The page https://www.treasury.gov/resource-cente ... data=yield makes no reference to treasuries of which durations they take as data points for the interpolated yield curve, if there are several durations with the same maturity and therefore presumably different yields.

Also, I still cannot make sense of the "futures yield" and "OTR yield" on https://www.cmegroup.com/tools-informat ... ytics.html

Image

For example the 2-year: CTD and OTR have the same maturity, and almost the same DV01 (OTR a bit higher DV01). But the CTD yield is a substantial 0.08% higher. How can that be. The OTR has lower coupon, higher DV01, but lower yield. Seems like the higher the DV01, the lower the yield. Shouldn't it be the other way around?

Also, higher coupon seems to translate to higher DV01. Example T-Bond future CTD vs OTR. OTR has lower coupon (along with higher maturity), but lower DV01. Shouldn't it be the other way around - everything else being equal, the more money is returned to the bondholder sooner, the lower the interest rate risk. Zero-coupon bonds have the highest duration risk right? And the higher the maturity and duration, the higher the DV01?

Even more confusing, the yield curve that I use seems to show the OTR yield (ZT) at the 2y point (ca. 0.45%), but the CTD yield (ZB) at the 15.5y point (ca. 1.85%).

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

Post by comeinvest »

I made two adjustments to the treasury futures portion of my portfolio tonight. They are mostly not meant to time the market (although I also played around a little bit), but to transition to my final strategic allocation:
- Eliminated all remaining short ZT positions that I established as a partial hedge of my long treasury futures to rising rates, when 2-year rates were on the floor i.e. close to nil. I did this today because I found out that the 2-year carry (ca. 0.8%, with yield to maturity of ca. 0.45%) just surpassed the carry of the 5-year (ca. 1.85% if my math was right) on a duration-adjusted basis, which creeped me out, and I couldn't expect the alpha from the pair trade any more that I expected based on papers advocating a dynamic positioning based on current carry per duration. I pocketed a nice profit, and the hedge did its job. I'm still playing a similar game in the European market.
- Transitioned from some of the ZB to TN+ZN. I should have done this on Monday directly from UB instead of moving from UB to ZB, but someone from Colorado ;) convinced me just this week to go with even shorter durations, so I ended up doing it in two steps. In the meantime, I made a tiny profit ("profit" as in "less loss") by holding ZB instead of TN+ZN for those 4 days. TN+ZN has almost the same DV01 as ZB, which made the transition easy on a DV01-neutral basis. I went with TN and ZN for diversification, because I have already a larger position in ZF.

I used limit orders at the bid (for buy) and ask (for sell) in the night. The volume in the night is lower, but I think the bid and ask sizes are lower too, such that passive limit orders might profit from liquidity based fills ("patient trading") just like by day. The spread is the same as by day. I'm not sure if it's statistically better to trade by day or night for minimizing transaction cost, but it seems to work well either way.

I was kind of sad to let my UB go this week, but it dawned me that it became a curse word in this message thread ;) My allocation comes now closer to an equidistribution between ZF/ZN/TN/ZB on duration-adjusted basis (it's currently still somewhere between a duration-based and notional-value-based equidistribution). I still have to define strict ratios and a suitable rebalancing strategy, so that I don't have to think too much every time in the future. Comments are welcome.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

Does any member of this thread have a link to a spline interpolated version of the yield curve? The one on the treasury page https://www.treasury.gov/resource-cente ... ation.aspx says it needs Adobe Flash, which seems a bit retarded in this day and age. My browsers no longer have Flash.
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Bentonkb
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Bentonkb »

comeinvest wrote: Fri Oct 22, 2021 2:15 am I have learned more about treasury futures just in the last few days than in my entire life before, . . .
You and me both. I am a smart guy, but this is a real mental workout. Many thanks to all the contributors and a hat tip to skier for doing the heavy lifting. :beer

One of the things that I've learned is the proper way to calculate the risk exposure of a bond future. I was wrong to think that the risk of the futures position is the same as a cash position in the CTD bond.

Equation 12 from this PDF convinced me of my error: http://www.yieldcurve.com/mktresearch/l ... utures.pdf
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by zkn »

I think we need to slow down a little bit and work thru the assumptions on relating the futures positions to mutual funds/ETFs. I did some analysis to try to figure out what is going on.

In my earlier analyses, I used the monthly SD from the spglobal data tool and daily max drawdown that I calculated myself from the spglobal datasets. Then I just scaled the returns by either measure of risk without accounting for leverage costs to do a risk-matched comparison on mean returns. Here, I downloaded the data and uploaded to portfoliovisualizer. This analysis accounts for leverage costs (CASHX) in both the mean returns and the risk adjusted returns (Sharpe), and should be straightforward to replicate.

Let's break down the issue: First, the financing cost of futures. Second, the comparability of the futures to mutual funds/ETFs used for backtesting the strategy. And maybe Third approximating the backtesting positions with futures if I break that into a third section.

1 Financing cost

I evaluated the financing costs by comparing the futures data from spglobal to the closest cash bond index data from spglobal (as previously established by the other posters here). We also established with both SD and max drawdown that the cash bond indices were more risky than the futures indices, so this needs to be corrected otherwise the financing costs of the futures will be overestimated. We could correct based on duration, but because the duration of both is changing over time, I prefer to match on SD to better account for differences in risk between the indices. I prefer SD to max drawdown not because SD is a better measure of "risk" in any psychological sense, but because every data point contributes to the SD but the max drawdown only reflects what happened at some extreme point in the series (i.e., it is more noisy measure of risk). I leverage up/down the futures data with CASHX to match the SD of the reference index and compare the differences in mean return and risk-adjusted return.

Note this is all an approximation. We would really need to compare to the CTD to be more precise. I'm comparing to something approximating the CTD and then trying to approximate out the differences with the SD correction. So, as long as we get in the ball park of the papers that did it properly, we should just trust the papers.

1a ZT futures

With ZT, we observe a loss of .11% in both the arithmetic and geometric annualized monthly means, consistent with the previous analysis and the papers. Notably the Sharpe ratio is notably smaller with the futures (.44) than the bond index (.57). So even though it is a small cost in the absolute return, we lose a lot of Sharpe because the bond index return was already small (1.08 -> .97 is a 11% lost in return).

Image

1b ZF futures

With ZF, we observe a loss of .13% and .12% in the arithmetic and geometric annualized monthly returns respectively. Again, this seems to be consistent according to my understanding. We have lost a lot less in the Sharpe with ZF than we did with ZT (.03 versus .13). However, the Sharpe on the 2-year index is so high that even with the inefficiency of ZT versus its index, ZT still has a higher Sharpe than ZF (.44 versus .43).

Image

1c ZN futures

With ZN, we observe a loss of .30% and .29% in the arithmetic and geometric annualized monthly returns respectively. So a little higher. In fact, the loss in Sharpe is bigger for ZN (.48 - .41 = .07) than for ZF (.43 - .40 = .03). It is also surprising that the Current 7-Year index had a better Sharpe than the Current 5-Year index (.48 vs .43). This might be specific to the time period examined here.

Image

As an aside, this contributes to the discussion of ZT vs ZF. I really like the short duration treasuries because they have the best Sharpe and most sensitivity to a drop in the federal funds rate in a crisis, but this analysis suggests that we might lose most of the improvement in Sharpe when accounting for financing. Skier also had the point that ZT would be more sensitive to cost fluctuations, just because any absolute difference is going to hurt ZT more than ZF because ZT has less risk/reward.

I'll continue to the second question in a later post. Hopefully in the later post it will become clear why I am not comparing the futures to the mutual funds directly to estimate the financing costs.
Last edited by zkn on Fri Oct 22, 2021 8:12 pm, edited 3 times in total.
Kbg
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Kbg »

Gents/Ladies,

Might I ask a simple question? What is the main point of this deep dive into financing cost when the reality is they are and will be variable as are the associated bond yields? We also know the yield curve will move based on Fed actions and collective market consensus as to the future. Finally, and particularly in this market, we know arbitrage will likely occur at a speed humans will not detect nor be able to capitalize on. In short, the future will happen and the above dynamics will be what they will be.

It seems to me a far more profitable line of inquiry is what maturities, what ratios and what level of risk/leverage to take on.(much of which was covered early in the thread). It just seems the focus is on gnats encountered vs. the lions that could take you out.
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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 »

zkn wrote: Fri Oct 22, 2021 10:45 am I think we need to slow down a little bit and work thru the assumptions on relating the futures positions to mutual funds/ETFs. I did some analysis to try to figure out what is going on.

In my earlier analyses, I used the monthly SD from the spglobal data tool and daily max drawdown that I calculated myself from the spglobal datasets. Then I just scaled the returns by either measure of risk without accounting for leverage costs to do a risk-matched comparison on mean returns. Here, I downloaded the data and uploaded to portfoliovisualizer. This analysis accounts for leverage costs (CASHX) in both the mean returns and the risk adjusted returns (Sharpe), and should be straightforward to replicate.

Let's break down the issue: First, the financing cost of futures. Second, the comparability of the futures to mutual funds/ETFs used for backtesting the strategy. And maybe Third approximating the backtesting positions with futures if I break that into a third section.

1 Financing cost

I evaluated the financing costs by comparing the futures data from spglobal to the closest constant bond index data from spglobal (as previously established by the other posters here). We also established with both SD and max drawdown that the constant bond indices are less risky than the futures indices, so this needs to be corrected otherwise the financing costs of the futures will be overestimated. We could correct based on duration, but because the duration of both is changing over time, I prefer to match on SD to better account for differences in risk between the indices. I prefer SD to max drawdown not because SD is a better measure of "risk" in any psychological sense, but because every data point contributes to the SD but the max drawdown only reflects what happened at some extreme point in the series (i.e., it is more noisy measure of risk). I leverage up/down the futures data with CASHX to match the SD of the reference index and compare the differences in mean return and risk-adjusted return.

Note this is all an approximation. We would really need to compare to the CTD to be more precise. I'm comparing to something approximating the CTD and then trying to approximate out the differences with the SD correction. So, as long as we get in the ball park of the papers that did it properly, we should just trust the papers.

1a ZT futures

With ZT, we observe a lost of .11% in both the arithmetic and geometric annualized monthly means, consistent with the previous analysis and the papers. Notably the Sharpe ratio is notably smaller with the futures (.44) than the bond index (.57). So even though it is a small cost in the absolute return, we lose a lot of Sharpe because the bond index return was already small (1.08 -> .97 is a 11% lost in return).

Image

2b ZF futures

With ZF, we observe a lost of .13% and .12% in the arithmetic and geometric annualized monthly returns respectively. Again, this seems to be consistent according to my understanding. We have lost a lot less in the Sharpe with ZF than we did with ZT (.03 versus .13). However, the Sharpe on the 2-year index is so high that even with the inefficiency of ZT versus its index, ZT still has a higher Sharpe than ZF (.44 versus .43).

Image

3c ZN futures

With ZN, we observe a lost of .30% and .29% in the arithmetic and geometric annualized monthly returns respectively. So a little higher. In fact, the loss in Sharpe is bigger for ZN (.48 - .41 = .07) than for ZF (.43 - .40 = .03). It is also surprising that the Current 7-Year index had a better Sharpe than the Current 5-Year index (.48 vs .43). This might be specific to the time period examined here.

Image

As an aside, this contributes to the discussion of ZT vs ZF. I really like the short duration treasuries because they have the best Sharpe and most sensitivity to a drop in the federal funds rate in a crisis, but this analysis suggests that we might lose most of the improvement in Sharpe when accounting for financing. Skier also had the point that ZT would be more sensitive to cost fluctuations, just because any absolute difference is going to hurt ZT more than ZF because ZT has less risk/reward.

I'll continue to the second question in a later post. Hopefully in the later post it will become clear why I am not comparing the futures to the mutual funds directly to estimate the financing costs.
deleted
Last edited by skierincolorado on Fri Oct 22, 2021 12:29 pm, edited 2 times in total.
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 »

2 Comparability of futures to mutual funds/ETFs

For mutual funds/ETFs to compare to the futures, I am using VFISX, VFITX, and IEF for ZT, ZF, and ZN, respectively. Once we add in mutual funds/ETFs, there are a couple of extra complications.

First, the two Vanguard funds are not only nominal treasuries. There are some other stuff in there like TIPS, Fannie Mae Strips, and Small Business Administration Participating Certs. I do not know why (Vanguard up to some funny business to try to sneak in some risk to try to beat its index/category average?). I'm going to assume it is small enough to be negligible, but it is there.
https://investor.vanguard.com/mutual-fu ... o-holdings
https://investor.vanguard.com/mutual-fu ... o-holdings

Second, and maybe more importantly, the funds/ETFs have a distribution of bonds with different maturities, but the futures track only one CTD per contract.

2a ZT futures

Here I repeated the analysis methodology from the previous post but used the real fund as the reference (VFISX) instead of the current bond index. A couple of things. First, VFISX is much riskier than VT in both SD and max drawdown. Second, VFISX does do a lot better than ZT. Even matched on SD, the arithmetic and geometric annualized monthly means are .19% better. The Sharpe ratio is .15 better for VFISX.

Image

In fact, even with a .2% expense ratio, VFISX still beats our Current 2-Year Index!

Image

I think what is going on here is that VFISX is a fund of multiple bonds, whereas our futures contracts and current bond indices only track one bond at a time. So they are not quite the same thing, and there may be diversification benefits captured by VFISX that may not be capturable with futures.

I tried to evaluate this hypothesis further. The benchmark if VFISX is not a current 2 year bond index but the Bloomberg US 1-5 Year Treasury Index. Lucky, we have data for the S&P 1-5 Year Treasury index from the spglobal data.

What we see here is that VFISX finally underperforms. The arithmetic and geometric annualized monthly returns are lower in VFISX by .06% and .05% respectively. Note that the 1-5 Year index is riskier than VFISX, so I leveraged down the index to make the comparison. The Sharpe ratio is lower by .04 (.63 vs .59).

Image

So when we compare ZT to VFISX there is a confound that ZT and VFISX are very different by construction. ZT tracks a single bond, whereas VFISX tracks a basket. We can see that the Current 2-Year index lags the more diversified 1-5 Year Index, and it is likely this difference which contributes a lot of the outperform of VFISX over ZT:

Image

The same issue applies to ZF vs VFITX.
Last edited by zkn on Fri Oct 22, 2021 9:29 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 »

Kbg wrote: Fri Oct 22, 2021 11:13 am Gents/Ladies,

Might I ask a simple question? What is the main point of this deep dive into financing cost when the reality is they are and will be variable as are the associated bond yields? We also know the yield curve will move based on Fed actions and collective market consensus as to the future. Finally, and particularly in this market, we know arbitrage will likely occur at a speed humans will not detect nor be able to capitalize on. In short, the future will happen and the above dynamics will be what they will be.

It seems to me a far more profitable line of inquiry is what maturities, what ratios and what level of risk/leverage to take on.(much of which was covered early in the thread). It just seems the focus is on gnats encountered vs. the lions that could take you out.
The financing cost is important because if it is high as some incorrect calculations showed, say 0.5% above the T-Bill rate or LIBOR, it would significantly eat into expected returns. It would change the whole optimization problem for stock vs bond ratio (more stock) and what duration of bond to leverage (longer requires less leverage).

I have generally been happy to use the OFR financing costs which were around 0.2% the last decade, but I do agree with others it has been good to validate it and I appreciate the discussion.

Also, there's alwasy financing cost which can be easily simulated using LIBOR, T-Bills, or CASHX in PV. What we're worried about is that the financing cost might be significantly above that market rate. Per the OFR papers, it is slightly above but only by about 0.2%. Enough to deter me from buying ZT, it doesn't change things too much for durations longer than ZT (2 years).
Last edited by skierincolorado on Fri Oct 22, 2021 12:20 pm, edited 2 times in total.
Kbg
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Kbg »

Absolutely agree the discussion has been fantastic. Many thanks to you and the other heavy lifters on this thread.
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: Fri Oct 22, 2021 12:19 pm Absolutely agree the discussion has been fantastic. Many thanks to you and the other heavy lifters on this thread.
Made a mistake in my last reply to you, edited now.
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: Fri Oct 22, 2021 11:39 am 2 Comparability of futures to mutual funds/ETFs

For mutual funds/ETFs to compare to the futures, I am using VFISX, VFITX, and IEF for ZT, ZF, and ZN, respectively. Once we add in mutual funds/ETFs, there are a couple of extra complications.

First, the two Vanguard funds are not only nominal treasuries. There are some other stuff in there like TIPS, Fannie Mae Strips, and Small Business Administration Participating Certs. I do not know why (Vanguard up to some funny business to try to sneak in some risk to try to beat its index/category average?). I'm going to assume it is small enough to be negligible, but it is there.
https://investor.vanguard.com/mutual-fu ... o-holdings
https://investor.vanguard.com/mutual-fu ... o-holdings

Second, and maybe more importantly, the funds/ETFs have a distribution of bonds with different maturities, but the futures track only one CTD per contract.

2a ZT futures

Here I repeated the analysis methodology from the previous post but used the real fund as the reference (VFISX) instead of the constant bond index. A couple of things. First, VFISX is much riskier than VT in both SD and max drawdown. Second, VFISX does do a lot better than ZT. Even matched on SD, the arithmetic and geometric annualized monthly means are .19% better. The Sharpe ratio is .15 better for VFISX.

Image

In fact, even with a .2% expense ratio, VFISX still beats our Current 2-Year Index!

Image

I think what is going on here is that VFISX is a fund of multiple bonds, whereas our futures contracts and current bond indices only track one bond at a time. So they are not quite the same thing, and there may be diversification benefits captured by VFISX that may not be capturable with futures.

I tried to evaluate this hypothesis further. The benchmark if VFISX is not a constant 2 year bond index but the Bloomberg US 1-5 Year Treasury Index. Lucky, we have data for the S&P 1-5 Year Treasury index from the spglobal data.

What we see here is that VFISX finally underperforms. The arithmetic and geometric annualized monthly returns are lower in VFISX by .06% and .05% respectively. Note that the 1-5 Year index is riskier than VFISX, so I leveraged down the index to make the comparison. The Sharpe ratio is lower by .04 (.63 vs .59).

Image

So when we compare ZT to VFISX there is a confound that ZT and VFISX are very different by construction. ZT tracks a single bond, whereas VFISX tracks a basket. We can see that the Current 2-Year index lags the more diversified 1-5 Year Index, and it is likely this difference which contributes a lot of the outperform of VFISX over ZT:

Image

The same issue applies to ZF vs VFITX.
I deleted my last post to you because I made a mistake so hopefully you haven't read that yet :oops:

I do think there's a very small issue in terms of the scalability we haven't tallked about yet. Probably so small it's not worth mentioning.

I agree that when scaling the scaling should be done using CASHX to lever/delever.

One problem is that we are also scaling the costs above CASHX, and those costs may not scale. In general though the scaling factors are so small that this should not matter.

So when we scale from 2 years to 3y for example, we would scale by 1.5x (or from 5% stdev to 7.5% stdev). When we scale we should be subtracting CASHX from the scaled portion as you have done. For example, if Cash is 1%, the 2y return is 3% and the 3y return is 4%, we don't just scale by 1.5 (1.5*3 = 4.5).. we scale by 1.5*3 - .5*1 = 4. OK so far so good that's what you did.

But what if the 3y return contains a finance cost above cashx ... we just multiplied that cost above cashx by 1.5. In general though as long as scaling is under 1.1x or 1.2x, it's pretty trivial.


Your analysis is on-point I believe regarding the difference between ZT and VFISX. It gets back to 'scaling a banana does not equal an apple.' If the interest rate from 0-2 years is 0%, and from 2-4 years it's 1%... ZT would yield 0%, while VFISX is going to yield more because it holds some of those 2-4 year bonds that actually have positive yield. Plus there's probably some diversification benefit even when the curve is linear. Which is something comeinvest brought up to me months ago and has stuck with me a ZF has been one of the worst performing durations in that span. Would have loved to have diversified ZF with ZN, maybe some TN as well.


Would love to see the above for ZF and ZN since that is what the majority are probably most interested in.
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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: Fri Oct 22, 2021 3:36 am I made two adjustments to the treasury futures portion of my portfolio tonight. They are mostly not meant to time the market (although I also played around a little bit), but to transition to my final strategic allocation:
- Eliminated all remaining short ZT positions that I established as a partial hedge of my long treasury futures to rising rates, when 2-year rates were on the floor i.e. close to nil. I did this today because I found out that the 2-year carry (ca. 0.8%, with yield to maturity of ca. 0.45%) just surpassed the carry of the 5-year (ca. 1.85% if my math was right) on a duration-adjusted basis, which creeped me out, and I couldn't expect the alpha from the pair trade any more that I expected based on papers advocating a dynamic positioning based on current carry per duration. I pocketed a nice profit, and the hedge did its job. I'm still playing a similar game in the European market.
- Transitioned from some of the ZB to TN+ZN. I should have done this on Monday directly from UB instead of moving from UB to ZB, but someone from Colorado ;) convinced me just this week to go with even shorter durations, so I ended up doing it in two steps. In the meantime, I made a tiny profit ("profit" as in "less loss") by holding ZB instead of TN+ZN for those 4 days. TN+ZN has almost the same DV01 as ZB, which made the transition easy on a DV01-neutral basis. I went with TN and ZN for diversification, because I have already a larger position in ZF.

I used limit orders at the bid (for buy) and ask (for sell) in the night. The volume in the night is lower, but I think the bid and ask sizes are lower too, such that passive limit orders might profit from liquidity based fills ("patient trading") just like by day. The spread is the same as by day. I'm not sure if it's statistically better to trade by day or night for minimizing transaction cost, but it seems to work well either way.

I was kind of sad to let my UB go this week, but it dawned me that it became a curse word in this message thread ;) My allocation comes now closer to an equidistribution between ZF/ZN/TN/ZB on duration-adjusted basis (it's currently still somewhere between a duration-based and notional-value-based equidistribution). I still have to define strict ratios and a suitable rebalancing strategy, so that I don't have to think too much every time in the future. Comments are welcome.

Assuming the duraiton on ZB is 11.5 years, I think this is good, but I think ZB is more like 17 years. Rules for the dynamic and static parts would be good too of course.

For ZB though did we ever figure out what the duration is? CME says it's currently 11.5... but the historical performance was more volatile that the S&P 10-20 year bond index, which has duration of 14.99 years. That would suggest it has duration of around 17 years which is quite similar to VUSTX which is the one I use in my backtesting since 1991 to show how much better VFITX is. While I am fully on-board with the diversification of not just being ZF, I would feel strongly that 17 years is too long if taking equal nominal amounts of each. If equal weighted by risk I would be on board I think. It might look something like this. I'm blue, you're orange, red is what you were before (or worse). I can't confidently say blue is better than orange - it's close enough. And this assumes ZB is 17 years duration. If it's shorter like 11.5 years, it would probably be the same as blue.

If you do do it, I like scaling on DV01 because it would mean less ZB than other measures of risk, like historical stdev or max-draw. As long as you're staying at or above that orange line, I think you're good. There are even a couple short periods where the orange line outperforms blue (2021, 1992-1994).

https://www.portfoliovisualizer.com/bac ... on4_3=-110
Last edited by skierincolorado on Fri Oct 22, 2021 1:42 pm, edited 4 times in total.
zkn
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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: Fri Oct 22, 2021 12:52 pm
zkn wrote: Fri Oct 22, 2021 11:39 am 2 Comparability of futures to mutual funds/ETFs

For mutual funds/ETFs to compare to the futures, I am using VFISX, VFITX, and IEF for ZT, ZF, and ZN, respectively. Once we add in mutual funds/ETFs, there are a couple of extra complications.

First, the two Vanguard funds are not only nominal treasuries. There are some other stuff in there like TIPS, Fannie Mae Strips, and Small Business Administration Participating Certs. I do not know why (Vanguard up to some funny business to try to sneak in some risk to try to beat its index/category average?). I'm going to assume it is small enough to be negligible, but it is there.
https://investor.vanguard.com/mutual-fu ... o-holdings
https://investor.vanguard.com/mutual-fu ... o-holdings

Second, and maybe more importantly, the funds/ETFs have a distribution of bonds with different maturities, but the futures track only one CTD per contract.

2a ZT futures

Here I repeated the analysis methodology from the previous post but used the real fund as the reference (VFISX) instead of the constant bond index. A couple of things. First, VFISX is much riskier than VT in both SD and max drawdown. Second, VFISX does do a lot better than ZT. Even matched on SD, the arithmetic and geometric annualized monthly means are .19% better. The Sharpe ratio is .15 better for VFISX.

Image

In fact, even with a .2% expense ratio, VFISX still beats our Current 2-Year Index!

Image

I think what is going on here is that VFISX is a fund of multiple bonds, whereas our futures contracts and current bond indices only track one bond at a time. So they are not quite the same thing, and there may be diversification benefits captured by VFISX that may not be capturable with futures.

I tried to evaluate this hypothesis further. The benchmark if VFISX is not a constant 2 year bond index but the Bloomberg US 1-5 Year Treasury Index. Lucky, we have data for the S&P 1-5 Year Treasury index from the spglobal data.

What we see here is that VFISX finally underperforms. The arithmetic and geometric annualized monthly returns are lower in VFISX by .06% and .05% respectively. Note that the 1-5 Year index is riskier than VFISX, so I leveraged down the index to make the comparison. The Sharpe ratio is lower by .04 (.63 vs .59).

Image

So when we compare ZT to VFISX there is a confound that ZT and VFISX are very different by construction. ZT tracks a single bond, whereas VFISX tracks a basket. We can see that the Current 2-Year index lags the more diversified 1-5 Year Index, and it is likely this difference which contributes a lot of the outperform of VFISX over ZT:

Image

The same issue applies to ZF vs VFITX.
I deleted my last post to you because I made a mistake so hopefully you haven't read that yet :oops:

I do think there's a very small issue in terms of the scalability we haven't tallked about yet. Probably so small it's not worth mentioning.

I agree that when scaling the scaling should be done using CASHX to lever/delever.

One problem is that we are also scaling the costs above CASHX, and those costs may not scale. In general though the scaling factors are so small that this should not matter.

So when we scale from 2 years to 3y for example, we would scale by 1.5x (or from 5% stdev to 7.5% stdev). When we scale we should be subtracting CASHX from the scaled portion as you have done. For example, if Cash is 1%, the 2y return is 3% and the 3y return is 4%, we don't just scale by 1.5 (1.5*3 = 4.5).. we scale by 1.5*3 - .5*1 = 4. OK so far so good that's what you did.

But what if the 3y return contains a finance cost above cashx ... we just multiplied that cost above cashx by 1.5. In general though as long as scaling is under 1.1x or 1.2x, it's pretty trivial.


Your analysis is on-point I believe regarding the difference between ZT and VFISX. It gets back to 'scaling a banana does not equal an apple.' If the interest rate from 0-2 years is 0%, and from 2-4 years it's 1%... ZT would yield 0%, while VFISX is going to yield more because it holds some of those 2-4 year bonds that actually have positive yield. Plus there's probably some diversification benefit even when the curve is linear. Which is something comeinvest brought up to me months ago and has stuck with me a ZF has been one of the worst performing durations in that span. Would have loved to have diversified ZF with ZN, maybe some TN as well.


Would love to see the above for ZF and ZN since that is what the majority are probably most interested in.
Thanks. I agree there is a nuance associated with the additional cost of financing over the return on collateral that scales with exposure and not leverage, which I did not account for. I think you're right that those costs would be leveraged in the analysis, but if we were leveraged ZT in the real world by removing collateral while keeping exposure constant those costs would be constant. I'm not bothered by it too much though because the uncertainty in the estimate is probably a lot bigger than just a 10 or 20% bias, so I don't think people should be considering those numbers that precisely anyway.

I'll follow up with ZF and ZN later.
zkn
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by zkn »

Kbg wrote: Fri Oct 22, 2021 11:13 am Gents/Ladies,

Might I ask a simple question? What is the main point of this deep dive into financing cost when the reality is they are and will be variable as are the associated bond yields? We also know the yield curve will move based on Fed actions and collective market consensus as to the future. Finally, and particularly in this market, we know arbitrage will likely occur at a speed humans will not detect nor be able to capitalize on. In short, the future will happen and the above dynamics will be what they will be.

It seems to me a far more profitable line of inquiry is what maturities, what ratios and what level of risk/leverage to take on.(much of which was covered early in the thread). It just seems the focus is on gnats encountered vs. the lions that could take you out.
To me it is as simple as that we have a lot more data for VFISX etc. so I want to know how the future contracts relate to those funds, in terms of costs of leverage (over the time varying bond yields), risk, and construction in order to inform portfolio construction using backtested data with those funds.
zkn
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by zkn »

2b ZF

As others have observed, ZF lags VFITX:

Image

But again ZF tracks a single bond but VFITX tracks a basket of bonds. The benchmark for VFITX is the Bloomberg US 5-10 Yr Treasury Index, comprising treasuries with 5-10 years to maturity. But 57% of the fund is outside of this range (<5 years)! So neither VFITX nor VFISX are exactly what they say on the box, with treasuries outside the range and some non-treasuries.

VFITX actually tracks a 50/50 composite of S&P 1-5 Year Index and 5-10 Year Index better than the 5-10 Year Index. I get about 50/50 plus or minus 10 regardless if I choose the weights by regressing VFITX on the two indices, based on the fund composition, or based on best match to the average duration. So for whatever reason, Vanguard is leaning VFITX to lower durations than the index.

VFITX lags its 50/50 composite index slightly. In addition, the 50/50 1-5 and 5-10 Year Index outperforms the 5 Year Index that better matches with ZF by a larger amount (.26%). So like ZT, a lot of the underperformance of ZF versus VFITX is really coming from differences in composition.

Image

2c ZN

Using IEF as the "real" fund for ZN, they track pretty closely:

Image

Unlike the Vanguard funds, IEF is pretty much exactly what it says it is in its portfolio holdings. It tracks but slightly underperforms the corresponding S&P 7-10 Index as expected. Interestingly, in this case the Current 7 Year index outperformed the 7-10 basket index, although this did not translate into ZN outperforming IEF.

Image
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: Fri Oct 22, 2021 3:56 pm 2b ZF

As others have observed, ZF lags VFITX:

Image

But again ZF tracks a single bond but VFITX tracks a basket of bonds. The benchmark for VFITX is the Bloomberg US 5-10 Yr Treasury Index, comprising treasuries with 5-10 years to maturity. But 57% of the fund is outside of this range (<5 years)! So neither VFITX nor VFISX are exactly what they say on the box, with treasuries outside the range and some non-treasuries.

VFITX actually tracks a 50/50 composite of S&P 1-5 Year Index and 5-10 Year Index better than the 5-10 Year Index. I get about 50/50 plus or minus 10 regardless if I choose the weights by regressing VFITX on the two indices, based on the fund composition, or based on best match to the average duration. So for whatever reason, Vanguard is leaning VFITX to lower durations than the index.

VFITX lags its 50/50 composite index slightly. In addition, the 50/50 1-5 and 5-10 Year Index outperforms the 5 Year Index that better matches with ZF by a larger amount (.26%). So like ZT, a lot of the underperformance of ZF versus VFITX is really coming from differences in composition.

Image

2c ZN

Using IEF as the "real" fund for ZN, they track pretty closely:

Image

Unlike the Vanguard funds, IEF is pretty much exactly what it says it is in its portfolio holdings. It tracks but slightly underperforms the corresponding S&P 7-10 Index as expected. Interestingly, in this case the Current 7 Year index outperformed the 7-10 basket index, although this did not translate into ZN outperforming IEF.

Image
This is excellent thank you.

There are two compelling questions I think

1) How do futures returns compare to corresponding ETFs? What we are seeing is that the ETFs do well because they diversify across a basket. This lowers SD and when we scale a future to the ETF SD, we end up with some underperformance. You've proven this by showing that single duration cash indexes also perorm worse than basket funds. This effect could likely be countered by holding 2 or 3 different futures contracts from ZT to TN.

ZF has .35% (.55% pre-fee) slippage vs VFITX (**note this is slippage, not cost. VFITX does better mostly because it is diversified, not lower cost)
ZN has 0.00% (0.20% pre-fee) slippage vs IEF (ZN likely does not have slippage because IEF is too far out on the curve and is a narrower less diversified basket)

2) How do futures returns compare to corresponding single duration indexes? This tells us how much we're actually paying in cost/financing. This is the comparison you don't actually graph but can be gathered from 1a and 1b and from 2a and 2b.

ZF has .14% cost compared to 5 year index (I say cost here because ZF is similar enough to the index that the difference is likely actual cost incurred by ZF)
ZN has .27% cost compared to the 7 year index (in the charts it is .34%, but this is scaled up significantly... .34% * 4.29/5.33 = .27)


Ultimately I think I care more about #2 than #1 because the effect of #1 could likely be countered by owning 2 or 3 futures durations, which would diversify and reduce risk, and allow one to take a smidge more risk in bonds.

I believe I could get similar performance to VFITX in a backtest using a combination of ZT, ZF and ZN. Would you mind trying this zkn or sending me the data? Guessing it would be something like 35/50/15 ZT/ZF/ZN or 40/45/20. If you have the data in PV already I think it should be easy to guess and check combinations of ZT/ZF/ZN to match the SD of VFITX. I think we want a combination with at least 30% ZT to simulate some of the lower durations that VFITX holds. Also guessing it would get us within 0.1% of VFITX peformance (0.3% pre-fees).

It might even be possible to beat VFITX using the right combination.
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: Fri Oct 22, 2021 1:01 pm
comeinvest wrote: Fri Oct 22, 2021 3:36 am I made two adjustments to the treasury futures portion of my portfolio tonight. They are mostly not meant to time the market (although I also played around a little bit), but to transition to my final strategic allocation:
- Eliminated all remaining short ZT positions that I established as a partial hedge of my long treasury futures to rising rates, when 2-year rates were on the floor i.e. close to nil. I did this today because I found out that the 2-year carry (ca. 0.8%, with yield to maturity of ca. 0.45%) just surpassed the carry of the 5-year (ca. 1.85% if my math was right) on a duration-adjusted basis, which creeped me out, and I couldn't expect the alpha from the pair trade any more that I expected based on papers advocating a dynamic positioning based on current carry per duration. I pocketed a nice profit, and the hedge did its job. I'm still playing a similar game in the European market.
- Transitioned from some of the ZB to TN+ZN. I should have done this on Monday directly from UB instead of moving from UB to ZB, but someone from Colorado ;) convinced me just this week to go with even shorter durations, so I ended up doing it in two steps. In the meantime, I made a tiny profit ("profit" as in "less loss") by holding ZB instead of TN+ZN for those 4 days. TN+ZN has almost the same DV01 as ZB, which made the transition easy on a DV01-neutral basis. I went with TN and ZN for diversification, because I have already a larger position in ZF.

I used limit orders at the bid (for buy) and ask (for sell) in the night. The volume in the night is lower, but I think the bid and ask sizes are lower too, such that passive limit orders might profit from liquidity based fills ("patient trading") just like by day. The spread is the same as by day. I'm not sure if it's statistically better to trade by day or night for minimizing transaction cost, but it seems to work well either way.

I was kind of sad to let my UB go this week, but it dawned me that it became a curse word in this message thread ;) My allocation comes now closer to an equidistribution between ZF/ZN/TN/ZB on duration-adjusted basis (it's currently still somewhere between a duration-based and notional-value-based equidistribution). I still have to define strict ratios and a suitable rebalancing strategy, so that I don't have to think too much every time in the future. Comments are welcome.

Assuming the duraiton on ZB is 11.5 years, I think this is good, but I think ZB is more like 17 years. Rules for the dynamic and static parts would be good too of course.

For ZB though did we ever figure out what the duration is? CME says it's currently 11.5... but the historical performance was more volatile that the S&P 10-20 year bond index, which has duration of 14.99 years. That would suggest it has duration of around 17 years which is quite similar to VUSTX which is the one I use in my backtesting since 1991 to show how much better VFITX is. While I am fully on-board with the diversification of not just being ZF, I would feel strongly that 17 years is too long if taking equal nominal amounts of each. If equal weighted by risk I would be on board I think. It might look something like this. I'm blue, you're orange, red is what you were before (or worse). I can't confidently say blue is better than orange - it's close enough. And this assumes ZB is 17 years duration. If it's shorter like 11.5 years, it would probably be the same as blue.

If you do do it, I like scaling on DV01 because it would mean less ZB than other measures of risk, like historical stdev or max-draw. As long as you're staying at or above that orange line, I think you're good. There are even a couple short periods where the orange line outperforms blue (2021, 1992-1994).

https://www.portfoliovisualizer.com/bac ... on4_3=-110
Regarding the ZB mystery: I pointed that already out in several posts before. We have not resolved it, and I think we should resolve it as at least I personally like to understand what I'm doing, especially with a major portion of my portfolio and in the long run. What happens to ZB might apply to the other futures too at some point. I think CME updates the analytics page daily or more often. Are you saying what they display is completely wrong including the CTD data? Where do you see 11.5, or did you calculate it from the DV01? 11.5 sounds right though. CTD maturity is definitely ca. 15.5 years. How can a 15.5 maturity bond have 17 years duration? It can't, right? I'm pretty sure is has been at 15.5 for a while - I think I monitored the analytics site for at least half a year periodically. Maybe we can look at the stddevs over the current or the last few contract quarters? Our assumption has been that the durations can be inferred from comparing stddevs, i.e. we have been assuming that risk is duration risk and not any kind of other artifact, and (if we take a step back) we have basically been trying to reverse-engineer core data of the bonds from very noisy observable signals of not even the underlying, but a derivative on it. I wouldn't disagree or argue against this approach, but I'm only 100% convinced of this conjecture once I see the actual durations.

Regarding your chart: Looks good, but I also looked at the chart of the difference between blue and orange. (I think this would now rebalance between the 2 solutions. I'm not sure if I can generate a cumulative difference chart in PV between two rebalancing portfolios, without also rebalancing between the portfolios.) If you look at the series of yearly returns of the yellow difference chart, I'm not sure if I can see a pattern that would convince me to extrapolate the past into the future. I would however agree that the yearly time series is probably naturally autocorrelated and it makes sense to look at the cumulative results.
https://www.portfoliovisualizer.com/bac ... ion4_3=-60

Regarding diversification: In finance, I am naturally hesitant to extrapolate anything from the past into the future, as I have been fooled too many times. In the case of treasury futures, I am somewhat inclined to somewhat diversify my bets across maturities for the following reasons:
1. Uncertainties regarding the performance of the underlying treasuries. If you look at the chart viewtopic.php?p=6285890#p6285890 for example in 2 out of 6 decades, the 7y performed better than the 5y. Additionally, the future may be different from the past.
2. Uncertainties in the implementation. Some uncertainties remain regarding the implied financing cost and anomalies.
3. What do "others" do? I assume WisdomTree hired at least one or two quantitative finance Ph.D.'s before they started NTSX, who probably spent significantly more time on studying treasury futures than I did, and who might be more familiar with the practicalities of the implementation. Would they start a fund with an equidistributed allocation if it were obvious to everybody in the quant community that the short maturities will outperform? Maybe they went with their solution as it is simple to explain for marketing purposes, but then again a single ZF position would be even simpler to explain and to show in backtesting and future performance charts (if it actually performs better) than an equidistributed ZF+ZN+TN+ZB.
4. Anomalies that have existed for decades may disappear at any time for any or no reason. For example, the availability and awareness of leverage via futures may be more widespread than in the past, regulatory constraints prohibiting leverage and pushing certain institutions to use LTT may have changed, or an anomaly can just disappear or even reverse for no obvious reason like many other anomalies in finance have.
Last edited by comeinvest on Fri Oct 22, 2021 6:26 pm, edited 3 times in total.
zkn
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by zkn »

skierincolorado wrote: Fri Oct 22, 2021 4:52 pm
zkn wrote: Fri Oct 22, 2021 3:56 pm ...
This is excellent thank you.

There are two compelling questions I think

1) How do futures returns compare to corresponding ETFs? What we are seeing is that the ETFs do well because they diversify across a basket. This lowers SD and when we scale a future to the ETF SD, we end up with some underperformance. You've proven this by showing that single duration cash indexes also perorm worse than basket funds. This effect could likely be countered by holding 2 or 3 different futures contracts from ZT to TN.

ZF has .35% (.55% pre-fee) slippage vs VFITX (**note this is slippage, not cost. VFITX does better mostly because it is diversified, not lower cost)
ZN has 0.00% (0.20% pre-fee) slippage vs IEF (ZN likely does not have slippage because IEF is too far out on the curve and is a narrower less diversified basket)

2) How do futures returns compare to corresponding single duration indexes? This tells us how much we're actually paying in cost/financing. This is the comparison you don't actually graph but can be gathered from 1a and 1b and from 2a and 2b.

ZF has .14% cost compared to 5 year index (I say cost here because ZF is similar enough to the index that the difference is likely actual cost incurred by ZF)
ZN has .27% cost compared to the 7 year index (in the charts it is .34%, but this is scaled up significantly... .34% * 4.29/5.33 = .27)


Ultimately I think I care more about #2 than #1 because the effect of #1 could likely be countered by owning 2 or 3 futures durations, which would diversify and reduce risk, and allow one to take a smidge more risk in bonds.

I believe I could get similar performance to VFITX in a backtest using a combination of ZT, ZF and ZN. Would you mind trying this zkn or sending me the data? Guessing it would be something like 35/50/15 ZT/ZF/ZN or 40/45/20. If you have the data in PV already I think it should be easy to guess and check combinations of ZT/ZF/ZN to match the SD of VFITX. I think we want a combination with at least 30% ZT to simulate some of the lower durations that VFITX holds. Also guessing it would get us within 0.1% of VFITX peformance (0.3% pre-fees).

It might even be possible to beat VFITX using the right combination.
I was thinking the same on both points and had already played around a bit on trying to get diversification from using multiple futures, and to explain VFITX with multiple futures. Using the three futures (ZT, ZF, ZN) in the regression, VFITX is best explained as 49% ZF, 48% ZN, and 3% CASH. It still does not quite match VFITX though:

Image

Playing around, it is really the underlying 1-5 year treasury index that is captured by VFISX and VFITX that is unique and hard to recreate from the future contracts. Maybe I am overfitting because there is only 10 years of data and maybe it is somehow specific to this time period and won't generalize, but that's where the outperformance is coming from and the 1-5 yr index cannot be explained (statistically) from the current bond indices or the futures. We only have the 2yr ZT in that range.

In the end though, it does not look like much is lost. Using mean-variance optimization to select a portfolio with a US total stock market + bonds with maximum Sharpe, the optimizer does want to use some of the funds over the futures. But if it is forced to use the futures, it makes basically no difference.

Image
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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: Fri Oct 22, 2021 5:41 pm
skierincolorado wrote: Fri Oct 22, 2021 1:01 pm
comeinvest wrote: Fri Oct 22, 2021 3:36 am I made two adjustments to the treasury futures portion of my portfolio tonight. They are mostly not meant to time the market (although I also played around a little bit), but to transition to my final strategic allocation:
- Eliminated all remaining short ZT positions that I established as a partial hedge of my long treasury futures to rising rates, when 2-year rates were on the floor i.e. close to nil. I did this today because I found out that the 2-year carry (ca. 0.8%, with yield to maturity of ca. 0.45%) just surpassed the carry of the 5-year (ca. 1.85% if my math was right) on a duration-adjusted basis, which creeped me out, and I couldn't expect the alpha from the pair trade any more that I expected based on papers advocating a dynamic positioning based on current carry per duration. I pocketed a nice profit, and the hedge did its job. I'm still playing a similar game in the European market.
- Transitioned from some of the ZB to TN+ZN. I should have done this on Monday directly from UB instead of moving from UB to ZB, but someone from Colorado ;) convinced me just this week to go with even shorter durations, so I ended up doing it in two steps. In the meantime, I made a tiny profit ("profit" as in "less loss") by holding ZB instead of TN+ZN for those 4 days. TN+ZN has almost the same DV01 as ZB, which made the transition easy on a DV01-neutral basis. I went with TN and ZN for diversification, because I have already a larger position in ZF.

I used limit orders at the bid (for buy) and ask (for sell) in the night. The volume in the night is lower, but I think the bid and ask sizes are lower too, such that passive limit orders might profit from liquidity based fills ("patient trading") just like by day. The spread is the same as by day. I'm not sure if it's statistically better to trade by day or night for minimizing transaction cost, but it seems to work well either way.

I was kind of sad to let my UB go this week, but it dawned me that it became a curse word in this message thread ;) My allocation comes now closer to an equidistribution between ZF/ZN/TN/ZB on duration-adjusted basis (it's currently still somewhere between a duration-based and notional-value-based equidistribution). I still have to define strict ratios and a suitable rebalancing strategy, so that I don't have to think too much every time in the future. Comments are welcome.

Assuming the duraiton on ZB is 11.5 years, I think this is good, but I think ZB is more like 17 years. Rules for the dynamic and static parts would be good too of course.

For ZB though did we ever figure out what the duration is? CME says it's currently 11.5... but the historical performance was more volatile that the S&P 10-20 year bond index, which has duration of 14.99 years. That would suggest it has duration of around 17 years which is quite similar to VUSTX which is the one I use in my backtesting since 1991 to show how much better VFITX is. While I am fully on-board with the diversification of not just being ZF, I would feel strongly that 17 years is too long if taking equal nominal amounts of each. If equal weighted by risk I would be on board I think. It might look something like this. I'm blue, you're orange, red is what you were before (or worse). I can't confidently say blue is better than orange - it's close enough. And this assumes ZB is 17 years duration. If it's shorter like 11.5 years, it would probably be the same as blue.

If you do do it, I like scaling on DV01 because it would mean less ZB than other measures of risk, like historical stdev or max-draw. As long as you're staying at or above that orange line, I think you're good. There are even a couple short periods where the orange line outperforms blue (2021, 1992-1994).

https://www.portfoliovisualizer.com/bac ... on4_3=-110
Regarding the ZB mystery: I pointed that already out in several posts before. We have not resolved it, and I think we should resolve it as at least I personally like to understand what I'm doing, especially with a major portion of my portfolio and in the long run. What happens to ZB might apply to the other futures too at some point. I think CME updates the analytics page daily or more often. Are you saying what they display is completely wrong including the CTD data? Where do you see 11.5, or did you calculate it from the DV01? 11.5 sounds right though. CTD maturity is definitely ca. 15.5 years. How can a 15.5 maturity bond have 17 years duration? It can't, right? I'm pretty sure is has been at 15.5 for a while - I think I monitored the analytics site for at least half a year periodically. Maybe we can look at the stddevs over the current or the last few contract quarters? Our assumption has been that the durations can be inferred from comparing stddevs, i.e. we have been assuming that risk is duration risk and not any kind of other artifact, and (if we take a step back) we have basically been trying to reverse-engineer core data of the bonds from very noisy observable signals of not even the underlying, but a derivative on it. I wouldn't disagree or argue against this approach, but I'm only 100% convinced of this conjecture once I see the actual durations.

Regarding your chart: Looks good, but I also looked at the chart of the difference between blue and orange. (I think this would now rebalance between the 2 solutions. I'm not sure if I can generate a cumulative difference chart in PV between two rebalancing portfolios, without also rebalancing between the portfolios.) If you look at the series of yearly returns of the yellow difference chart, I'm not sure if I can see a pattern that would convince me to extrapolate the past into the future. I would however agree that the yearly time series is probably naturally autocorrelated and it makes sense to look at the cumulative results.
https://www.portfoliovisualizer.com/bac ... ion4_3=-60

Regarding diversification: In finance, I am naturally hesitant to extrapolate anything from the past into the future, as I have been fooled too many times. In the case of treasury futures, I am somewhat inclined to somewhat diversify my bets across maturities for the following reasons:
1. Uncertainties regarding the performance of the underlying treasuries. If you look at the chart viewtopic.php?p=6285890#p6285890 for example in 2 out of 6 decades, the 7y performed better than the 5y. Additionally, the future may be different from the past.
2. Uncertainties in the implementation. Some uncertainties remain regarding the implied financing cost and anomalies.
3. What do "others" do? I assume WisdomTree hired at least one or two quantitative finance Ph.D.'s before they started NTSX, who probably spent significantly more time on studying treasury futures than I did, and who might be more familiar with the practicalities of the implementation. Would they start a fund with an equidistributed allocation if it were obvious to everybody in the quant community that the short maturities will outperform? Maybe they went with their solution as it is simple to explain for marketing purposes, but then again a single ZF position would be even simpler explain and to show in backtesting and future performance charts than an equidistributed ZF+ZN+TN+ZB.
4. Anomalies that have existed for decades may disappear at any time for any or no reason. For example, the availability and awareness of leverage via futures may be more widespread than in the past, regulatory constraints prohibiting leverage and pushing certain institutions to use LTT may have changed, or an anomaly can just disappear for no obvious reason like many other anomalies in finance have.
I can't figure out why ZB says duration of only 11.5 while historically the SD is that of 17 year duration. If someone figures it out please let us know!

1) The chart is actually of carry not performance. Of course the two are not the same, and neglect roll yield and actual interest rate changes. Also, If I am reading the chart the two "decades" where 7 was better than 5 were the not actually decades.. it's the 70s and 2020s which, but these are both cutoff since the data starts in 1977 and ends in 2021.
2) Yes some but not much, .17% and .27% for ZF and ZN consistent with OFR
3) I haven't read a ton of what others do, but the few papers I've read all stay shorter than 10 years (hedge funds and pensions)
4) Strongly agree. I probably should get more diversified primarily for this reason and the diversification benefit shown by zkn.
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: Fri Oct 22, 2021 4:52 pm This is excellent thank you.

There are two compelling questions I think

1) How do futures returns compare to corresponding ETFs? What we are seeing is that the ETFs do well because they diversify across a basket. This lowers SD and when we scale a future to the ETF SD, we end up with some underperformance. You've proven this by showing that single duration cash indexes also perorm worse than basket funds. This effect could likely be countered by holding 2 or 3 different futures contracts from ZT to TN.

ZF has .35% (.55% pre-fee) slippage vs VFITX (**note this is slippage, not cost. VFITX does better mostly because it is diversified, not lower cost)
ZN has 0.00% (0.20% pre-fee) slippage vs IEF (ZN likely does not have slippage because IEF is too far out on the curve and is a narrower less diversified basket)

2) How do futures returns compare to corresponding single duration indexes? This tells us how much we're actually paying in cost/financing. This is the comparison you don't actually graph but can be gathered from 1a and 1b and from 2a and 2b.

ZF has .14% cost compared to 5 year index (I say cost here because ZF is similar enough to the index that the difference is likely actual cost incurred by ZF)
ZN has .27% cost compared to the 7 year index (in the charts it is .34%, but this is scaled up significantly... .34% * 4.29/5.33 = .27)


Ultimately I think I care more about #2 than #1 because the effect of #1 could likely be countered by owning 2 or 3 futures durations, which would diversify and reduce risk, and allow one to take a smidge more risk in bonds.

I believe I could get similar performance to VFITX in a backtest using a combination of ZT, ZF and ZN. Would you mind trying this zkn or sending me the data? Guessing it would be something like 35/50/15 ZT/ZF/ZN or 40/45/20. If you have the data in PV already I think it should be easy to guess and check combinations of ZT/ZF/ZN to match the SD of VFITX. I think we want a combination with at least 30% ZT to simulate some of the lower durations that VFITX holds. Also guessing it would get us within 0.1% of VFITX peformance (0.3% pre-fees).

It might even be possible to beat VFITX using the right combination.
I have to catch up with this thread, skipped a few posts. But I am very much looking forward to an all-in comparison as you suggest. I'll ask more difficult questions later once we have the results :) I am not sure how much spreading out the maturities around a single point matters. Intuitively I would have thought not that much, especially in a max draw calculation that is governed by interest rate changes, because treasuries of similar, adjacent maturities usually move very much in tandem, and actually have to move in tandem for fundamental reasons as the theoretical yield curve can have no strange bumps. But if it indeed turns out that a portfolio of treasuries and/or futures in a range gives better risk-adjusted returns than a single maturity, that might be an additional argument for having a diversified basket of futures - we would at least have more than one CTD. For all-in results, we would also have to verify if it still matters in an equities+treasuries portfolio.
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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 »

zkn wrote: Fri Oct 22, 2021 6:23 pm
skierincolorado wrote: Fri Oct 22, 2021 4:52 pm
zkn wrote: Fri Oct 22, 2021 3:56 pm ...
This is excellent thank you.

There are two compelling questions I think

1) How do futures returns compare to corresponding ETFs? What we are seeing is that the ETFs do well because they diversify across a basket. This lowers SD and when we scale a future to the ETF SD, we end up with some underperformance. You've proven this by showing that single duration cash indexes also perorm worse than basket funds. This effect could likely be countered by holding 2 or 3 different futures contracts from ZT to TN.

ZF has .35% (.55% pre-fee) slippage vs VFITX (**note this is slippage, not cost. VFITX does better mostly because it is diversified, not lower cost)
ZN has 0.00% (0.20% pre-fee) slippage vs IEF (ZN likely does not have slippage because IEF is too far out on the curve and is a narrower less diversified basket)

2) How do futures returns compare to corresponding single duration indexes? This tells us how much we're actually paying in cost/financing. This is the comparison you don't actually graph but can be gathered from 1a and 1b and from 2a and 2b.

ZF has .14% cost compared to 5 year index (I say cost here because ZF is similar enough to the index that the difference is likely actual cost incurred by ZF)
ZN has .27% cost compared to the 7 year index (in the charts it is .34%, but this is scaled up significantly... .34% * 4.29/5.33 = .27)


Ultimately I think I care more about #2 than #1 because the effect of #1 could likely be countered by owning 2 or 3 futures durations, which would diversify and reduce risk, and allow one to take a smidge more risk in bonds.

I believe I could get similar performance to VFITX in a backtest using a combination of ZT, ZF and ZN. Would you mind trying this zkn or sending me the data? Guessing it would be something like 35/50/15 ZT/ZF/ZN or 40/45/20. If you have the data in PV already I think it should be easy to guess and check combinations of ZT/ZF/ZN to match the SD of VFITX. I think we want a combination with at least 30% ZT to simulate some of the lower durations that VFITX holds. Also guessing it would get us within 0.1% of VFITX peformance (0.3% pre-fees).

It might even be possible to beat VFITX using the right combination.
I was thinking the same on both points and had already played around a bit on trying to get diversification from using multiple futures, and to explain VFITX with multiple futures. Using the three futures (ZT, ZF, ZN) in the regression, VFITX is best explained as 49% ZF, 48% ZN, and 3% CASH. It still does not quite match VFITX though:

Image

Playing around, it is really the underlying 1-5 year treasury index that is captured by VFISX and VFITX that is unique and hard to recreate from the future contracts. Maybe I am overfitting because there is only 10 years of data and maybe it is somehow specific to this time period and won't generalize, but that's where the outperformance is coming from and the 1-5 yr index cannot be explained (statistically) from the current bond indices or the futures. We only have the 2yr ZT in that range.

In the end though, it does not look like much is lost. Using mean-variance optimization to select a portfolio with a US total stock market + bonds with maximum Sharpe, the optimizer does want to use some of the funds over the futures. But if it is forced to use the futures, it makes basically no difference.

Image
Perfect thank you! What if you force something like 40/40/20 ZT/ZF/ZN (but adjust to match SD, just at least 30-40% ZT). I'm not sure a regression would work for this..


Good to know that when in a whole portfolio there is almost no cost to using futures whatsoever. Mind excluding ZT from the analysis or limiting it to a certain %? I think many here are hesitent about using ZT in as high a % as the MVO shows.
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: Fri Oct 22, 2021 6:33 pm 1) The chart is actually of carry not performance. Of course the two are not the same, and neglect roll yield and actual interest rate changes. Also, If I am reading the chart the two "decades" where 7 was better than 5 were the not actually decades.. it's the 70s and 2020s which, but these are both cutoff since the data starts in 1977 and ends in 2021.
(bold mine)

https://www.simplify.us/blog/efficient- ... -investing :
Carry is simply the expected return of the bond when the yield curve is unchanged and is equal to the sum of “roll yield” and “coupon yield”.
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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: Fri Oct 22, 2021 7:07 pm
skierincolorado wrote: Fri Oct 22, 2021 6:33 pm 1) The chart is actually of carry not performance. Of course the two are not the same, and neglect roll yield and actual interest rate changes. Also, If I am reading the chart the two "decades" where 7 was better than 5 were the not actually decades.. it's the 70s and 2020s which, but these are both cutoff since the data starts in 1977 and ends in 2021.
https://www.simplify.us/blog/efficient- ... -investing :
Carry is simply the expected return of the bond when the yield curve is unchanged and is equal to the sum of “roll yield” and “coupon yield”.
Some sites define carry as separate from roll yield. It's good that it's both, but I'd expect the actual returns by decade to show a lot more variance by duration as interest rates the shape of the curve change. Generaly tendency for longer to return less should still be apparent though.
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: Fri Oct 22, 2021 7:07 pm
skierincolorado wrote: Fri Oct 22, 2021 6:33 pm 1) The chart is actually of carry not performance. Of course the two are not the same, and neglect roll yield and actual interest rate changes. Also, If I am reading the chart the two "decades" where 7 was better than 5 were the not actually decades.. it's the 70s and 2020s which, but these are both cutoff since the data starts in 1977 and ends in 2021.
https://www.simplify.us/blog/efficient- ... -investing :
Carry is simply the expected return of the bond when the yield curve is unchanged and is equal to the sum of “roll yield” and “coupon yield”.
Some sites define carry as separate from roll yield. It's good that it's both, but I'd expect the actual returns by decade to show a lot more variance by duration as interest rates the shape of the curve change. Generaly tendency for longer to return less should still be apparent though.

I've never done an ITT vs LTT comparison by decade, but I have done it since 1955 and broken that into two chunks. Also since 1978 and since 1991. I'm sure that as you transition from LTT to ITT the consistency of the ITT outperformance fades, I'm just not sure ZB is getting into that transition zone yet, even with the diversification benefit as part of a larger portfolio. Wish we could find some chart of historical duration, but if I had to bet, the duration was longer than 11.5 at least historically given the historical variance. Even so, the argument that future may not be like any of these backtests is still a valid reason to hold some ZB.

The ITT outperformance does fade over time. My memory is the term premium past 5-10 years increased in the 80s and 90s. But of course the ITT are still a solid win even since 2000.
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: Fri Oct 22, 2021 7:10 pm
comeinvest wrote: Fri Oct 22, 2021 7:07 pm
skierincolorado wrote: Fri Oct 22, 2021 6:33 pm 1) The chart is actually of carry not performance. Of course the two are not the same, and neglect roll yield and actual interest rate changes. Also, If I am reading the chart the two "decades" where 7 was better than 5 were the not actually decades.. it's the 70s and 2020s which, but these are both cutoff since the data starts in 1977 and ends in 2021.
https://www.simplify.us/blog/efficient- ... -investing :
Carry is simply the expected return of the bond when the yield curve is unchanged and is equal to the sum of “roll yield” and “coupon yield”.
Some sites define carry as separate from roll yield. It's good that it's both, but I'd expect the actual returns by decade to show a lot more variance by duration as interest rates the shape of the curve change. Generaly tendency for longer to return less should still be apparent though.
Frankly it didn't occur to me before that the author didn't go the extra step of comparing total returns. But I think the intent was to exactly filter out the effects of interest rate changes, as they are either mean-reverting, or stay the same, or are temporarily trending, and if trending, they cannot trend forever in the same direction. Also, they are probably the most difficult part in the equation to predict. So I think the author wanted to present the "average carry" as a more predictable way of comparing expected returns, agnostic of future interest rate changes.
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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: Fri Oct 22, 2021 7:36 pm
skierincolorado wrote: Fri Oct 22, 2021 7:10 pm
comeinvest wrote: Fri Oct 22, 2021 7:07 pm
skierincolorado wrote: Fri Oct 22, 2021 6:33 pm 1) The chart is actually of carry not performance. Of course the two are not the same, and neglect roll yield and actual interest rate changes. Also, If I am reading the chart the two "decades" where 7 was better than 5 were the not actually decades.. it's the 70s and 2020s which, but these are both cutoff since the data starts in 1977 and ends in 2021.
https://www.simplify.us/blog/efficient- ... -investing :
Carry is simply the expected return of the bond when the yield curve is unchanged and is equal to the sum of “roll yield” and “coupon yield”.
Some sites define carry as separate from roll yield. It's good that it's both, but I'd expect the actual returns by decade to show a lot more variance by duration as interest rates the shape of the curve change. Generaly tendency for longer to return less should still be apparent though.
Frankly it didn't occur to me before that the author didn't go the extra step of comparing total returns. But I think the intent was to exactly filter out the effects of interest rate changes, as they are either mean-reverting, or stay the same, or temporarily trending, and if trending, they cannot trend forever in the same direction. Also, they are probably the most difficult part in the equation to predict. So I think the author wanted to present the "average carry" as a more predictable way of comparing expected returns, agnostic of future interest rate changes.
Yes I think the graph makes the authors point nicely. I think some of the annual variance you observed in the relative performance of ITT and LTT a few posts back would be similarly mean-reverting for the same reason.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Fri Oct 22, 2021 7:13 pm
comeinvest wrote: Fri Oct 22, 2021 7:07 pm
skierincolorado wrote: Fri Oct 22, 2021 6:33 pm 1) The chart is actually of carry not performance. Of course the two are not the same, and neglect roll yield and actual interest rate changes. Also, If I am reading the chart the two "decades" where 7 was better than 5 were the not actually decades.. it's the 70s and 2020s which, but these are both cutoff since the data starts in 1977 and ends in 2021.
https://www.simplify.us/blog/efficient- ... -investing :
Carry is simply the expected return of the bond when the yield curve is unchanged and is equal to the sum of “roll yield” and “coupon yield”.
Some sites define carry as separate from roll yield. It's good that it's both, but I'd expect the actual returns by decade to show a lot more variance by duration as interest rates the shape of the curve change. Generaly tendency for longer to return less should still be apparent though.

I've never done an ITT vs LTT comparison by decade, but I have done it since 1955 and broken that into two chunks. Also since 1978 and since 1991. I'm sure that as you transition from LTT to ITT the consistency of the ITT outperformance fades, I'm just not sure ZB is getting into that transition zone yet, even with the diversification benefit as part of a larger portfolio. Wish we could find some chart of historical duration, but if I had to bet, the duration was longer than 11.5 at least historically given the historical variance. Even so, the argument that future may not be like any of these backtests is still a valid reason to hold some ZB.

The ITT outperformance does fade over time. My memory is the term premium past 5-10 years increased in the 80s and 90s. But of course the ITT are still a solid win even since 2000.
I think the CTD maturities of all the treasury futures were close to the lower end of the allowable range since the time the interest rates dropped below the reference rate, and I forgot the reasoning why that so is, I think it has to do with the delivery process and conversions that you are currently more familiar with. I don't know if we can ever expect that to change again, but if so, what is you plan - adjust the allocation so you have constant DV01 over time in relation to your portfolio size? We should, if we want to simulate a treasuries portfolio leveraged with other methods like margin, or the ETFs. Same question for when the durations change even when maturities stay similar to where they are now - are you going to monitor and adjust, or just keep it constant dollars (notional value) per maturity? Not sure if you saw my questions from last night about the interpretation of the data on the treasury analytics page and the yield curves.

Regarding charts, comparison charts that show the cumulative difference over time are always nice. Ideally it would be a monotonously increasing curve. Not sure if you can generate one easily for the long periods that you backtested. Then back out the interest rate changes to show just the carry :) Lol
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by LTCM »

zkn wrote: Fri Oct 22, 2021 11:39 am I think what is going on here is that VFISX is a fund of multiple bonds, whereas our futures contracts and current bond indices only track one bond at a time. So they are not quite the same thing, and there may be diversification benefits captured by VFISX that may not be capturable with futures.
I may be off here. But that doesn't seem quite right. The futures contract tracks a basket of bonds and then allows the short to choose which one to deliver. Obviously they're going to pick the one most advantageous to their position which would explain slippage faster than any lack of diversification benefits.

Or have you considered that already?
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Hfearless »

skierincolorado wrote: Wed Oct 20, 2021 8:45 am It’s a market timing strategy which we should be inherently skeptical of given EMH.
A consequence of EMH is that market timing can’t gain you anything.

But a consequence of EMH is also that market timing can’t lose you anything.

So assuming EMH, a strategy having an element of market timing does not automatically disqualify it.
skierincolorado wrote:Most of our peers (younger retail investors) are in stocks, not bonds. Being so heavily in bonds exposes you to the unique risk of returning less than the average retail investor.
There’s a criterion called average investor equity allocation, a form of market timing. Its predictions are not bad. Acting on it suggests exactly the opposite of what you say—having an allocation unlike that of your peers is profitable.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

LTCM wrote: Fri Oct 22, 2021 8:19 pm
zkn wrote: Fri Oct 22, 2021 11:39 am I think what is going on here is that VFISX is a fund of multiple bonds, whereas our futures contracts and current bond indices only track one bond at a time. So they are not quite the same thing, and there may be diversification benefits captured by VFISX that may not be capturable with futures.
I may be off here. But that doesn't seem quite right. The futures contract tracks a basket of bonds and then allows the short to choose which one to deliver. Obviously they're going to pick the one most advantageous to their position which would explain slippage faster than any lack of diversification benefits.

Or have you considered that already?
@LTCM: All that is already factored in. The likely CTD is known by all market participants at any given time, along with the probabilities that it changes to any of the other available bonds between now and the time of expiration. The only possible reasoning that I can see is that if you are saying, if the durations of the alternative eligible bonds that might become CTD between a given time and the time of expiration are measurably different from the duration of the current likely CTD, then I guess we would have to calculate an average of those durations weighted by their respective probabilities of becoming CTD., to arrive at an "effective duration" for a futures contract. I'm not sure if all that would make a measurable difference. I think the reference CTD doesn't change that often.
Last edited by comeinvest on Fri Oct 22, 2021 8:38 pm, edited 5 times in total.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Fri Oct 22, 2021 8:11 pm
skierincolorado wrote: Fri Oct 22, 2021 7:13 pm
comeinvest wrote: Fri Oct 22, 2021 7:07 pm
skierincolorado wrote: Fri Oct 22, 2021 6:33 pm 1) The chart is actually of carry not performance. Of course the two are not the same, and neglect roll yield and actual interest rate changes. Also, If I am reading the chart the two "decades" where 7 was better than 5 were the not actually decades.. it's the 70s and 2020s which, but these are both cutoff since the data starts in 1977 and ends in 2021.
https://www.simplify.us/blog/efficient- ... -investing :
Carry is simply the expected return of the bond when the yield curve is unchanged and is equal to the sum of “roll yield” and “coupon yield”.
Some sites define carry as separate from roll yield. It's good that it's both, but I'd expect the actual returns by decade to show a lot more variance by duration as interest rates the shape of the curve change. Generaly tendency for longer to return less should still be apparent though.

I've never done an ITT vs LTT comparison by decade, but I have done it since 1955 and broken that into two chunks. Also since 1978 and since 1991. I'm sure that as you transition from LTT to ITT the consistency of the ITT outperformance fades, I'm just not sure ZB is getting into that transition zone yet, even with the diversification benefit as part of a larger portfolio. Wish we could find some chart of historical duration, but if I had to bet, the duration was longer than 11.5 at least historically given the historical variance. Even so, the argument that future may not be like any of these backtests is still a valid reason to hold some ZB.

The ITT outperformance does fade over time. My memory is the term premium past 5-10 years increased in the 80s and 90s. But of course the ITT are still a solid win even since 2000.
I think the CTD maturities of all the treasury futures were close to the lower end of the allowable range since the time the interest rates dropped below the reference rate, and I forgot the reasoning why that so is, I think it has to do with the delivery process and conversions that you are currently more familiar with. I don't know if we can ever expect that to change again, but if so, what is you plan - adjust the allocation so you have constant DV01 over time in relation to your portfolio size? We should, if we want to simulate a treasuries portfolio leveraged with other methods like margin, or the ETFs. Same question for when the durations change even when maturities stay similar to where they are now - are you going to monitor and adjust, or just keep it constant dollars (notional value) per maturity? Not sure if you saw my questions from last night about the interpretation of the data on the treasury analytics page and the yield curves.

Regarding charts, comparison charts that show the cumulative difference over time are always nice. Ideally it would be a monotonously increasing curve. Not sure if you can generate one easily for the long periods that you backtested. Then back out the interest rate changes to show just the carry :) Lol
I don't think I'd use DV01. As the duration went up I'd adjust based on the new durations and the historical max draw of that duration. Of course I'll have to have a better understanding of the actual duration then. Not too concerning right now unless rates went up a ton.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

Hfearless wrote: Fri Oct 22, 2021 8:23 pm
skierincolorado wrote: Wed Oct 20, 2021 8:45 am It’s a market timing strategy which we should be inherently skeptical of given EMH.
A consequence of EMH is that market timing can’t gain you anything.

But a consequence of EMH is also that market timing can’t lose you anything.

So assuming EMH, a strategy having an element of market timing does not automatically disqualify it.
skierincolorado wrote:Most of our peers (younger retail investors) are in stocks, not bonds. Being so heavily in bonds exposes you to the unique risk of returning less than the average retail investor.
There’s a criterion called average investor equity allocation, a form of market timing. Its predictions are not bad. Acting on it suggests exactly the opposite of what you say—having an allocation unlike that of your peers is profitable.
It is not a consequence of EMH that market timing can't lose you anything.

It is a consequence of EMH that market timing can't cost you expected value. But just because the E[X] is the same does not mean that the variance of X is the same.

As an extreme example, the expected value of buying meme stocks is the same as buying index funds. But the variance of outcomes is infinitely greater. You've picked a stock with high beta, and you've lost the diversification benefit of reduced variance.

Likewise, switching between STT and ITT (the actual example being discussed) has the same expected value as just staying in ITT the whole time. But you've increased the variance because you may have switched at a bad time, and lost out on any mean reversion. Own both and achieve the diversification benefit.

Also, and this comes to your second point, performing *different* than the market is a risk. If most retail investors are rolling in it because they bought stocks, and you are missing out because you bought much more bonds than most, you may be priced out of buying a home for example. It's also a psychological burden and increases the odds you will abandon ship - further increasing your risk.

What I'm saying is not actually the opposite of the investor equity allocation. Both can be true simultaneously.

This all comes back to the concept of diversifyable risk. Owning ITT first and then STT is a diversifiable risk. The risk that one does poorly can be diversified away by owning both. https://www.investopedia.com/terms/u/un ... icrisk.asp. This is actually the concept that underlies all of index investing and the entire boglehead philosophy. By diversifying we can maintain the same expected value with lower variance. Market timing is inherently less diversified and therefore has higher variance.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

Bentonkb wrote: Fri Oct 22, 2021 10:25 am
comeinvest wrote: Fri Oct 22, 2021 2:15 am I have learned more about treasury futures just in the last few days than in my entire life before, . . .
You and me both. I am a smart guy, but this is a real mental workout. Many thanks to all the contributors and a hat tip to skier for doing the heavy lifting. :beer

One of the things that I've learned is the proper way to calculate the risk exposure of a bond future. I was wrong to think that the risk of the futures position is the same as a cash position in the CTD bond.

Equation 12 from this PDF convinced me of my error: http://www.yieldcurve.com/mktresearch/l ... utures.pdf
Sorry I have neither read the paper yet nor did I participate in the part of this thread discussing the CF, but did we ever apply the CF as per equation (12) in the paper that Bentonkb referenced, for the risk-adjusted return comparisons between the futures and the S&P bond indexes or ETFs? "VolCTD/fut is the relative volatility of the CTD bond compared to that of the future." I think volatility is not normalized there.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by LTCM »

comeinvest wrote: Fri Oct 22, 2021 8:24 pm
LTCM wrote: Fri Oct 22, 2021 8:19 pm
zkn wrote: Fri Oct 22, 2021 11:39 am I think what is going on here is that VFISX is a fund of multiple bonds, whereas our futures contracts and current bond indices only track one bond at a time. So they are not quite the same thing, and there may be diversification benefits captured by VFISX that may not be capturable with futures.
I may be off here. But that doesn't seem quite right. The futures contract tracks a basket of bonds and then allows the short to choose which one to deliver. Obviously they're going to pick the one most advantageous to their position which would explain slippage faster than any lack of diversification benefits.

Or have you considered that already?
@LTCM: All that is already factored in. The likely CTD is known by all market participants at any given time, along with the probabilities that it changes to any of the other available bonds between now and the time of expiration. The only possible reasoning that I can see is that if you are saying, if the durations of the alternative eligible bonds that might become CTD between a given time and the time of expiration are measurably different from the duration of the current likely CTD, then I guess we would have to calculate an average of those durations weighted by their respective probabilities of becoming CTD., to arrive at an "effective duration" for a futures contract. I'm not sure if all that would make a measurable difference. I think the reference CTD doesn't change that often.
I was more saying that the cheapest to deliver bond in a basket will likely underperform an average of a similar basket, but that should be factored into the price paid, so indeed, shouldn't matter. The shorts have to offer a premium for the optionality they enjoy.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

LTCM wrote: Sat Oct 23, 2021 2:32 am I was more saying that the cheapest to deliver bond in a basket will likely underperform an average of a similar basket, but that should be factored into the price paid, so indeed, shouldn't matter. The shorts have to offer a premium for the optionality they enjoy.
Correct, the effect of the optionality is known and should be already reflected in the futures price, and should cancel out in the long long. It's a technicality that should have no impact on performance. I think we discussed that earlier in this thread or in another one.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by sundevil_jay »

Can someone point me some primer on how to trade ITT/STT? I have not read this entire thread but after reading for 2-3 pages, this has piqued my interest tremendously. Just need to learn how to trade this with leveraged in real world. Any help would appreciated. Thanks
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by LTCM »

sundevil_jay wrote: Sat Oct 23, 2021 8:08 pm Can someone point me some primer on how to trade ITT/STT? I have not read this entire thread but after reading for 2-3 pages, this has piqued my interest tremendously. Just need to learn how to trade this with leveraged in real world. Any help would appreciated. Thanks
https://www.tdameritrade.com/education/ ... rading.htm

https://www.tastytrade.com/shows/futures-for-rookies
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by constructor »

skierincolorado wrote: Fri Oct 22, 2021 12:53 am
constructor wrote: Thu Oct 21, 2021 8:16 pm
skierincolorado wrote: Wed Oct 20, 2021 5:45 pm
This explains the statement by CME and others that 10M in bonds is hedged by just 81 contracts when the CF is .81. Or taking the inverse, 81 contracts has equal exposure to 10M in bonds. Not 8.1M.

https://us.etrade.com/knowledge/library ... -to-market
The only puzzle in my whole understanding is: With CF = 0.81, and say I long 1 contract till expiration for actual delivery. This means I need to be delivered a face value of $100,000 / 0.81 = $123,456. But each treasury has face value of $1,000 right? How do I receive 123 and then 456/1000 treasuries? Can one own/deliver a fraction of a $1,000 treasury?
The delivery is just $100k face value in CTD bonds. Or futures price * CF in market value of the CTD.

That's the whole confusing part. If the delivery is just futures price * CF, how do my returns reflect the full futures price? It took me a while - but they do.
OK after an evening of math and reading, I am closer to the answer but I believe it is more complicated than I thought it would be. Maybe you are way ahead of me here, but I thought you might be interested in this PDF from CME too, skierincolorado: https://www.cmegroup.com/education/file ... pdf#page=9

On page 9, before declaring the intent to deliver, the hedge ratio is the Conversion Factor:
... conversion-factor weighting and DV01 weighting effectively result in the same ratio for any basis spread between a Treasury futures contract and its CTD security
However after the trader "declares intent to deliver" (and if you are not familiar yet, actual delivery of treasury is a whole complicated mess of dates...): (bold mine)
Consider a long position in a Treasury basis spread during the interval between the futures contract’s First Intention Day and its last trading day. The delivery tail arises at the moment the holder declares intent to deliver on the spread’s short futures position. Up to that point, the ratio between the spread’s cash leg and futures leg is weighted according to the applicable conversion factor. Thereafter the pertinent ratio between cash and futures is strictly 1-to-1.

Both the magnitude of the tail and the consequences for the basis position holder depend entirely upon the conversion factor’s value. To see this, return to the setup in Examples 1 and 2, in which a long position in the TNU6 basis spread comprises $10 mln face value of the CTD note held long and 69 TNU6 contracts held short. At any time prior to notice of intent to deliver, the legs of the spread position are in balance, in the sense that their DV01s are almost equal and opposite. At the point the futures position is declared for delivery, however, the holder is obliged to deliver $6.9 mln face value of Treasury notes – 69 units of $100,000 face value each, with one unit for each futures contract – at the contract delivery invoice price. Thus, the 1-to-1 matching imposed by physical delivery produces an unhedged delivery tail, the residual long holding of $3.1 mln face value of Treasury notes.
Assuming the value of treasury future hinges upon the delivery process, then to fully understand pricing before the declaration of intent to deliver (which is when we are trading - I assume no one here is eligible to take delivery) we need to properly value this "unhedged delivery tail". I think intuitively this tail compensates for the difference, but I am not mathematically fully convinced yet.

Anyhow either way I have enough empirical evidence to convince me that treasury futures work and I only need to look at the market value column in my account. Maybe another weekend I will come back to this.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

constructor wrote: Sat Oct 23, 2021 10:08 pm
skierincolorado wrote: Fri Oct 22, 2021 12:53 am
constructor wrote: Thu Oct 21, 2021 8:16 pm
skierincolorado wrote: Wed Oct 20, 2021 5:45 pm
This explains the statement by CME and others that 10M in bonds is hedged by just 81 contracts when the CF is .81. Or taking the inverse, 81 contracts has equal exposure to 10M in bonds. Not 8.1M.

https://us.etrade.com/knowledge/library ... -to-market
The only puzzle in my whole understanding is: With CF = 0.81, and say I long 1 contract till expiration for actual delivery. This means I need to be delivered a face value of $100,000 / 0.81 = $123,456. But each treasury has face value of $1,000 right? How do I receive 123 and then 456/1000 treasuries? Can one own/deliver a fraction of a $1,000 treasury?
The delivery is just $100k face value in CTD bonds. Or futures price * CF in market value of the CTD.

That's the whole confusing part. If the delivery is just futures price * CF, how do my returns reflect the full futures price? It took me a while - but they do.
OK after an evening of math and reading, I am closer to the answer but I believe it is more complicated than I thought it would be. Maybe you are way ahead of me here, but I thought you might be interested in this PDF from CME too, skierincolorado: https://www.cmegroup.com/education/file ... pdf#page=9

On page 9, before declaring the intent to deliver, the hedge ratio is the Conversion Factor:
... conversion-factor weighting and DV01 weighting effectively result in the same ratio for any basis spread between a Treasury futures contract and its CTD security
However after the trader "declares intent to deliver" (and if you are not familiar yet, actual delivery of treasury is a whole complicated mess of dates...): (bold mine)
Consider a long position in a Treasury basis spread during the interval between the futures contract’s First Intention Day and its last trading day. The delivery tail arises at the moment the holder declares intent to deliver on the spread’s short futures position. Up to that point, the ratio between the spread’s cash leg and futures leg is weighted according to the applicable conversion factor. Thereafter the pertinent ratio between cash and futures is strictly 1-to-1.

Both the magnitude of the tail and the consequences for the basis position holder depend entirely upon the conversion factor’s value. To see this, return to the setup in Examples 1 and 2, in which a long position in the TNU6 basis spread comprises $10 mln face value of the CTD note held long and 69 TNU6 contracts held short. At any time prior to notice of intent to deliver, the legs of the spread position are in balance, in the sense that their DV01s are almost equal and opposite. At the point the futures position is declared for delivery, however, the holder is obliged to deliver $6.9 mln face value of Treasury notes – 69 units of $100,000 face value each, with one unit for each futures contract – at the contract delivery invoice price. Thus, the 1-to-1 matching imposed by physical delivery produces an unhedged delivery tail, the residual long holding of $3.1 mln face value of Treasury notes.
Assuming the value of treasury future hinges upon the delivery process, then to fully understand pricing before the declaration of intent to deliver (which is when we are trading - I assume no one here is eligible to take delivery) we need to properly value this "unhedged delivery tail". I think intuitively this tail compensates for the difference, but I am not mathematically fully convinced yet.

Anyhow either way I have enough empirical evidence to convince me that treasury futures work and I only need to look at the market value column in my account. Maybe another weekend I will come back to this.

Think of it this way. Up until the final settlement price, we are basically betting on what the final invoice price will be, but all of our bets are divided by the CF and marked to market daily.

That's the one sentence summary here. Once I understood that, it all fell into place. If the expected invoice price falls by $1000, the futures price falls by ~$1210 and CME takes $1210 from each of the longs and gives it to each of the shorts (the daily mark to market).

Once the settlement price is reach at 2pm CT, this mark to market stops. The invoice price is now known and the CF no longer matters. Only ~100k in bonds will be delivered at the invoice price, so if more bonds were held as part of the original hedged position, those undelivered bonds are now a naked long position.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by constructor »

hdas wrote: Thu Oct 21, 2021 9:26 pm
comeinvest wrote: Thu Oct 21, 2021 9:17 pm
hdas wrote: Thu Oct 21, 2021 8:41 pm While your point it's true, it just doesn't explain away the underperformance of futures. I added ZN funded, which has a duration of 6+ years and that also underperforms VFITX.
skier and zkn thought they explained it with duration discrepancies
Both the higher (ZN) and the lower (ZF) duration futures underperform VFITX, so that is not the factor. It must be the implied financing and the fact that you are not making anything in the funded position 3m T-bills. The difference is very significant, 2-2.5% in 2 years....Imagine the compound error of this on those imaginary 30y backtests of PV, total delusion.
I have recreated your chart with two differences: (1) realign your chart at today's price rather than in 2019 and (2) I have also added a 50% ZN + 50% ZF (roughly)

Image

How does it look now?

In March 2020 there was significant turmoil in the market and it also coincided with the roll date (and I had to manually pick out roll dates from a continuous series and so I don't have close to close roll data, basically each roll it's missing the overnight return). Also remember that before March 2020 the 3 month treasury rate is 1.6%, though I have no idea what was the repo rate back then.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

constructor wrote: Sun Oct 24, 2021 12:02 am
hdas wrote: Thu Oct 21, 2021 9:26 pm
comeinvest wrote: Thu Oct 21, 2021 9:17 pm
hdas wrote: Thu Oct 21, 2021 8:41 pm While your point it's true, it just doesn't explain away the underperformance of futures. I added ZN funded, which has a duration of 6+ years and that also underperforms VFITX.
skier and zkn thought they explained it with duration discrepancies
Both the higher (ZN) and the lower (ZF) duration futures underperform VFITX, so that is not the factor. It must be the implied financing and the fact that you are not making anything in the funded position 3m T-bills. The difference is very significant, 2-2.5% in 2 years....Imagine the compound error of this on those imaginary 30y backtests of PV, total delusion.
I have recreated your chart with two differences: (1) realign your chart at today's price rather than in 2019 and (2) I have also added a 50% ZN + 50% ZF (roughly)

Image

How does it look now?

In March 2020 there was significant turmoil in the market and it also coincided with the roll date (and I had to manually pick out roll dates from a continuous series and so I don't have close to close roll data, basically each roll it's missing the overnight return). Also remember that before March 2020 the 3 month treasury rate is 1.6%, though I have no idea what was the repo rate back then.
VGIT also holds a lot of ZT-like durations which has the best returns of the three during that time period. Your chart still shows ZF+ZN underperfming significantly, but it's because it doesn't have the ZT. The ZF/ZN/ZT timeseries from ZPGlobal include returns from investing the funded amount in 3-month t-bill. hdas has manually done something similar with a different data source, but missed the ZT as I mentioned.

zkn's charts show all this nicely. Would love to see a 40/40/20 ZT/ZF/ZN combo vs VFITX though.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Hfearless »

With the obvious caveat that market timing methods that do better than chance are few and far between, and that the ones that backtest well don’t come with any guarantees either—
skierincolorado wrote: Fri Oct 22, 2021 8:38 pm By diversifying we can maintain the same expected value with lower variance. Market timing is inherently less diversified and therefore has higher variance.
Conditional on the existence of a market timing method that actually works, doesn’t switching from one diversified portfolio to a different diversified portfolio reduce risk?

Note that the entire concept of rebalancing has a market timing element to it—you trade what performed better for what performed worse and expect the latter to revert to the mean, bringing in some profit.
skierincolorado wrote: Fri Oct 22, 2021 8:38 pm Also, and this comes to your second point, performing *different* than the market is a risk. If most retail investors are rolling in it because they bought stocks, and you are missing out because you bought much more bonds than most, you may be priced out of buying a home for example. It's also a psychological burden and increases the odds you will abandon ship - further increasing your risk.
So primarily a psychological concern.

To what extent does your suggestion of 125:200 include this concern? What would the allocation be under the sole goal of maximizing the long-term gain, assuming the mental fortitude not to deviate from the IPS?
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