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: Fri Oct 15, 2021 9:42 am
skierincolorado wrote: Fri Oct 15, 2021 8:43 am Tried to PM you my email but it looks like you have PM turned off?
I have enabled PM now.

skierincolorado wrote: Fri Oct 15, 2021 8:43 am You said the UB futures data was a different source?
Yes, this is high quality tick data which I pay good money for.

H
Does this other source have ZN? Perhaps we could validate the SPGlobal ZN data using your paid data. Or if you only have UB, we could validate SPGlobal's UB data.

I've always felt pretty comfortable relying on the SPGlobal data (which match up well with treasury bond fund returns for similar durations), it seems unlikely that such a major analytics company would provide invalid data, but it can't hurt to validate it.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

millennialmillions wrote: Fri Oct 15, 2021 11:26 am Based on the posts from skier and the backtest results (assuming the above discussion on ZF gets resolved), I’m now convinced that I should hold ITT instead of LTT. I’ve also decided to go with an allocation of 140% equity (98% domestic, 42% international) and 140% ITT. I transferred my Roth IRA to IBKR so I can now hold futures. Here are my planned holdings:
Image

A few remaining questions I would appreciate any input on:
  • Thoughts on my allocation across accounts? I don’t have any treasuries in my “Other Rtmt” accounts because they can’t trade futures, and it seems any other mechanism of treasury exposure is subpar.
  • The participants of this thread have still not reached consensus on the correct amount to use when determining treasury allocation. Based on the CME resource Bentonkb provided, I believe it should be the Principal Invoice Price (quoted futures price * the conversion factor), so that’s what I’m using. MES seems more straightforward – just 5 * the index value, right?
  • How does everyone decide the buffer on your futures margin requirement you’re comfortable with? E.g. if I have 14 MES contracts in a Roth IRA and I want to be able to withstand a 30% drop, I need 14 * 4,400 * 5 * 0.3 = $93,000 extra cash beyond the initial margin requirement. But what about the possibility of changing margin requirements, since they increase with market volatility?
  • How does everyone hold their “buffer” cash that is not currently used to meet margin requirements in retirement accounts? Do you put it in a fund like ICSH, JPST, or MINT? Is there a way to ensure that would be liquidated first in case extra cash is needed to meet margin requirements?
EDIT: also I agree with comeinvest that there is some benefit to diversifying across the yield curve slightly. personally for me that means owning ZF and a little ZN. Not a lot of diversification, not a lot of added complexity, still in the belly of the curve.

Also keep in mind when you decided on the 140% ITT allocation, that was for the duration of VFITX I think, which is a little over 5 years I think. ZF is under 5 years. So adding in some ZN could get you back to that 5.5 year average you were targeting.

Also I am curious how you decided on 140% ITT? Is it because it maximizes the 10th percentile of returns historically?

I calculate the margin requirement in the IRA to be 57k at IB (14*1679*2+6*828*2). That leaves you with 146k in cash. If the equity portion lost 30%, and you did not rebalance during the drop, you would lose 93k, and still have 53k in cash remaining. If you rebalanced back to your target leverage ratio at some point during the decline, you would lose less. So you could hold a substantial portion of the 146k in STT, like ICSH. But it would be more efficient to hold less MES, and more VTI. Holding ICSH does not compensate you fully for the .3-.4% (above LIBOR) financing cost implicit in MES. Furthermore, the broker does not consider ICSH collateral in an IRA, only cash, so only some of the cash could be held in ICSH.

I would reccomend in that IRA:
9 MES (198k)
112k VTI
6 ZF (587k)
98k cash

total equities and ZF stays the same at 310k/587k
you would have 98k cash to cover the 40k margin requirement (9*1679*2+6*828*2). You could endure an 18.7% market drop before margin call. If more buffer is desired, do one more MES and 22k less VTI. You would have the same problem with ICSH - the broker will not consider this as collateral - only cash is collateral. Thus we want to strike a reasonable balance between how much cash we hold and how often we need to monitor the market for drops that would bring us close to a margin call.

One consideration, that might allow for holding less cash than in my example, is if you determined and felt confident that the broker would liquidate the minimum amount of MES/ZF/or VTI necessary. Preferably VTI. If the market dropped this much, you would want to sell some stock anyways to maintain your target leverage ratio.

While I am not a small/value tilter, I don't believe this is a good time to underweight small/value. So a second modification I would make to the IRA holdings would be to substitute some VB/VBR and/or VO for VTI to counteract the large-cap bias of MES. Thus:

9 MES (198k)
72k VTI
40k VBR
6 ZF (587k)
98k cash

Some VB/VBR/VO could be held in retirement accounts to compensate for the UPRO. I personally don't think the amount of VB/VBR/VO needs to be rebalanced regularly, so there is no added complexity. I just think we need to hold some to compensate for the MES and UPRO. The exact amount isn't important IMO. Just hold some and forget about it. Since it's highly correlated with large caps, it probably wouldn't need to be rebalanced more than once a decade.

Otherwise, what you've outlined is very similar to what I hold. Only remaining difference is that I'm 130/200 insteada of 140/140. And within equity I'm 35/65 vs 30/70. So very similar... also in tems of how it's spread across accounts is nearly identical. Like you I have 2 401ks, one of which allows LETFs and options, the other does not. I chose LEAPs instead of LETF. I think LEAPs are a little better, but LETF are easier.

How do you plan to rebalance? One of the reasons I hold a little less stock leverage than you currently, is that I do not plan to rebalance my leverage ratio other than to keep at at 1.3x or higher. In a market decline I would let the leverage increase up to close to 2x before capping it. This is a subtle bet on the market being in a bubble currently, but it's pretty subtle given I'm still leveraged in equities!
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LTCM
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by LTCM »

millennialmillions wrote: Fri Oct 15, 2021 11:26 am Based on the posts from skier and the backtest results (assuming the above discussion on ZF gets resolved), I’m now convinced that I should hold ITT instead of LTT.
Did you ever get the chance to backtest STT?
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hdas
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by hdas »

skierincolorado wrote: Fri Oct 15, 2021 12:16 pm Does this other source have ZN? Perhaps we could validate the SPGlobal ZN data using your paid data. Or if you only have UB, we could validate SPGlobal's UB data.

I've always felt pretty comfortable relying on the SPGlobal data (which match up well with treasury bond fund returns for similar durations), it seems unlikely that such a major analytics company would provide invalid data, but it can't hurt to validate it.
h
Last edited by hdas on Tue Oct 26, 2021 6:38 pm, edited 1 time in total.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

hdas wrote: Fri Oct 15, 2021 2:39 pm
skierincolorado wrote: Fri Oct 15, 2021 12:16 pm Does this other source have ZN? Perhaps we could validate the SPGlobal ZN data using your paid data. Or if you only have UB, we could validate SPGlobal's UB data.

I've always felt pretty comfortable relying on the SPGlobal data (which match up well with treasury bond fund returns for similar durations), it seems unlikely that such a major analytics company would provide invalid data, but it can't hurt to validate it.
So, I looked at the SPGlobal data, and that seems correct. So I think we can discard the other data. However, a question for folks in this thread is how do you simulate the 3x returns of ZN futures?. Because, you do realize that the futures don't incorporate interest payments and the associated compounding of reinvesting such payments.... so you can't multiply the data of the SPGlobal data (or VFITX) * 3 and simulate the performance you are going to get. The cash that futures free up for investing is fixed, weather you leverage 3, 4x or whatever.

Hope ppl understand the above and the logical conclusion that all the backtests that have been used are useless. H
This is why we don't simply take ZN * 3. We take ZN * 3 - Cash * 2. This simulates the fact that when leveraging 100k 3x into ZN, the first 100k we invested in ZN freed up 100k of cash, which the SPGlobal data places in Cash earning LIBOR, the next 100k and the next 100k don't earn this cash rate, and we must subtract it. If SPGlobal held the fully funded amount in STT, we would subtract 2 * STT to simulate a 3x position.

All of the backtests do this, and are therefore accurate.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by LTCM »

LTCM wrote: Thu Sep 16, 2021 3:01 am My current plan is to go 100/900 stocks/STT. 4xZT contracts which have a nominal value of 880,000 (I think) and then 98,000 VTI. I like that all the treasuries are futures and all the stock is ETF. I like the balance of 1:9. The math is easy. I like the backtesting. Best sharpe ratio since 1955 while keeping it simple. Minimal cash drag. Will sell VTI if margin called and rebalance every quarter as needed. I’d like to go over 100% VTI but I don’t think I can justify the increased volatility.

I’m going to road test in thinkorswim for a little while and then dive in.

Taking comments now!
1 month update:

Initial balance: $100,000
Current Balance: $96,897
/ZT ($3031)
VGSH ($15)
VTI ($17)
TOTAL ($3063)

I've sold 5 units of VTI over the month to avoid/pay for margin calls.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by renelv »

Hi everyone.

How would you go implementing this 130/200 Stocks/ITT split with a small account? I would like to get my feet wet with 10k and start building from there. With futures, you will be working with 23k stock allocations (1 /MES contract) and/or 100k ITT chunks (/ZF or even more if you opt for /ZN etc). On the other hand there is not enough leveraged ETFs to get these allocations (for the TT at least since I guess you could use UPRO for the stocks), so something like 43% UPRO and 57% TYD would only get you around 130/170.

Also, you are not getting portfolio margin with that small account size as far as I know(in IBKR at least). Is the only way that makes sense to go with the original UPRO/TMF split, until the account grows and you can move to higher ITT leverage? For a big account these concerns should be irrelevant, it's just for us with little money to spare :D
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by millennialmillions »

Thanks again for the helpful post skier. The suggestion to hold more VTI rather than cash makes complete sense. As you said, I'll just need to monitor and sell some VTI if needed.
skierincolorado wrote: Fri Oct 15, 2021 12:51 pm EDIT: also I agree with comeinvest that there is some benefit to diversifying across the yield curve slightly. personally for me that means owning ZF and a little ZN. Not a lot of diversification, not a lot of added complexity, still in the belly of the curve.

Also keep in mind when you decided on the 140% ITT allocation, that was for the duration of VFITX I think, which is a little over 5 years I think. ZF is under 5 years. So adding in some ZN could get you back to that 5.5 year average you were targeting.
Yep I used VSIGX (same as VFITX, just admiral shares). I agree adding a little ZN gets me closer to the average maturity in the model, so I will do that. It's not that easy with the size of these contracts though...has anyone used the new micro treasury futures at all?
skierincolorado wrote: Fri Oct 15, 2021 12:51 pm Also I am curious how you decided on 140% ITT? Is it because it maximizes the 10th percentile of returns historically?
Yes, assuming the cost of borrowing equal to the T-Bill, 140/140 has a 10th percentile result equal to 140/180 and higher than 125/200. Obviously 140/140 is significantly better than the others for higher costs of leverage, which I also considered given my funds in a regular taxable account. In general, I lean toward higher stock, lower leverage allocations when things are about even.
skierincolorado wrote: Fri Oct 15, 2021 12:51 pm While I am not a small/value tilter, I don't believe this is a good time to underweight small/value. So a second modification I would make to the IRA holdings would be to substitute some VB/VBR and/or VO for VTI to counteract the large-cap bias of MES.
Personally, this doesn't concern me given how closely S&P 500 returns have tracked total market returns. Your proposal to hold some and forget about it makes it easy, but I would rather keep the portfolio just a little bit simpler. I also have some company stock not considered in this portfolio that I can't sell for another ~9 months, which gives me some "diversification" to the S&P 500.
skierincolorado wrote: Fri Oct 15, 2021 12:51 pm How do you plan to rebalance? One of the reasons I hold a little less stock leverage than you currently, is that I do not plan to rebalance my leverage ratio other than to keep at at 1.3x or higher. In a market decline I would let the leverage increase up to close to 2x before capping it. This is a subtle bet on the market being in a bubble currently, but it's pretty subtle given I'm still leveraged in equities!
Since I only used annual return data in my simulations, all of those results assume annual rebalancing, with no rebalancing bands. Generally, I like my production algorithm to match the modeled one as closely as possible. However, that is not entirely feasible due to margin requirements and the fact that I will continuously contribute throughout the year rather than one lump sum at the start of the year. So my plan is to use my ongoing contributions to rebalance to the extent they can (without selling anything). I plan to do a full rebalance annually. And outside of that, I am only planning to rebalance as needed to meet margin requirements. Does that sound reasonable to you?
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by millennialmillions »

LTCM wrote: Fri Oct 15, 2021 2:07 pm Did you ever get the chance to backtest STT?
I have not yet, but I can now. I will use VSBSX historical returns and the T-Bill for cost of borrowing. Any specific allocations you'd like to test?

Note that as you increase the overall leverage, the results become very sensitive to the cost of borrowing, which would concern me. I also seem to lean toward lower leverage allocations than most in this thread.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by LTCM »

millennialmillions wrote: Sat Oct 16, 2021 4:21 pm
LTCM wrote: Fri Oct 15, 2021 2:07 pm Did you ever get the chance to backtest STT?
I have not yet, but I can now. I will use VSBSX historical returns and the T-Bill for cost of borrowing. Any specific allocations you'd like to test?

Note that as you increase the overall leverage, the results become very sensitive to the cost of borrowing, which would concern me. I also seem to lean toward lower leverage allocations than most in this thread.
Allocation of 1:9 please. 100% stocks. 900% STT. I can't remember if your method tests different volatility goals so perhaps 50% stocks and 450% STT too if you have the time. 150% Stocks 1350% STT if you're feeling crazy (this usually bottoms out from memory).
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by LTCM »

millennialmillions wrote: Sat Oct 16, 2021 4:13 pm has anyone used the new micro treasury futures at all?
They don't work the way we want them too. It may be possible but it's probably beyond the talents of amateur investors.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

renelv wrote: Sat Oct 16, 2021 3:37 pm Hi everyone.

How would you go implementing this 130/200 Stocks/ITT split with a small account? I would like to get my feet wet with 10k and start building from there. With futures, you will be working with 23k stock allocations (1 /MES contract) and/or 100k ITT chunks (/ZF or even more if you opt for /ZN etc). On the other hand there is not enough leveraged ETFs to get these allocations (for the TT at least since I guess you could use UPRO for the stocks), so something like 43% UPRO and 57% TYD would only get you around 130/170.

Also, you are not getting portfolio margin with that small account size as far as I know(in IBKR at least). Is the only way that makes sense to go with the original UPRO/TMF split, until the account grows and you can move to higher ITT leverage? For a big account these concerns should be irrelevant, it's just for us with little money to spare :D
I definitely would not do TMF. The exact ratio is not exceptionally important. There are people in this thread using much lower and higher ratios. The amount of leverage you are able/willing to take in stocks is the impotant factor to long-term returns. More leverage in ITT will of course matter too, but 170 vs 200 would be pretty immaterial.

I would do UPRO and TYD. My understanding is that you could leverage this slightly at IBKR even under Reg T requirements (would need to confirm). I think the Reg T requirement is 75%. You wouldn't want to get close to that limit at all because you want to avoid margin calls. For example:

44 UPRO / 66 TYD. With 10k of equity, that would be a 1k margin loan. If the portfolio lost 50% of its value (-5.5k) you would have 4.5k of equity remaining with a 1k margin loan. The 5.5k of assets would have a margin requirement of 4.125k. You would not hit a margin call in this situation. This is with a 50% portfolio drop - still no margin call. And in fact, even before reaching this point you would have voluntarily rebalanced to sell some assets in order to maintain your target leverage.

So you should be able to do 130/200 with UPRO + TYD on Reg T. Even if you chose not to, I personally would still do TYD and not TMF. The risk-adjusted returns are just a lot better for TYD - I don't want to touch TMF if I can help it. I'd do the 130/170 as you said.

You could also consider MES + TYD. If MES went up a lot though your AA would become heavier on stocks. Which is fine in my opinion. The benefit is that MES is lower fee than UPRO. So that is probably what I would do. MES + TYD. I'm assuming funds would be added to the account at some point?

Also, if this is not your only account, I strongly suggest looking at your AA holistically and not just on an account basis. Using high fee LETFs in one account, while using no leverage in another account, does not make sense.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

millennialmillions wrote: Sat Oct 16, 2021 4:13 pm Thanks again for the helpful post skier. The suggestion to hold more VTI rather than cash makes complete sense. As you said, I'll just need to monitor and sell some VTI if needed.
skierincolorado wrote: Fri Oct 15, 2021 12:51 pm EDIT: also I agree with comeinvest that there is some benefit to diversifying across the yield curve slightly. personally for me that means owning ZF and a little ZN. Not a lot of diversification, not a lot of added complexity, still in the belly of the curve.

Also keep in mind when you decided on the 140% ITT allocation, that was for the duration of VFITX I think, which is a little over 5 years I think. ZF is under 5 years. So adding in some ZN could get you back to that 5.5 year average you were targeting.
Yep I used VSIGX (same as VFITX, just admiral shares). I agree adding a little ZN gets me closer to the average maturity in the model, so I will do that. It's not that easy with the size of these contracts though...has anyone used the new micro treasury futures at all?
skierincolorado wrote: Fri Oct 15, 2021 12:51 pm Also I am curious how you decided on 140% ITT? Is it because it maximizes the 10th percentile of returns historically?
Yes, assuming the cost of borrowing equal to the T-Bill, 140/140 has a 10th percentile result equal to 140/180 and higher than 125/200. Obviously 140/140 is significantly better than the others for higher costs of leverage, which I also considered given my funds in a regular taxable account. In general, I lean toward higher stock, lower leverage allocations when things are about even.
skierincolorado wrote: Fri Oct 15, 2021 12:51 pm While I am not a small/value tilter, I don't believe this is a good time to underweight small/value. So a second modification I would make to the IRA holdings would be to substitute some VB/VBR and/or VO for VTI to counteract the large-cap bias of MES.
Personally, this doesn't concern me given how closely S&P 500 returns have tracked total market returns. Your proposal to hold some and forget about it makes it easy, but I would rather keep the portfolio just a little bit simpler. I also have some company stock not considered in this portfolio that I can't sell for another ~9 months, which gives me some "diversification" to the S&P 500.
skierincolorado wrote: Fri Oct 15, 2021 12:51 pm How do you plan to rebalance? One of the reasons I hold a little less stock leverage than you currently, is that I do not plan to rebalance my leverage ratio other than to keep at at 1.3x or higher. In a market decline I would let the leverage increase up to close to 2x before capping it. This is a subtle bet on the market being in a bubble currently, but it's pretty subtle given I'm still leveraged in equities!
Since I only used annual return data in my simulations, all of those results assume annual rebalancing, with no rebalancing bands. Generally, I like my production algorithm to match the modeled one as closely as possible. However, that is not entirely feasible due to margin requirements and the fact that I will continuously contribute throughout the year rather than one lump sum at the start of the year. So my plan is to use my ongoing contributions to rebalance to the extent they can (without selling anything). I plan to do a full rebalance annually. And outside of that, I am only planning to rebalance as needed to meet margin requirements. Does that sound reasonable to you?
Very similar thinking to me as usual. On the micro futures I think LCTM is correct - these are not what we want they are a zero sum game.

On the rebalancing question, you say you want to match the modeled one. I think your spreadsheet rebalances annually? But the PV backtests some of them rebalance quarterly. And I think there is a bump for more frequent (would need to confirm). If only doing annual, be prepared to see some pretty extreme leverage in some situations which could be stressful. But if you are confident sticking to the backtest and the plan this shouldn't be a problem. I think part of why I chose 1.3 is to ease things from a psychological perspective. It takes a pretty serious drop for 1.3x to turn into 2x.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by millennialmillions »

LTCM wrote: Sat Oct 16, 2021 4:25 pm Allocation of 1:9 please. 100% stocks. 900% STT. I can't remember if your method tests different volatility goals so perhaps 50% stocks and 450% STT too if you have the time. 150% Stocks 1350% STT if you're feeling crazy (this usually bottoms out from memory).
Here's the output assuming the cost of borrowing equals T-Bill annual returns (pulled from the Simba backtesting sheet)
Image

Clearly, the 100/900 allocation looks amazing. However, as I mentioned prior to running it, the results are very sensitive to borrowing costs. To illustrate, here are the results if I instead assume the cost of borrowing is equal to the 10-year treasury rate
Image

Based on everything in this thread, it seems the costs should be much closer to the T-Bill than the 10-year. But if I was using this much leverage, I would definitely want to put more rigor into estimating borrowing costs and the precise performance of futures relative to the underlying asset than I have so far. For example, I doubt the assumed borrowing cost of < 0.1% from 2010-2015 was the cost in reality. Rather than try to get super sophisticated on estimating these costs, I have chosen to go with an allocation that performs well at either the optimistic or pessimistic cost. If someone is able to provide a more sophisticated borrowing cost by year, I would happily incorporate it, though.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by LTCM »

millennialmillions wrote: Sat Oct 16, 2021 5:52 pm Based on everything in this thread, it seems the costs should be much closer to the T-Bill than the 10-year. But if I was using this much leverage, I would definitely want to put more rigor into estimating borrowing costs and the precise performance of futures relative to the underlying asset than I have so far.
I agree. It is hard to nail down the financing cost. On the other hand these are 3 month contracts trading in the trillions of dollars. It's going to be a highly efficient market very close to the 3-month rate.

If you had the choice of lending someone cash for 3 months in return for a 2 year treasury as collateral or a 30 year treasury as collateral which would you pick? Which would you change a lower rate for?

If you have the stamina and determination you might be able to parse it out of this tool:
https://www.cmegroup.com/tools-informat ... lysis.html

It's beyond me I think.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by keith6014 »

LTCM wrote: Sat Oct 16, 2021 4:03 am
LTCM wrote: Thu Sep 16, 2021 3:01 am My current plan is to go 100/900 stocks/STT. 4xZT contracts which have a nominal value of 880,000 (I think) and then 98,000 VTI. I like that all the treasuries are futures and all the stock is ETF. I like the balance of 1:9. The math is easy. I like the backtesting. Best sharpe ratio since 1955 while keeping it simple. Minimal cash drag. Will sell VTI if margin called and rebalance every quarter as needed. I’d like to go over 100% VTI but I don’t think I can justify the increased volatility.

I’m going to road test in thinkorswim for a little while and then dive in.

Taking comments now!
1 month update:

Initial balance: $100,000
Current Balance: $96,897
/ZT ($3031)
VGSH ($15)
VTI ($17)
TOTAL ($3063)

I've sold 5 units of VTI over the month to avoid/pay for margin calls.
Thankyou. Looking forward for your updates!
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by millennialmillions »

LTCM wrote: Thu Sep 16, 2021 3:01 am My current plan is to go 100/900 stocks/STT. 4xZT contracts which have a nominal value of 880,000 (I think) and then 98,000 VTI. I like that all the treasuries are futures and all the stock is ETF. I like the balance of 1:9. The math is easy. I like the backtesting. Best sharpe ratio since 1955 while keeping it simple. Minimal cash drag. Will sell VTI if margin called and rebalance every quarter as needed. I’d like to go over 100% VTI but I don’t think I can justify the increased volatility.

I’m going to road test in thinkorswim for a little while and then dive in.

Taking comments now!
I believe you may be slightly overstating your STT exposure since you are not multiplying by the conversion factor. Bentonkb linked to this CME paper, which describes how to calculate the Principal Invoice Price, a better representation of the market value.

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

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

Note it doesn't appear there is consensus on this calculation, but this seems to directly align with the CME paper, and I haven't seen a good reason to use any other number. Also, the conversion factor for STT is closer to 1 than ITT or LTT, so it doesn't have as much of an impact.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by LTCM »

Yes. Bentonkb corrected me after that initial post. I scaled back the VTI to approx 93k and put the rest (approx 5k) into VGSH. So it was initially:

837k /ZT
5k VGSH
93k VTI

I suppose I should have sold some VGSH rather than all VTI if I wanted to stay as close to the 1:9 ratio as possible.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by L2F »

It is possible to use UPRO and VTI to achieve any desirable leverage level between 1 and 3, for example:
Target leverage 1.5, use 75% VTI and 25% UPRO.
When stocks rise, leverage will be greater than needed until rebalanced.

It is also possible to get some leverage using futures, example:
Target leverage 1.5, buy 1 /MES contract with notional value $22k and use $14.7 cash as collateral.
When stocks rise, leverage will be lower than needed.

Question:
Is it possible to combine VTI, UPRO and /MES in such a way that leverage level would be constant (even without rebalancing) to fight volatility decay of UPRO?
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

L2F wrote: Mon Oct 18, 2021 3:13 am It is possible to use UPRO and VTI to achieve any desirable leverage level between 1 and 3, for example:
Target leverage 1.5, use 75% VTI and 25% UPRO.
When stocks rise, leverage will be greater than needed until rebalanced.

It is also possible to get some leverage using futures, example:
Target leverage 1.5, buy 1 /MES contract with notional value $22k and use $14.7 cash as collateral.
When stocks rise, leverage will be lower than needed.

Question:
Is it possible to combine VTI, UPRO and /MES in such a way that leverage level would be constant (even without rebalancing) to fight volatility decay of UPRO?
One could use sso.

However, maintaining a fixed leverage ratio does not eliminate the risk of volatility decay or low volatility boost.

Eliminating volatility decay would be done by leveraging in a way that does not sell assets when markets drop, for example futures. However futures also don’t buy assets when markets go up, so you must decide when to buy more in order to stop the leverage ratio from falling. If
markets keep going up, which they usually do, you miss out.

There are pros and cons of all leverage rebalance strategies, and no one method is clearly better than another.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by constructor »

millennialmillions wrote: Sun Oct 17, 2021 9:14 am
LTCM wrote: Thu Sep 16, 2021 3:01 am My current plan is to go 100/900 stocks/STT. 4xZT contracts which have a nominal value of 880,000 (I think) and then 98,000 VTI. I like that all the treasuries are futures and all the stock is ETF. I like the balance of 1:9. The math is easy. I like the backtesting. Best sharpe ratio since 1955 while keeping it simple. Minimal cash drag. Will sell VTI if margin called and rebalance every quarter as needed. I’d like to go over 100% VTI but I don’t think I can justify the increased volatility.

I’m going to road test in thinkorswim for a little while and then dive in.

Taking comments now!
I believe you may be slightly overstating your STT exposure since you are not multiplying by the conversion factor. Bentonkb linked to this CME paper, which describes how to calculate the Principal Invoice Price, a better representation of the market value.

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

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

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

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

Well basically these two points are the same point.

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

Edit: On page 12 it does say:
E .g ., if one held $10 million face value of the 2-3/8%-8/24 note, one might sell 81 December 2017 futures by reference to the conversion factor of 0 .8072 to execute a hedge .
So this confirms that the nominal value is correct, that one future contract hedges more than "one treasury", given the ration of (1 / conversion factor). Though my question remains how the delivery work, since this almost seems you might need to deliver fraction of a treasury, and what the invoice price really means in the delivery process.
Last edited by constructor on Mon Oct 18, 2021 4:37 pm, edited 1 time in total.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

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

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

EDIT: The maturity of ZB is only 15.5 years, with 1.75% yield. That makes my transition a little less convincing. I would prefer a 17y or 20y, but what can I do.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

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

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

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

Also do consider that owning 2 ZB with 1.75% each (or 2 TN with 1.5% each) should provide a lot more return than 1 UB at 2%! There's only so much farther rates on those durations can rise before they also start pushing up the 20+ year rates. And that's not even factoring in the potential roll yield.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

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

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

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

Also do consider that owning 2 ZB with 1.75% each (or 2 TN with 1.5% each) should provide a lot more return than 1 UB at 2%! There's only so much farther rates on those durations can rise before they also start pushing up the 20+ year rates. And that's not even factoring in the potential roll yield.
I'm not really proud of the results, and I recognize I was somewhat lucky. In the long run I would expect to generate an excess return with a dynamic strategy as per the papers that I think were linked earlier in this thread.

I would not expect to get even close to 2% with ZF or any treasury future. Keep in mind your expected returns should be based on the expected future difference between the short-term rates and the rates with maturity of the future that you are holding, and on the expected future roll-down yields, not on the current carry or roll-down yields. For the same reason, it is not graved in stone that 2 ZB or 2 TN generate more return than one UB. For example, if short-term rates rise to 1.5%, everything else being equal and everything stabilizing there, your TN would return nothing after that, actually negative after implied financing cost (more on that later), while UB would still generate carry and roll returns (although probably not after implied financing cost, which is higher than I previously thought - more on that later). But you already know that, as we already discussed term premiums. I understand your argument for ITT.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Mon Oct 18, 2021 6:11 pm
skierincolorado wrote: Mon Oct 18, 2021 4:32 pm
comeinvest wrote: Mon Oct 18, 2021 3:39 pm I looked at my portfolio today and saw that my UB futures went up big time, while most others went down, a trend that already manifested itself over the last few months and weeks. Those who read my previous posts know that I'm running a dynamic treasury futures strategy that is "diversified" across the yield curve.
I looked at the yield curve, and saw that it is almost flat between 20y and 30y.
Consequently I finally replaced my UB with 2 ZB today as part of my dynamic strategy. The yield curve shows ca. 1.9% at 17y (ZB maturity) vs 2.0% at 20y-30y. Unless the yield curve inverts on the far end, there is now little to no conceivable reason to have UB, therefore I deleted UB from my diversified treasury futures allocation, until there is again a measurable slope on the far end. Luckily, the DV01 of 2 ZB is almost equal to the DV01 of one UB, which made the switch easy.
I have to catch up with this message thread.

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

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

Also do consider that owning 2 ZB with 1.75% each (or 2 TN with 1.5% each) should provide a lot more return than 1 UB at 2%! There's only so much farther rates on those durations can rise before they also start pushing up the 20+ year rates. And that's not even factoring in the potential roll yield.
I'm not really proud of the results, and I recognize I was somewhat lucky. In the long run I would expect to generate an excess return with a dynamic strategy as per the papers that I think were linked earlier in this thread.

I would not expect to get even close to 2% with ZF or any treasury future. Keep in mind your expected returns should be based on the expected future difference between the short-term rates and the rates with maturity of the future that you are holding, and on the expected future roll-down yields, not on the current carry or roll-down yields. For the same reason, it is not graved in stone that 2 ZB or 2 TN generate more return than one UB. For example, if short-term rates rise to 1.5%, everything else being equal and everything stabilizing there, your TN would return nothing after that, actually negative after implied financing cost (more on that later), while UB would still generate carry and roll returns (although probably not after implied financing cost, which is higher than I previously thought - more on that later). But you already know that, as we already discussed term premiums. I understand your argument for ITT.
Yeah I don’t actually expect 2% but I think expected returns are higher than they were 3 months ago, maybe over .5% now.

While it’s certainly possible that the yield curve could be flat at 1.5% from 0-10 years, but positively sloped past 10 years, it seems unlikely. And even if that happened, you’d still be better off in the interim with TN until short term rates actual got above 1%. You’d be collecting the carry and most of the roll yield until the short rates got closer to 1.5%. Every day that went by that short rates remained low you’d be getting the 1.1% carry and 1% roll. Even as the short rates rose you’d collect most of that. Only if ITT rates rise do you really lose in the short term, but that just gets you more carry and potential roll for the future.
Last edited by skierincolorado on Mon Oct 18, 2021 7:10 pm, edited 1 time in total.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Mon Oct 18, 2021 6:51 pm Yeah I don’t actually expect 2% but I think expected returns are higher than they were 3 months ago, maybe over .5% now.
That would be nice. I'm pessimistic after I finally calculated / verified myself the actual implied financing cost of treasury futures above the risk-free rate during the last few years, and discovered there is ca. 0.3-0.7% p.a. "slippage". I previously thought treasury futures would closely track cash treasuries minus the rate on T-Bills.

Treasuries are still nowhere close even to expected inflation. If and when at any time in the future there are again positive expected real returns and a verifiably higher expected term premium, I will double if not "triple" down on treasury futures.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Mon Oct 18, 2021 7:05 pm
skierincolorado wrote: Mon Oct 18, 2021 6:51 pm Yeah I don’t actually expect 2% but I think expected returns are higher than they were 3 months ago, maybe over .5% now.
That would be nice. I'm pessimistic after I finally calculated / verified myself the actual implied financing cost of treasury futures above the risk-free rate during the last few years, and discovered there is ca. 0.3-0.7% p.a. "slippage". I previously thought treasury futures would closely track cash treasuries minus the rate on T-Bills.

Treasuries are still nowhere close even to expected inflation. If and when at any time in the future there are again positive expected real returns and a verifiably higher expected term premium, I will double if not "triple" down on treasury futures.
You calculated this for your own personal returns or is this some dataset? I’m mostly basing lower financing cost off of the SPGlobal timeries, and the office of financial research paper that both find very near risk free.

Do you think you may have rolled at inopportune times? Were you using the cme roll tool? If this were true it would be very actionable for me as I would move from zf and zn to tn most likely.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Mon Oct 18, 2021 7:14 pm
comeinvest wrote: Mon Oct 18, 2021 7:05 pm
skierincolorado wrote: Mon Oct 18, 2021 6:51 pm Yeah I don’t actually expect 2% but I think expected returns are higher than they were 3 months ago, maybe over .5% now.
That would be nice. I'm pessimistic after I finally calculated / verified myself the actual implied financing cost of treasury futures above the risk-free rate during the last few years, and discovered there is ca. 0.3-0.7% p.a. "slippage". I previously thought treasury futures would closely track cash treasuries minus the rate on T-Bills.

Treasuries are still nowhere close even to expected inflation. If and when at any time in the future there are again positive expected real returns and a verifiably higher expected term premium, I will double if not "triple" down on treasury futures.
You calculated this for your own personal returns or is this some dataset? I’m mostly basing lower financing cost off of the SPGlobal timeries, and the office of financial research paper that both find very near risk free.
I will post my findings soon. As a heads up, I used several methods: my own returns / Interactive Brokers continuous futures charts (a good way to verify total returns) / S&P futures total return charts / comparison to VGSH, VGIT, VGLT total returns over same time periods (with appropriate adjustments) (I think VGSH and VGLT have maturities very similar to 2y and T-Bond futures respectively) / also, recent papers on the rise of the implied financing cost. Unfortunately I don't know how to get cash treasury returns for easier comparison.

Another method I used is looking at the IB continuous futures chart, pinpointing (looking at the historical yields on FRED) 2 points in time in history one or several years apart that had the exact same cash treasury yield of a specific maturity. *** Do this for any time period when the T-Bill rate was around 0.1% ***. I would expect the futures total return during this time period to be equal to or close to the initial yield minus ca. 0.1% (if there was no slippage). I didn't find this to be the case. I did a strikethrough because as skierincolorado pointed out this method wouldn't reflect rolldown returns and variations in interest rates between different contracts.

Also, it is my understanding that the approach for calculating the "implied repo rate" on the https://www.cmegroup.com/tools-informat ... ytics.html could be used to estimate your expected slippage when entering or rolling a position, but as the caveat on the instructions to that page says, you would have to provide your own, more accurate cash treasuries data. Somehow the numbers on that page are not real-time and/or the timing of futures and cash treasury yields doesn't match.

Can you please link the paper that you are referring to, and your slippage calculation based on SPGlobal timeseries? Don't rely on pre-2015 data or papers. Times changed.
Last edited by comeinvest on Mon Oct 18, 2021 10:57 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 LTCM »

comeinvest wrote: Mon Oct 18, 2021 7:05 pm I finally calculated / verified myself the actual implied financing cost of treasury futures above the risk-free rate during the last few years, and discovered there is ca. 0.3-0.7% p.a. "slippage". I previously thought treasury futures would closely track cash treasuries minus the rate on T-Bills.
Looking forward to hearing about this.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

LTCM wrote: Mon Oct 18, 2021 7:49 pm
comeinvest wrote: Mon Oct 18, 2021 7:05 pm I finally calculated / verified myself the actual implied financing cost of treasury futures above the risk-free rate during the last few years, and discovered there is ca. 0.3-0.7% p.a. "slippage". I previously thought treasury futures would closely track cash treasuries minus the rate on T-Bills.
Looking forward to hearing about this.
I will. I'm being distracted by my day job ;) I think understanding the slippage is material to the objectives and the discussion in this thread, because if my findings are true, the slippage would basically eat up the entire expected term premium which historically has been only like 0.5% or so if I'm not mistaken (correct me if I'm wrong here), and thereby the entire long-term expected returns from treasury futures positions.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Mon Oct 18, 2021 7:22 pm
skierincolorado wrote: Mon Oct 18, 2021 7:14 pm
comeinvest wrote: Mon Oct 18, 2021 7:05 pm
skierincolorado wrote: Mon Oct 18, 2021 6:51 pm Yeah I don’t actually expect 2% but I think expected returns are higher than they were 3 months ago, maybe over .5% now.
That would be nice. I'm pessimistic after I finally calculated / verified myself the actual implied financing cost of treasury futures above the risk-free rate during the last few years, and discovered there is ca. 0.3-0.7% p.a. "slippage". I previously thought treasury futures would closely track cash treasuries minus the rate on T-Bills.

Treasuries are still nowhere close even to expected inflation. If and when at any time in the future there are again positive expected real returns and a verifiably higher expected term premium, I will double if not "triple" down on treasury futures.
You calculated this for your own personal returns or is this some dataset? I’m mostly basing lower financing cost off of the SPGlobal timeries, and the office of financial research paper that both find very near risk free.
I will post my findings soon. As a heads up, I used several methods: my own returns / Interactive Brokers continuous futures charts (a good way to verify total returns) / S&P futures total return charts / comparison to VGSH, VGIT, VGLT total returns over same time periods (with appropriate adjustments) (I think VGSH and VGLT have maturities very similar to 2y and T-Bond futures respectively) / also, recent papers on the rise of the implied financing cost. Unfortunately I don't know how to get cash treasury returns for easier comparison.

Another method I used is looking at the IB continuous futures chart, pinpointing (looking at the historical yields on FRED) 2 points in time in history one or several years apart that had the exact same cash treasury yield of a specific maturity. *** Do this for any time period when the T-Bill rate was around 0.1% ***. I would expect the futures total return during this time period to be equal to or close to the initial yield minus ca. 0.1% (if there was no slippage). I didn't find this to be the case.

Also, it is my understanding that the approach for calculating the "implied repo rate" on the https://www.cmegroup.com/tools-informat ... ytics.html could be used to estimate your expected slippage when entering or rolling a position, but as the caveat on the instructions to that page says, you would have to provide your own, more accurate cash treasuries data. Somehow the numbers on that page are not real-time and/or the timing of futures and cash treasury yields doesn't match.

Can you link the paper that you are referring to, and your slippage calculation based on SPGlobal timeseries? Don't rely on pre-2015 data or papers. Times changed.
The primary evidence I've relied upon is this paper from the Office of Financial Research which I considered to be a reliable neutral source. Figure 5 shows that borrowing costs for the 5 year have averaged .1-.2% but varies between -.1% and +.4%.
https://www.financialresearch.gov/brief ... Trades.pdf

I compared SPGlobal fully-funded ZN vs VFITX. Very close, but ZN has slightly longer duration. I will try to update this by weighted averaging with something longer duration and then calculating borrowing cost from that. It looks like it would be pretty low though.
viewtopic.php?p=6274858#p6274858
Last edited by skierincolorado on Mon Oct 18, 2021 9:38 pm, edited 1 time in total.
Topic Author
skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Mon Oct 18, 2021 7:22 pm
skierincolorado wrote: Mon Oct 18, 2021 7:14 pm
comeinvest wrote: Mon Oct 18, 2021 7:05 pm
skierincolorado wrote: Mon Oct 18, 2021 6:51 pm Yeah I don’t actually expect 2% but I think expected returns are higher than they were 3 months ago, maybe over .5% now.
That would be nice. I'm pessimistic after I finally calculated / verified myself the actual implied financing cost of treasury futures above the risk-free rate during the last few years, and discovered there is ca. 0.3-0.7% p.a. "slippage". I previously thought treasury futures would closely track cash treasuries minus the rate on T-Bills.

Treasuries are still nowhere close even to expected inflation. If and when at any time in the future there are again positive expected real returns and a verifiably higher expected term premium, I will double if not "triple" down on treasury futures.
You calculated this for your own personal returns or is this some dataset? I’m mostly basing lower financing cost off of the SPGlobal timeries, and the office of financial research paper that both find very near risk free.
I will post my findings soon. As a heads up, I used several methods: my own returns / Interactive Brokers continuous futures charts (a good way to verify total returns) / S&P futures total return charts / comparison to VGSH, VGIT, VGLT total returns over same time periods (with appropriate adjustments) (I think VGSH and VGLT have maturities very similar to 2y and T-Bond futures respectively) / also, recent papers on the rise of the implied financing cost. Unfortunately I don't know how to get cash treasury returns for easier comparison.

Another method I used is looking at the IB continuous futures chart, pinpointing (looking at the historical yields on FRED) 2 points in time in history one or several years apart that had the exact same cash treasury yield of a specific maturity. *** Do this for any time period when the T-Bill rate was around 0.1% ***. I would expect the futures total return during this time period to be equal to or close to the initial yield minus ca. 0.1% (if there was no slippage). I didn't find this to be the case.

Also, it is my understanding that the approach for calculating the "implied repo rate" on the https://www.cmegroup.com/tools-informat ... ytics.html could be used to estimate your expected slippage when entering or rolling a position, but as the caveat on the instructions to that page says, you would have to provide your own, more accurate cash treasuries data. Somehow the numbers on that page are not real-time and/or the timing of futures and cash treasury yields doesn't match.

Can you link the paper that you are referring to, and your slippage calculation based on SPGlobal timeseries? Don't rely on pre-2015 data or papers. Times changed.
ZN is 6.25 duration per the analytics page. IEF is 8.02 effective duration. VFITX is 5.3 years. A 65/35 VFITX/IEF blend has weighted duration 6.25. I exported the returns of this portfolio from PV and graphed vs the SPGlobal in excel. The returns are very nearly identical. SPGlobal is a fully funded position that includes investing the funding amount at 3-month T-Bill. I calculate an additional financing cost of .05% makes the two perfectly identical. However, this does not consider the .2% ER on VFITX or the .15% on IEF. That would be a weighted average fee on the funds of .18%. So the financing on ZN would have had to have been .23%. Instead of paying .18% in fees, you pay .23% in financing. Of course, there are lower fee versions available. But ultimately I calculate a financing cost of .23% above the T-Bill. Of course, when backtesting using VFITX you don't have to make any adjustment because VFITX already makes the adjustment for us with the .2% fee.

In short, this methodology supports a financing cost nearly identical to the VFITX expense ratio and supports the use of VFITX in backtesting.

Image

https://www.spglobal.com/spdji/en/docum ... utures.pdf

https://www.portfoliovisualizer.com/bac ... tion2_1=35
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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: Mon Oct 18, 2021 7:22 pm
skierincolorado wrote: Mon Oct 18, 2021 7:14 pm
comeinvest wrote: Mon Oct 18, 2021 7:05 pm
skierincolorado wrote: Mon Oct 18, 2021 6:51 pm Yeah I don’t actually expect 2% but I think expected returns are higher than they were 3 months ago, maybe over .5% now.
That would be nice. I'm pessimistic after I finally calculated / verified myself the actual implied financing cost of treasury futures above the risk-free rate during the last few years, and discovered there is ca. 0.3-0.7% p.a. "slippage". I previously thought treasury futures would closely track cash treasuries minus the rate on T-Bills.

Treasuries are still nowhere close even to expected inflation. If and when at any time in the future there are again positive expected real returns and a verifiably higher expected term premium, I will double if not "triple" down on treasury futures.
You calculated this for your own personal returns or is this some dataset? I’m mostly basing lower financing cost off of the SPGlobal timeries, and the office of financial research paper that both find very near risk free.

Another method I used is looking at the IB continuous futures chart, pinpointing (looking at the historical yields on FRED) 2 points in time in history one or several years apart that had the exact same cash treasury yield of a specific maturity. *** Do this for any time period when the T-Bill rate was around 0.1% ***. I would expect the futures total return during this time period to be equal to or close to the initial yield minus ca. 0.1% (if there was no slippage). I didn't find this to be the case.
I don't think this method is quite correct for two reasons

1) I would actually expect the return to be higher than the initial YTM minus T-Bill, due to roll yield. You're not holding the bonds to maturity, so you should get higher returns than YTM, assuming a positively sloped yield curve.

2) If the interest rate is higher or lower during the intervening period, this will strongly effect returns. For example, if rates start at 2%, immediately fall to 0.5% and rise back to 2% near the end, I would expect returns a lot closer to 0.5% (plus some roll yield).
Last edited by skierincolorado on Mon Oct 18, 2021 9:55 pm, edited 1 time in total.
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millennialmillions
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by millennialmillions »

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

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

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

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

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

Well basically these two points are the same point.

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

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

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

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

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

The best way to settle this would be to use actual futures returns data compared against a fund to determine how much TLT is needed to replicate the results of 1 UB contract. Your point that "the volatility of UB is identical to TLT" doesn't answer this question of how much is needed.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Mon Oct 18, 2021 7:22 pm
skierincolorado wrote: Mon Oct 18, 2021 7:14 pm
comeinvest wrote: Mon Oct 18, 2021 7:05 pm
skierincolorado wrote: Mon Oct 18, 2021 6:51 pm Yeah I don’t actually expect 2% but I think expected returns are higher than they were 3 months ago, maybe over .5% now.
That would be nice. I'm pessimistic after I finally calculated / verified myself the actual implied financing cost of treasury futures above the risk-free rate during the last few years, and discovered there is ca. 0.3-0.7% p.a. "slippage". I previously thought treasury futures would closely track cash treasuries minus the rate on T-Bills.

Treasuries are still nowhere close even to expected inflation. If and when at any time in the future there are again positive expected real returns and a verifiably higher expected term premium, I will double if not "triple" down on treasury futures.
You calculated this for your own personal returns or is this some dataset? I’m mostly basing lower financing cost off of the SPGlobal timeries, and the office of financial research paper that both find very near risk free.
I will post my findings soon. As a heads up, I used several methods: my own returns / Interactive Brokers continuous futures charts (a good way to verify total returns) / S&P futures total return charts / comparison to VGSH, VGIT, VGLT total returns over same time periods (with appropriate adjustments) (I think VGSH and VGLT have maturities very similar to 2y and T-Bond futures respectively) / also, recent papers on the rise of the implied financing cost. Unfortunately I don't know how to get cash treasury returns for easier comparison.

Another method I used is looking at the IB continuous futures chart, pinpointing (looking at the historical yields on FRED) 2 points in time in history one or several years apart that had the exact same cash treasury yield of a specific maturity. *** Do this for any time period when the T-Bill rate was around 0.1% ***. I would expect the futures total return during this time period to be equal to or close to the initial yield minus ca. 0.1% (if there was no slippage). I didn't find this to be the case.

Also, it is my understanding that the approach for calculating the "implied repo rate" on the https://www.cmegroup.com/tools-informat ... ytics.html could be used to estimate your expected slippage when entering or rolling a position, but as the caveat on the instructions to that page says, you would have to provide your own, more accurate cash treasuries data. Somehow the numbers on that page are not real-time and/or the timing of futures and cash treasury yields doesn't match.

Can you link the paper that you are referring to, and your slippage calculation based on SPGlobal timeseries? Don't rely on pre-2015 data or papers. Times changed.
The IB continuous futures charts do not agree with the SPGlobal ones. It is likely that the IB ones do not include investing the funding at 3-month T-Bill.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Mon Oct 18, 2021 10:41 pm The IB continuous futures charts do not agree with the SPGlobal ones. It is likely that the IB ones do not include investing the funding at 3-month T-Bill.
Of course they don't. That's why I said: *** Do this for any time period when the T-Bill rate was around 0.1% ***. I would expect the futures total return during this time period to be equal to or close to the initial yield minus ca. 0.1% (if there was no slippage).
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Mon Oct 18, 2021 9:54 pm
comeinvest wrote: Mon Oct 18, 2021 7:22 pm Another method I used is looking at the IB continuous futures chart, pinpointing (looking at the historical yields on FRED) 2 points in time in history one or several years apart that had the exact same cash treasury yield of a specific maturity. *** Do this for any time period when the T-Bill rate was around 0.1% ***. I would expect the futures total return during this time period to be equal to or close to the initial yield minus ca. 0.1% (if there was no slippage). I didn't find this to be the case.
I don't think this method is quite correct for two reasons

1) I would actually expect the return to be higher than the initial YTM minus T-Bill, due to roll yield. You're not holding the bonds to maturity, so you should get higher returns than YTM, assuming a positively sloped yield curve.

2) If the interest rate is higher or lower during the intervening period, this will strongly effect returns. For example, if rates start at 2%, immediately fall to 0.5% and rise back to 2% near the end, I would expect returns a lot closer to 0.5% (plus some roll yield).
I think you are correct. This method only works for short time periods that include no roll between different contracts, and we would have to add an estimate for the rolldown return. I eliminated this method from my scrapbook.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

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

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

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

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

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

Well basically these two points are the same point.

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

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

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

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

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

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

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

Thus we get:

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

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

The higher number is the correct one (100k/CF)
Last edited by skierincolorado on Mon Oct 18, 2021 11:04 pm, edited 1 time in total.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

Slippage calculations: I am copying my calculations from the scrap book. The time periods are a bit arbitrary as I didn't have a whole lot of time, but I think all data that I looked at show significant slippage. We can do more calculations to get better statistics on slippage for each futures maturity tenor. There was a regulatory regime change ca. 2015 that supposedly increased implied financing rates of various derivatives. I am highlighting the 2015+ estimates in bold face.

ZT: note: VGSH has almost the same average maturity as ZT!
2-year S&P chart: Sep 30 2011 167.61 Sep 30 2016 171.95 Oct 1 2021 184.15
=> total returns: entire period: 1.0987 -> CAGR 0.94% / Sep 30 2011 to Sep 30 2016: 1.0259 -> CAGR 0.51% / Sep 30 2016 - Oct 1 2021: 1.071 -> CAGR 1.4%
Vanguard Short-Term Treasury ETF (VGSH) per web site: 10-year NAV return per 2021-09-30: 1.10% 5-year NAV return: 1.58%
VGSH per IB chart (check "adjust for dividends"): Sep 30 2011 55 -> Sep 30 2016 56.7 -> Oct 1 2021 61.42
=> total returns: entire period: 1.117 -> CAGR 1.1% / Sep 30 2011 to Sep 30 2016: 1.031 -> CAGR 0.61% / Sep 30 2016 - Oct 1 2021: 1.083 -> CAGR 1.6%
=> slippage ca.: entire period: 0.16% / 2011-2016: 0.1% / 2016-2021: 0.2%

ZF: note: VGIT has ca. 1 year longer average maturity than the ZF future!
5-year S&P chart: Sep 30 2011 511.41 Oct 1 2021 604.06 Sep 30 2016 553.60
=> total returns: entire period: 1.181 -> CAGR 1.68% / Sep 30 2011 to Sep 30 2016: 1.082 -> CAGR 1.59% / Sep 30 2016 - Oct 1 2021: 1.091 -> CAGR 1.76%
VGIT (ca. 5.5yr maturity/duration): 10-year NAV return per Vanguard web site: 2.23% / 5-year performance: 2.21%
VGIT per IB chart (check "adjust for dividends"): Sep 30 2011 53.79 -> Sep 30 2016 59.97 -> Oct 1 2021 67.62
=> total returns: entire period: 1.257 -> CAGR 2.31% / Sep 30 2011 to Sep 30 2016: 1.115 -> CAGR 2.2% / Sep 30 2016 - Oct 1 2021: 1.128 -> CAGR 2.44% (possibly calculation error? different from NAV return per Vanguard web site)
adjustment for 5.5 year maturity of VGIT vs. 4.5 year maturity of ZF: very rough estimate (please verify and adjust): 0.15%
=> slippage ca.: entire period: 0.4% / 2011-2016: 0.46% / 2016-2021: 0.3% (using Vanguard 5-year performance data point) / 0.53% (using IB chart)

UB: note: VGLT has almost the same average maturity as UB!
Dec 21 2011 - Mar 8 2019 (3% yield beginning and end of period): total return (theoretical): 1.03^7.216 = 1.24 (forgot to subtract T-Bill rate > 0)
per S&P total return futures chart: 137.93 -> 163.61 => total return 1.19
Nov 22 2016 - Mar 8 2019 (27.5 months) (3% yield beginning and end of period): total return (theoretical): 1.03^2.396 = 1.0734 (forgot to subtract T-Bill rate > 0)
per S&P total return futures chart: 154.6 -> 163.31 => total return 1.056 => CAGR: 1.056 ^ (12 / 27.5) -> 2.4%
VGLT per IB performance chart: ? (deleted data point in scrap book) -> 70.895 => 1.063 => CAGR: 1.063 ^ (12 / 27.5) => 2.7%
=> slippage ca. 0.3%
Nov 30 2011 - Sep 23 2021
per S&P total return chart 136.26 -> 206.43 => total return 1.515 => CAGR: 1.515 ^ (1/9.85) -> 4.3%
VGLT per IB performance chart: 55.83 -> 89.97 => total return 1.61 => CAGR: 1.61 ^ (1/9.85) -> 4.95%
=> slippage ca. 0.65% p.a.

I just realized that S&P also has performance data for several cash treasury tenors. I will add those as additional data points.

Duration-adjusted slippage per tenor, normalized to the duration of UB: (UB slippage to be added later)
ZT (maturity 23.5 months): 0.2% / 23.5 * 304 = 2.6%
ZF (maturity 40.6 months): 0.4% / 40.6 * 304 = 3%
ZB (maturity 187 months)
UB (maturity 304 months) (using 10-year period slippage estimate for now): 0.65%

My initial conclusions:
1. Treasury futures might incur financing rates equal if not higher than equity futures or options box spreads.
2. The higher the maturity, the higher the slippage.
3. The lower the maturity, the higher the duration-adjusted slippage. We might have to do-over all calcs comparing leveraged treasury futures strategies that were based on cash treasury returns, to include the financing cost per unit of duration for each maturity.
Last edited by comeinvest on Tue Oct 19, 2021 12:44 am, edited 15 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: Mon Oct 18, 2021 10:48 pm
skierincolorado wrote: Mon Oct 18, 2021 10:41 pm The IB continuous futures charts do not agree with the SPGlobal ones. It is likely that the IB ones do not include investing the funding at 3-month T-Bill.
Of course they don't. That's why I said: *** Do this for any time period when the T-Bill rate was around 0.1% ***. I would expect the futures total return during this time period to be equal to or close to the initial yield minus ca. 0.1% (if there was no slippage).
Ah right. But that still doesn't quite explain the difference for me.

From June 2019 to present I get 8.59% return for SPGlobal but only 6.79% for IB. Nearly 2 full percent or ~0.9% annualized. Too large to be explained by the investment of the funding in the SPGlobal method. Perhaps it's a combination of that plus using slightly different dates.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Mon Oct 18, 2021 11:03 pm
comeinvest wrote: Mon Oct 18, 2021 10:48 pm
skierincolorado wrote: Mon Oct 18, 2021 10:41 pm The IB continuous futures charts do not agree with the SPGlobal ones. It is likely that the IB ones do not include investing the funding at 3-month T-Bill.
Of course they don't. That's why I said: *** Do this for any time period when the T-Bill rate was around 0.1% ***. I would expect the futures total return during this time period to be equal to or close to the initial yield minus ca. 0.1% (if there was no slippage).
Ah right. But that still doesn't quite explain the difference for me.

From June 2019 to present I get 8.59% return for SPGlobal but only 6.79% for IB. Nearly 2 full percent or ~0.9% annualized. Too large to be explained by the investment of the funding in the SPGlobal method. Perhaps it's a combination of that plus using slightly different dates.
We should try to explain the discrepancy. Data should not lie. Make sure the dates match, and you copy the values correctly from the IB chart. And estimate the T-Bill rate correctly as an average from the chart.
EDIT: If you subtract the funding rate from the IB chart results, it could be about right. What futures tenor did you calculate? I think there was a lot of slippage especially in the long term tenors lately. This method is not very accurate for the other reasons that you mentioned before.
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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: Mon Oct 18, 2021 11:00 pm

ZF: note: VGIT has ca. 1 year longer average maturity than the ZF future!
5-year S&P chart: Sep 30 2011 511.41 Oct 1 2021 604.06 Sep 30 2016 553.60
=> total returns: entire period: 1.181 -> CAGR 1.68% / Sep 30 2011 to Sep 30 2016: 1.082 -> CAGR 1.59% / Sep 30 2016 - Oct 1 2021: 1.091 -> CAGR 1.76%
VGIT (ca. 5.5yr maturity/duration): 10-year NAV return per Vanguard web site: 2.23% / 5-year performance: 2.21%
VGIT per IB chart (check "adjust for dividends"): Sep 30 2011 53.79 -> Sep 30 2016 59.97 -> Oct 1 2021 67.62
=> total returns: entire period: 1.257 -> CAGR 2.31% / Sep 30 2011 to Sep 30 2016: 1.115 -> CAGR 2.2% / Sep 30 2016 - Oct 1 2021: 1.128 -> CAGR 2.44% (possibly calculation error? different from NAV return per Vanguard web site)
adjustment for 5.5 year maturity of VGIT vs. 4.5 year maturity of ZF: very rough estimate (please verify and adjust): 0.15%
=> slippage ca.: entire period: 0.4% / 2011-2016: 0.46% / 2016-2021: 0.3% (using Vanguard 5-year performance data point) / 0.53% (using IB chart)
OK so I'll start with ZF. Duration for ZF is 4.3 years. VGIT is 5.7 or 5.4. BSV is 2.9 or 2.8. I am not sure if should use maturity or effective duration. Thus we want a weighted average of 50/50 or 58/42.

Using 58/42 in PV I get CAGR of 2.03% for Sep 30 2011 - Sep 30 2021.

This compares to the SPGlobal 1.68% you found. Thus ZF returned .35% less than the funds. Add in .05% ER, and you find financing of 0.4%. This is a bit higher than the 0.23% I found for ZN using the same method. If using the 50/50 blend, I find financing of 0.36% for ZF.

I am surprised that the financing using the same methodology is so much higher for ZF than for ZN (0.4% vs 0.23%). It is possible that the duration of the CTD has changed over time. If the duration was shorter, like 3.8 years, we should be using a shorter duration bond fund likes 30% VGIT/ 70% BSV. Financing of 0.4% is inconsistent with what is in the OFR paper I posted earlier.

https://www.portfoliovisualizer.com/bac ... tion2_1=42


PV also confirms the Vanguard lower returns not the higher IB ones for VGIT.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Mon Oct 18, 2021 11:31 pm
comeinvest wrote: Mon Oct 18, 2021 11:00 pm

ZF: note: VGIT has ca. 1 year longer average maturity than the ZF future!
5-year S&P chart: Sep 30 2011 511.41 Oct 1 2021 604.06 Sep 30 2016 553.60
=> total returns: entire period: 1.181 -> CAGR 1.68% / Sep 30 2011 to Sep 30 2016: 1.082 -> CAGR 1.59% / Sep 30 2016 - Oct 1 2021: 1.091 -> CAGR 1.76%
VGIT (ca. 5.5yr maturity/duration): 10-year NAV return per Vanguard web site: 2.23% / 5-year performance: 2.21%
VGIT per IB chart (check "adjust for dividends"): Sep 30 2011 53.79 -> Sep 30 2016 59.97 -> Oct 1 2021 67.62
=> total returns: entire period: 1.257 -> CAGR 2.31% / Sep 30 2011 to Sep 30 2016: 1.115 -> CAGR 2.2% / Sep 30 2016 - Oct 1 2021: 1.128 -> CAGR 2.44% (possibly calculation error? different from NAV return per Vanguard web site)
adjustment for 5.5 year maturity of VGIT vs. 4.5 year maturity of ZF: very rough estimate (please verify and adjust): 0.15%
=> slippage ca.: entire period: 0.4% / 2011-2016: 0.46% / 2016-2021: 0.3% (using Vanguard 5-year performance data point) / 0.53% (using IB chart)
OK so I'll start with ZF. Duration for ZF is 4.3 years. VGIT is 5.7 or 5.4. BSV is 2.9 or 2.8. I am not sure if should use maturity or effective duration. Thus we want a weighted average of 50/50 or 58/42.

Using 58/42 in PV I get CAGR of 2.03% for Sep 30 2011 - Sep 30 2021.

This compares to the SPGlobal 1.68% you found. Thus ZF returned .35% less than the funds. Add in .05% ER, and you find financing of 0.4%. This is a bit higher than the 0.23% I found for ZN using the same method. If using the 50/50 blend, I find financing of 0.36% for ZF.

I am surprised that the financing using the same methodology is so much higher for ZF than for ZN (0.4% vs 0.23%). It is possible that the duration of the CTD has changed over time. If the duration was shorter, like 3.8 years, we should be using a shorter duration bond fund likes 30% VGIT/ 70% BSV. Financing of 0.4% is inconsistent with what is in the OFR paper I posted earlier.

https://www.portfoliovisualizer.com/bac ... tion2_1=42


PV also confirms the Vanguard lower returns not the higher IB ones for VGIT.
Don't forget you are still doing some linear interpolation here. I think the comparisons of the futures results to the Vanguard ETF results are more accurate in the ZT and ZB scenarios. In any case, the results don't look pretty to me.

What ETFs did you use for the ZN scenario?
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: Mon Oct 18, 2021 11:42 pm
skierincolorado wrote: Mon Oct 18, 2021 11:31 pm
comeinvest wrote: Mon Oct 18, 2021 11:00 pm

ZF: note: VGIT has ca. 1 year longer average maturity than the ZF future!
5-year S&P chart: Sep 30 2011 511.41 Oct 1 2021 604.06 Sep 30 2016 553.60
=> total returns: entire period: 1.181 -> CAGR 1.68% / Sep 30 2011 to Sep 30 2016: 1.082 -> CAGR 1.59% / Sep 30 2016 - Oct 1 2021: 1.091 -> CAGR 1.76%
VGIT (ca. 5.5yr maturity/duration): 10-year NAV return per Vanguard web site: 2.23% / 5-year performance: 2.21%
VGIT per IB chart (check "adjust for dividends"): Sep 30 2011 53.79 -> Sep 30 2016 59.97 -> Oct 1 2021 67.62
=> total returns: entire period: 1.257 -> CAGR 2.31% / Sep 30 2011 to Sep 30 2016: 1.115 -> CAGR 2.2% / Sep 30 2016 - Oct 1 2021: 1.128 -> CAGR 2.44% (possibly calculation error? different from NAV return per Vanguard web site)
adjustment for 5.5 year maturity of VGIT vs. 4.5 year maturity of ZF: very rough estimate (please verify and adjust): 0.15%
=> slippage ca.: entire period: 0.4% / 2011-2016: 0.46% / 2016-2021: 0.3% (using Vanguard 5-year performance data point) / 0.53% (using IB chart)
OK so I'll start with ZF. Duration for ZF is 4.3 years. VGIT is 5.7 or 5.4. BSV is 2.9 or 2.8. I am not sure if should use maturity or effective duration. Thus we want a weighted average of 50/50 or 58/42.

Using 58/42 in PV I get CAGR of 2.03% for Sep 30 2011 - Sep 30 2021.

This compares to the SPGlobal 1.68% you found. Thus ZF returned .35% less than the funds. Add in .05% ER, and you find financing of 0.4%. This is a bit higher than the 0.23% I found for ZN using the same method. If using the 50/50 blend, I find financing of 0.36% for ZF.

I am surprised that the financing using the same methodology is so much higher for ZF than for ZN (0.4% vs 0.23%). It is possible that the duration of the CTD has changed over time. If the duration was shorter, like 3.8 years, we should be using a shorter duration bond fund likes 30% VGIT/ 70% BSV. Financing of 0.4% is inconsistent with what is in the OFR paper I posted earlier.

https://www.portfoliovisualizer.com/bac ... tion2_1=42


PV also confirms the Vanguard lower returns not the higher IB ones for VGIT.
Don't forget you are still doing some linear interpolation here. I think the comparisons of the futures results to the Vanguard ETF results are more accurate in the ZT and ZB scenarios. In any case, the results don't look pretty to me.

What ETFs did you use for the ZN scenario?
I used VFITX and IEF, which have higher fees, but I added the fees to calculate financing cost.

The 0.36-0.40% I calculate for ZF is not that far off from the OFR paper, but I still feel like we are making a mistake somewhere. It's possible that it's the non-linearity issue you mention, and that the return of a 4.3 duration bond was closer to BSV than to VGIT during the last decade. Given there were times when rates were near 0% for these durations, that seems possible. It could be another mistake as well. The composition of the bond funds could have changed. Also, while the average duration of VGIT is 5.4 years, it holds a broad portfolio with durations up to 7 years or more I think. Given large parts of the last decade had rates below 1% on anything less than 4-5 years, this may have significantly contributed to the return of VGIT.

I would still trust the rates published in a research paper using the actual CTD security over back of the envelope calculations.

I also trust the ZN calculation I did more than the ZF, because it is mostly based on VFITX with modest IEF.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Mon Oct 18, 2021 11:48 pm
comeinvest wrote: Mon Oct 18, 2021 11:42 pm
skierincolorado wrote: Mon Oct 18, 2021 11:31 pm
comeinvest wrote: Mon Oct 18, 2021 11:00 pm

ZF: note: VGIT has ca. 1 year longer average maturity than the ZF future!
5-year S&P chart: Sep 30 2011 511.41 Oct 1 2021 604.06 Sep 30 2016 553.60
=> total returns: entire period: 1.181 -> CAGR 1.68% / Sep 30 2011 to Sep 30 2016: 1.082 -> CAGR 1.59% / Sep 30 2016 - Oct 1 2021: 1.091 -> CAGR 1.76%
VGIT (ca. 5.5yr maturity/duration): 10-year NAV return per Vanguard web site: 2.23% / 5-year performance: 2.21%
VGIT per IB chart (check "adjust for dividends"): Sep 30 2011 53.79 -> Sep 30 2016 59.97 -> Oct 1 2021 67.62
=> total returns: entire period: 1.257 -> CAGR 2.31% / Sep 30 2011 to Sep 30 2016: 1.115 -> CAGR 2.2% / Sep 30 2016 - Oct 1 2021: 1.128 -> CAGR 2.44% (possibly calculation error? different from NAV return per Vanguard web site)
adjustment for 5.5 year maturity of VGIT vs. 4.5 year maturity of ZF: very rough estimate (please verify and adjust): 0.15%
=> slippage ca.: entire period: 0.4% / 2011-2016: 0.46% / 2016-2021: 0.3% (using Vanguard 5-year performance data point) / 0.53% (using IB chart)
OK so I'll start with ZF. Duration for ZF is 4.3 years. VGIT is 5.7 or 5.4. BSV is 2.9 or 2.8. I am not sure if should use maturity or effective duration. Thus we want a weighted average of 50/50 or 58/42.

Using 58/42 in PV I get CAGR of 2.03% for Sep 30 2011 - Sep 30 2021.

This compares to the SPGlobal 1.68% you found. Thus ZF returned .35% less than the funds. Add in .05% ER, and you find financing of 0.4%. This is a bit higher than the 0.23% I found for ZN using the same method. If using the 50/50 blend, I find financing of 0.36% for ZF.

I am surprised that the financing using the same methodology is so much higher for ZF than for ZN (0.4% vs 0.23%). It is possible that the duration of the CTD has changed over time. If the duration was shorter, like 3.8 years, we should be using a shorter duration bond fund likes 30% VGIT/ 70% BSV. Financing of 0.4% is inconsistent with what is in the OFR paper I posted earlier.

https://www.portfoliovisualizer.com/bac ... tion2_1=42


PV also confirms the Vanguard lower returns not the higher IB ones for VGIT.
Don't forget you are still doing some linear interpolation here. I think the comparisons of the futures results to the Vanguard ETF results are more accurate in the ZT and ZB scenarios. In any case, the results don't look pretty to me.

What ETFs did you use for the ZN scenario?
I used VFITX and IEF, which have higher fees, but I added the fees to calculate financing cost.

The 0.36-0.40% I calculate for ZF is not that far off from the OFR paper, but I still feel like we are making a mistake somewhere. It's possible that it's the non-linearity issue you mention, and that the return of a 4.3 duration bond was closer to BSV than to VGIT during the last decade. Given there were times when rates were near 0% for these durations, that seems possible. It could be another mistake as well. The composition of the bond funds could have changed. Also, while the average duration of VGIT is 5.4 years, it holds a broad portfolio with durations up to 7 years or more I think. Given large parts of the last decade had rates below 1% on anything less than 4-5 years, this may have significantly contributed to the return of VGIT.

I would still trust the rates published in a research paper using the actual CTD security over back of the envelope calculations.

I also trust the ZN calculation I did more than the ZF, because it is mostly based on VFITX with modest IEF.
I added duration-adjusted slippage estimates per tenor to my post above with my calcs. I'm curious what the impact is for the STT vs ITT vs LTT discussion.
Duration-adjusted slippage per tenor, normalized to the duration of UB: (UB slippage to be added later)
ZT (maturity 23.5 months): 0.2% / 23.5 * 304 = 2.6%
ZF (maturity 40.6 months): 0.4% / 40.6 * 304 = 3%
ZB (maturity 187 months)
UB (maturity 304 months) (using 10-year period slippage estimate for now): 0.65%

My initial conclusions:
1. Treasury futures might incur financing rates equal if not higher than equity futures or options box spreads.
2. The higher the maturity, the higher the slippage.
3. The lower the maturity, the higher the duration-adjusted slippage. We might have to do-over all calcs comparing leveraged treasury futures strategies that were based on cash treasury returns, to include the financing cost per unit of duration for each maturity.
We should also look at the S&P cash treasury performance data as an additional data point. Although at the end of the day, the comparisons to the Vanguard funds might be more meaningful to the investor for purpose of calculating all-in cost of leverage, as those are real investable alternatives to using futures. The rates of cash treasuries of the exact same tenor as the available futures contracts might be "pushed down" by investors' demand for the futures and the futures/cash treasuries cash-and-carry arbitrage. Not sure about that, just a possibility.
Last edited by comeinvest on Tue Oct 19, 2021 12:45 am, edited 5 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 »

Here's ZB:

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

VGLT average duration is 17.9 years

ZB CTD duration is currently 11.6 years.

Am I doing the duration wrong? VGLT is much longer duration than ZB.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Mon Oct 18, 2021 11:48 pm I would still trust the rates published in a research paper using the actual CTD security over back of the envelope calculations.
I wouldn't disagree, but also consider what I said in my other post: "Although at the end of the day, the comparisons to the Vanguard funds might be more meaningful to the investor for purpose of calculating all-in cost of leverage, as those are real investable alternatives to using futures. The rates of cash treasuries of the exact same tenor as the available futures contracts (especially the deliverable CTD itself) might be artificially "pushed down" by investors' demand for the futures and the futures/cash treasuries cash-and-carry arbitrage." Demand for long futures positions should translate to demand for the CTD from the hedging counterparties.
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skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Tue Oct 19, 2021 12:10 am
skierincolorado wrote: Mon Oct 18, 2021 11:48 pm I would still trust the rates published in a research paper using the actual CTD security over back of the envelope calculations.
I wouldn't disagree, but also consider what I said in my other post: "Although at the end of the day, the comparisons to the Vanguard funds might be more meaningful to the investor for purpose of calculating all-in cost of leverage, as those are real investable alternatives to using futures. The rates of cash treasuries of the exact same tenor as the available futures contracts (especially the deliverable CTD itself) might be artificially "pushed down" by investors' demand for the futures and the futures/cash treasuries cash-and-carry arbitrage." Demand for long futures positions should translate to demand for the CTD by the hedging counterparties.
But there isn't a single tenor for futures contract, but rather a basket. If one tenor is pushed down, a different tenor would become CTD. I could see how this could be the case though if CTD clusters around a few tenors.

Not sure if you saw my question on VGLT vs ZB.
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skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Tue Oct 19, 2021 12:10 am
skierincolorado wrote: Mon Oct 18, 2021 11:48 pm I would still trust the rates published in a research paper using the actual CTD security over back of the envelope calculations.
I wouldn't disagree, but also consider what I said in my other post: "Although at the end of the day, the comparisons to the Vanguard funds might be more meaningful to the investor for purpose of calculating all-in cost of leverage, as those are real investable alternatives to using futures. The rates of cash treasuries of the exact same tenor as the available futures contracts (especially the deliverable CTD itself) might be artificially "pushed down" by investors' demand for the futures and the futures/cash treasuries cash-and-carry arbitrage." Demand for long futures positions should translate to demand for the CTD from the hedging counterparties.
It appears that this was slightly true on March 11, 2020 in the peak of illiquidity. Some CTDs had yields ~.05% different from non CTD securities. See figure 38 here:

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

Assuming this is the peak deviation, and any deviations outside of period of extreme illiquidity are usually less than this, I don't think this would be a concern.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Tue Oct 19, 2021 12:17 am
comeinvest wrote: Tue Oct 19, 2021 12:10 am
skierincolorado wrote: Mon Oct 18, 2021 11:48 pm I would still trust the rates published in a research paper using the actual CTD security over back of the envelope calculations.
I wouldn't disagree, but also consider what I said in my other post: "Although at the end of the day, the comparisons to the Vanguard funds might be more meaningful to the investor for purpose of calculating all-in cost of leverage, as those are real investable alternatives to using futures. The rates of cash treasuries of the exact same tenor as the available futures contracts (especially the deliverable CTD itself) might be artificially "pushed down" by investors' demand for the futures and the futures/cash treasuries cash-and-carry arbitrage." Demand for long futures positions should translate to demand for the CTD by the hedging counterparties.
But there isn't a single tenor for futures contract, but rather a basket. If one tenor is pushed down, a different tenor would become CTD. I could see how this could be the case though if CTD clusters around a few tenors.
Hard to reverse-engineer the market forces for me as a layman. All I'm saying is that the comparison to the Vanguard funds might be meaningful for purpose of estimating an "all-in" cost of leverage, as in comparing to alternative methods of leverage like equity futures or options box spreads. What I know is that investors' demand for leverage together with regulatory constraints starting around 2015 caused implied financing rates of various derivatives to go up.
Last edited by comeinvest on Tue Oct 19, 2021 12:32 am, edited 4 times in total.
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