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

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

Post by skierincolorado »

https://www.portfoliovisualizer.com/bac ... on4_3=-465

Personally, HFEA is too much risk for me. But can we achieve the returns of HFEA with lower risk by diversifying across higher returning assets like ITT instead of LTT? A modified HFEA strategy using futures and ITT is essentially an optimization and fusion of several important threads on this forum. Lifecycle investing is about finding an optimal leverage glidepath over the course of one's life to diversify one's investments across time. HFEA diversifies across asset classes. While HFEA used TMF long-term treasuries for the bond allocation, this was because leveraging shorter durations requires more leverage than a 3x LETF can provide. Historically 1960-2018 the diversification benefit of ITT was higher, and the return per unit of risk is much greater. We just need to own more to achieve the same level of risk/variance and diversification as TMF. If we already have our whole portfolio allocated to UPRO and TMF, we can't achieve any more leverage without using futures contracts. Neither HFEA, nor the Lifecycle Investing book's 100% equity AA, have been on the efficient frontier historically, nor are they likely to ever be.

Leveraging during your working years is less risky in the long-run and provides diversification of your investments across time. Instead of having your largest lifetime investments be in your late 40s and 50s, spread your investments out over a long time horizon by leveraging in your 20s and 30s and early 40s and deleverage with time. There is a tremendous amount of knowledge and resources contained in this thread, starting with the original post by Steve Reading which contains numerous links: viewtopic.php?f=10&t=274390
This thread goes over the optimal ways to achieve leverage in taxable vs tax-adantaged accounts. To summarize, in an IRA use futures for leverage. In a taxable account, use box-spreads and/or margin for equity leverage, and futures for Treasury leverage.

Futures contracts have several advantages over LETF:
1) avoid 0.9% fees on LETF
2) eliminate daily rebalancing which can cause volatility decay in sideways markets (but also enhance returns in vertical markets)
3) allow for more leverage of shorter durations Treasuries

ITT are an improvement over LTT:
1) A portfolio of ITT+stocks has been less dependent on the performance of stocks than a portfolio of LTT+stocks. The benefit from diversification has been better. See exhibit 17 here: https://www.pimco.com/handlers/displayd ... d%2BfxA%3D
2) ITT have much better risk adjusted returns historically.
3) The ITT market is much larger than the LTT market, and owning ITT puts us much closer to market weight across asset classes

Now for the backtest. HFEA is a 165/135 stock/LTT AA. We can have a much less risky AA of 125/270 stock/ITT and achieve the same return since 1991. The max-drawdown is reduced from 66.6% to 47.8%. The 270% allocation to ITT is substantially less risky than the 135% allocation to LTT. The ITT in the backtest have a duration of 5 years, and the LTT have a duration of 20 years, making the max-drawdown in a bond crash nearly 4x larger for LTT. The duration risk of LTT is 4x ITT. Instead of replacing the LTT in HFEA with 4:1 ITT, we could do a modest 2:1 and still get the same returns as HFEA, with much less risk. We can even reduce the stock leverage from 165% to 125%, and still get the same return as HFEA. If we wanted to take the same level of risk as HFEA, we would do an AA of 165/400 stock/ITT. Since 1991, this has actually been much less risky, with a max-drawdown of 59.2% (vs 66.6% for HFEA).

Backtest 165/135 stock/LTT (HFEA) vs 125/270 stock/ITT vs 165/400 stock/ITT.
https://www.portfoliovisualizer.com/bac ... on4_3=-465

Why do LTT have such terrible risk adjusted returns? http://pages.stern.nyu.edu/~lpederse/pa ... stBeta.pdf

Optimizing the bond portion of the portfolio using a max-carry strategy: https://www.efmaefm.org/0EFMAMEETINGS/E ... lpaper.pdf
https://www.pimco.com/handlers/displayd ... d%2BfxA%3D

Is this just taking advantage of nearly continuously falling rates since 1982?
No. This has less risk in bonds than HFEA. A backtest that includes the 1970s and 1980s would substantially outperform HFEA because it has substantially less duration risk than HFEA.

Other helpful links:
Futures in an IRA: viewtopic.php?t=289144

HFEA: viewtopic.php?t=288192&start=6500

NTSX provides a 90/60 AA with reasonable fees: viewtopic.php?f=10&t=302218

Borrowing costs of treasury futures with focus on 2008 and 2020: https://www.financialresearch.gov/brief ... Trades.pdf
Last edited by skierincolorado on Tue Sep 14, 2021 10:51 am, edited 1 time in total.
chillpenguin
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by chillpenguin »

Remember that the main point of LTT in HFEA was due to the theory that investors will flock to LTT during a stock market crash. It is basically crash insurance, as opposed to something that theoretically drives more returns on its own compared to other asset classes.

The leveraged ETFs were also a big part of what made HFEA what it was. So really I don't think this should be called "HFEA", as this is more just using leverage with stocks and bonds in some other way, of which there are many other variations as well.

Overall I think you have a perfectly valid strategy though.

I think you would like this thread to go further in this direction: A mean variance framework for portfolio optimization
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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 »

Back test of SPY/8xSTT since 1991:

Image

Back test of SPY/3xITT since 1991:

Image

Back test of SPY/LTT since 1991:

Image

Adjust volatility to taste.

8/9 portfolios do worst in 1994 when markets were flat and the short term borrowing cost was at 4%.
Last edited by LTCM on Sat Sep 04, 2021 3:33 am, 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 LTCM »

chillpenguin wrote: Sat Sep 04, 2021 3:16 am the main point of LTT in HFEA was due to the theory that investors will flock to LTT during a stock market crash. It is basically crash insurance, as opposed to something that theoretically drives more returns on its own compared to other asset classes.
STT/ITT also provide crash insurance, but a smaller amount due to the shorter durations. That's why STT/ITT need to be leveraged at a much higher ratio. HFEA uses LTT because it comes in a 3x fund that balances well with 3x stocks.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by LTCM »

skierincolorado wrote: Fri Sep 03, 2021 10:27 pm Backtest 165/135 stock/LTT (HFEA) vs 125/270 stock/ITT vs 165/400 stock/ITT.
https://www.portfoliovisualizer.com/bac ... on4_3=-465
Here's an alternative backtest:
https://www.portfoliovisualizer.com/bac ... n5_3=-1215

Image

LTT duration is 17.9 years, ITT duration is 5.1 years and STT duration is 2.1 years. I've scaled the ITT/STT to the same interest rate sensitivity as the original HFEA/LTT portfolio.

ITT: 135*(17.9/5.1)=474
STT: 135*(17.9/2.1)=1151
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

Placeholder - best IRAs for futures
DMoogle
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by DMoogle »

Apologies if I missed it in the other thread, but have you guys done any work to analyze optimal ratios of stocks:treasuries? In the backtests above, it looks like you're applying 1:8 for STT, 1:3 for ITT, and 1:1 for LTT. Would be curious to see what a few graphs look like of different allocations against Sharpe, total return, and max drawdown.

Also, is there any benefit to diversifying across treasury classes (i.e. duration diversification)?
perfectuncertainty
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by perfectuncertainty »

skierincolorado wrote: Fri Sep 03, 2021 10:27 pm
Leveraging during your working years is less risky in the long-run and provides diversification of your investments across time. Instead of having your largest lifetime investments be in your late 40s and 50s, spread your investments out over a long time horizon by leveraging in your 20s and 30s and early 40s and deleverage with time. There is a tremendous amount of knowledge and resources contained in this thread, starting with the original post by Steve Reading which contains numerous links: viewtopic.php?f=10&t=274390
This thread goes over the optimal ways to achieve leverage in taxable vs tax-adantaged accounts. To summarize, in an IRA use futures for leverage. In a taxable account, use box-spreads and/or margin for equity leverage, and futures for Treasury leverage.

Futures contracts have several advantages over LETF:
1) avoid 0.9% fees on LETF
2) eliminate daily rebalancing which can cause volatility decay in sideways markets (but also enhance returns in vertical markets)
3) allow for more leverage of shorter durations Treasuries
Other helpful links:
Futures in an IRA: viewtopic.php?t=289144

HFEA: viewtopic.php?t=288192&start=6500

NTSX provides a 90/60 AA with reasonable fees: viewtopic.php?f=10&t=302218
How are you handling the futures - continuous contract with rolling?
What is your actual proposed portfolio - versus the fund substitutes?

Thanks for the interesting thread :-)
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

DMoogle wrote: Tue Sep 07, 2021 7:16 pm Apologies if I missed it in the other thread, but have you guys done any work to analyze optimal ratios of stocks:treasuries? In the backtests above, it looks like you're applying 1:8 for STT, 1:3 for ITT, and 1:1 for LTT. Would be curious to see what a few graphs look like of different allocations against Sharpe, total return, and max drawdown.

Also, is there any benefit to diversifying across treasury classes (i.e. duration diversification)?
I did 1:2 for ITT w/ a duration of 5 years. ZF futures are a little shorter than that, ZN a little longer. TYD LETF is substantially longer.

My decision was based more on a rough estimate of max-drawdown in 1981 because portfolio visualizer available funds only go back to 1991. I think you can take pretty ridiculous leverage in ITT in PV and keep increasing the sharpe ratio, because the only significant drawdown in bonds since 1991 is 1994 and even 1994 wasn't that bad for bonds.

For example, going 1:4 stock/ITT instead of 1:2 bumps the sharpe ratio from .95 to .97. But 500% leverage in bonds would likely have been too much leverage in 1981.

https://www.portfoliovisualizer.com/bac ... on3_2=-525
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by LTCM »

If you test back to 1972 it suggests the efficient portfolio is 1:4 stocks/STT
https://www.portfoliovisualizer.com/eff ... rtTreasury

If you test back to 1986 it suggests the efficient portfolio is 1:9 stocks/STT
https://www.portfoliovisualizer.com/eff ... rtTreasury

I’m not sure which is a better test. I tend towards the feeling that fed policies have changed enough since the 1970s for the more recent period to be more informative. Happy to hear disagreement.

1972 onwards suggests 3:7 stocks/ITT
https://www.portfoliovisualizer.com/eff ... teTreasury

1986 onwards suggests 1:3 stocks/ITT
https://www.portfoliovisualizer.com/eff ... teTreasury

None of these tests account for the cost of short term borrowing which is unfortunate. We’d probably need to load data into PV to get a proper back test into the 1970s.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by DMoogle »

LTCM wrote: Wed Sep 08, 2021 1:53 amNone of these tests account for the cost of short term borrowing which is unfortunate.
Since absolute expected returns for treasuries are lower than stocks, I think we can assume the efficient frontier ratios are lower. It's also a stronger case for higher-duration, since you don't have to borrow as much.

On that note, is there any value to diversifying across duration?
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

LTCM wrote: Wed Sep 08, 2021 1:53 am If you test back to 1972 it suggests the efficient portfolio is 1:4 stocks/STT
https://www.portfoliovisualizer.com/eff ... rtTreasury

If you test back to 1986 it suggests the efficient portfolio is 1:9 stocks/STT
https://www.portfoliovisualizer.com/eff ... rtTreasury

I’m not sure which is a better test. I tend towards the feeling that fed policies have changed enough since the 1970s for the more recent period to be more informative. Happy to hear disagreement.

1972 onwards suggests 3:7 stocks/ITT
https://www.portfoliovisualizer.com/eff ... teTreasury

1986 onwards suggests 1:3 stocks/ITT
https://www.portfoliovisualizer.com/eff ... teTreasury

None of these tests account for the cost of short term borrowing which is unfortunate. We’d probably need to load data into PV to get a proper back test into the 1970s.
My guess is accounting for the cost of borrowing would shift the ratio lower, because you have to borrow more for bonds than for stocks. I'm also more comfortable with the ratio used going back to the 1970s because it includes a serious inflation event and bond crash. Such a scenario seems unlikely under current Fed policy, but policy has relaxed slightly and if this is a 30 year plan it needs to account for all possibilities however remote.

Also, if we kept the same ratio from HFEA but adjusted for the duration I think it would be a ratio of 2.8. But this doesn't account for the fact that ITT and STT rates tend to be more volatile than LTT rates, or that bond pricing is not linearly rate to duration. So I think I still end up back at 2:1.

A third reason I don't like to go all-in on bonds is that most retail investors take much more risk in stocks. I think that's wrong, but I also don't want to be totally left out if stocks do well and bonds do poorly. Losing money, or making less money, while everyone else does well, is a unique risk and is less desirable than losing money at the same time as everyone else (for both psychological and practical reasons like inflation).

A 4th approach is to calculate the max-drawdown of ITT under various interest rate scenarios, assuming a 5 year bond and using a bond price calculator:

For a 2% rate increase: 9.3% decline
For a 4% rate increase: 17.6% decline
For a 6% rate increase: 25.8% decline

If we are 150% in stocks, using a 1:3 ratio, that would be 450% in bonds. Leveraging a 25.8% decline 450% seems like too much risk to me. I estimate that this would experience a 90% drawdown event, assuming stocks were mostly flat, and assuming monthly rebalancing or fairly narrow rebalancing bands. If stocks decline significantly (perhaps not as much) at the same time, it could be a 100% drawdown. If rebalancing is less frequent, it could be a 100% drawdown. I fudged this PV and took 450% leverage in stocks during a 27% drawdown, and 150% leverage in VSGMX which was basically flat. The portfolio takes a 90% drawdown. If rates rose higher than 6.8%, then the drawdown would be even worse. If you think 6.8% rates are impossible, by all means take 450% leverage in ITT.

https://www.portfoliovisualizer.com/bac ... ion3_3=100


Personally I like 125/250 or 150/300 depending on risk appetite. 150/300 would only experience a 75% drawdown if ITT crashed 25% while stocks were flat, again assuming monthly rebalancing.

https://www.portfoliovisualizer.com/bac ... ion3_3=100

It's tempting to be drawn into massive ITT or STT leverage based on the last couple of decades of consistently falling rates. I don't think that's sustainable. I think one has to be prepared for the possibility of one significant rate cycle increase in the next 30 years.'

Finally, it's not necessary to go beyond a 1:2 ratio to see significant improvement over HFEA. A 125/250 portfolio has nearly as much return as HFEA, with dramatically less risk. A 150/300 has more return than HFEA, with much less risk. IMO, there's no reason to go beyond this.

HFEA would be an 80% drawdown if rates rose 6%, while both of these portfolios would drawdown 75% or less. If you go much above 1:2 ratio, you would be taking more risk in bonds than HFEA. Although ITT have less than 1/3 the duration risk to small/modest rate increasing, bond pricing isn't linear to large changes in rates.

final value / max drawdown for:

HFEA: 4.9M / 65%
125/250: 2.8M / 47%
150/300: 6.6M / 54%

https://www.portfoliovisualizer.com/bac ... ion4_3=150

Personally, I'm currently 125/200 but could go to either of the above in the future.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Bentonkb »

I think it is interesting to run the asset allocation optimizer at PV for a series of backtests using 5 or 10 year periods. You get a different picture of what an efficient portfolio looked like in a variety of different markets. Running one long backtest that covers 30 or 40 years of historical data gives the impression that there is one "efficient" portfolio.

My objective was to find a portfolio that was not optimized for any particular economic environment, but was a reasonable choice for an arbitrarily chosen environment that is similar to something we have seen in the past.

I settled on 180 stocks/140 treasuries/80 gold. It works pretty well with treasuries in the 10 to 20 year duration range. In most of the backtests, the risk is tilted toward stocks - but sometimes the risk is roughly equal. The gold allocation is, in my opinion, an upper bound for a reasonable portfolio. The treasuries allocation is close to the lower bound.

In practice I am using ZB futures, which currently have a duration of 12 years, and GOVT, which currently has a duration of 6 years. For a effective duration of 11 years. The articles that skierincolorado posted about BAB and yield curve surfing have me rethinking my approach. I might be convinced to shift from ZB to ZN, which would bring my effective duration down to 6 years. I'm not sure if I would go all the way up to 280% treasuries in that case.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

Bentonkb wrote: Wed Sep 08, 2021 10:34 am I think it is interesting to run the asset allocation optimizer at PV for a series of backtests using 5 or 10 year periods. You get a different picture of what an efficient portfolio looked like in a variety of different markets. Running one long backtest that covers 30 or 40 years of historical data gives the impression that there is one "efficient" portfolio.

My objective was to find a portfolio that was not optimized for any particular economic environment, but was a reasonable choice for an arbitrarily chosen environment that is similar to something we have seen in the past.

I settled on 180 stocks/140 treasuries/80 gold. It works pretty well with treasuries in the 10 to 20 year duration range. In most of the backtests, the risk is tilted toward stocks - but sometimes the risk is roughly equal. The gold allocation is, in my opinion, an upper bound for a reasonable portfolio. The treasuries allocation is close to the lower bound.

In practice I am using ZB futures, which currently have a duration of 12 years, and GOVT, which currently has a duration of 6 years. For a effective duration of 11 years. The articles that skierincolorado posted about BAB and yield curve surfing have me rethinking my approach. I might be convinced to shift from ZB to ZN, which would bring my effective duration down to 6 years. I'm not sure if I would go all the way up to 280% treasuries in that case.
While the efficient portfolio certainly changes by decade, looking at 40+ years has the advantage of telling us that while in 3 decades the efficient portfolio could have been 1:4 stocks/bonds, such a portfolio did so poorly in the 4th decade it blew up the performance. To end up being efficient over 40 years, you can't take too much risk in any single asset class. So we can look at the most efficient portfolio over many decades, or we could independently calculate the maximum risk we can take in each asset class and then put it back together. Because each asset class is at least reasonably uncorrelated (optimistically at times negatively correlated) we can have confidence that going forward such a portfolio will be reasonably efficient. It's really two ways of asking the same question, and both lead to similar results. Using either method, as I did in my last post, I get around 1:2 stocks:ITT and I find ITT to be exclusively better than LTT. I haven't gone so far as to include a 3rd asset, such as gold. My guess is that efficiency could be improved slightly, but most of the improvement can be achieved with adding bonds to stocks. While gold's correlation with stocks and bonds is less than 1, it also has lower returns. Is there a ticker I can use in PV for gold back to at least 1991?
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Bentonkb »

skierincolorado wrote: Wed Sep 08, 2021 11:05 am While the efficient portfolio certainly changes by decade, looking at 40+ years has the advantage of telling us that while in 3 decades the efficient portfolio could have been 1:4 stocks/bonds, such a portfolio did so poorly in the 4th decade it blew up the performance. To end up being efficient over 40 years, you can't take too much risk in any single asset class. So we can look at the most efficient portfolio over many decades, or we could independently calculate the maximum risk we can take in each asset class and then put it back together. Because each asset class is at least reasonably uncorrelated (optimistically at times negatively correlated) we can have confidence that going forward such a portfolio will be reasonably efficient. It's really two ways of asking the same question, and both lead to similar results. Using either method, as I did in my last post, I get around 1:2 stocks:ITT and I find ITT to be exclusively better than LTT. I haven't gone so far as to include a 3rd asset, such as gold. My guess is that efficiency could be improved slightly, but most of the improvement can be achieved with adding bonds to stocks. While gold's correlation with stocks and bonds is less than 1, it also has lower returns. Is there a ticker I can use in PV for gold back to at least 1991?
It is certainly a good idea to run backtests covering as much history as you can. I just prefer to do it in bite size pieces, rather than one long test.

You are right that adding the second asset provides the biggest diversification benefit. Going from all stock to a stock/bond mix is pretty good. Gold is the obvious third asset. After that there are diminishing returns and it isn't clear what would be the next addition. Some would look at the equities that are least correlated with stocks, which would be things like emerging markets stocks, REITs, or maybe utilities. Some go for alternative investing strategies like trend following managed futures or long volatility trading. I'm just looking to get a good base portfolio going using futures and the big three are all readily available as futures contracts, so I did stocks/bonds/gold.

You can't go back very far in PV using tickers. I think GLD only goes back to 2005. You can go back into the 1970s if you look at asset allocations, though. I also ran similar tests on Portfolio Charts, which is helpful. You can enter in a negative value for T-bills to get the leverage you want.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by LTCM »

skierincolorado wrote: Wed Sep 08, 2021 9:46 am My guess is accounting for the cost of borrowing would shift the ratio lower
This seems to check out. I ran tests from 1992 onwards. Efficient frontier suggest 1:9 stocks/STT. sharpe ratio came out at 1.08 in PV backtest.

Once levered 10x 100/900 that fell to 1.01. Changing the ratios at that point had an equal effect either way. By going to 80/920 or 120/880 sharpe on both fell to 1.00.

On the other hand deleveraging to 100/800 increased sharpe to 1.02 and increasing leverage to 100/1000 decreased sharpe to 1.00.

So all other things being equal less leverage is more efficient. Somewhat obviously I guess. Put another way lower ratios are better because of less leverage not because of the lower ratio.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

LTCM wrote: Wed Sep 08, 2021 12:41 pm
skierincolorado wrote: Wed Sep 08, 2021 9:46 am My guess is accounting for the cost of borrowing would shift the ratio lower
This seems to check out. I ran tests from 1992 onwards. Efficient frontier suggest 1:9 stocks/STT. sharpe ratio came out at 1.08 in PV backtest.

Once levered 10x 100/900 that fell to 1.01. Changing the ratios at that point had an equal effect either way. By going to 80/920 or 120/880 sharpe on both fell to 1.00.

On the other hand deleveraging to 100/800 increased sharpe to 1.02 and increasing leverage to 100/1000 decreased sharpe to 1.00.

So all other things being equal less leverage is more efficient. Somewhat obviously I guess. Put another way lower ratios are better because of less leverage not because of the lower ratio.
Doesn't this show I was wrong? The ratio is still 1:9 even when using leverage. For leveraged and unleveraged I get a 1:9 ratio with a sharpe of 1.02. I think this is because sharpe ratios already subtract out the risk free rate.

I think my other reasons for using a lower ratio are still valid though.
1) longer backtest is better because rates have fallen nearly constantly since 1992.
2) being way more into bonds than other retail investors is a unique risk
3) max-drawdown calculations for 6% interest rate hike limit us to ~300-400% in 5 year bonds
4) extreme bond leverage requires frequent rebalancing
5) we can already significantly improve the sharpe ratio compared to HFEA by using a 1:2 ratio for ITT (5-yr duration)
Last edited by skierincolorado on Wed Sep 08, 2021 1:04 pm, edited 2 times in total.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by DMoogle »

The Sharpe ratio may subtract the risk-free rate by default, but in practice, leverage costs more than that. So Sharpe should decrease as more leverage is introduced.

Because of that, higher leverage will favor investments with higher returns per unit of leverage.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

DMoogle wrote: Wed Sep 08, 2021 1:00 pm The Sharpe ratio may subtract the risk-free rate by default, but in practice, leverage costs more than that. So Sharpe should decrease as more leverage is introduced.

Because of that, higher leverage will favor investments with higher returns per unit of leverage.
In my testing, it doesn't. 1:9 ratio has the highest sharpe ratio for both leveraged and unleveraged. I think this is because PV uses CASH as the cost of leverage and as the risk-free rate. In practice, leverage may cost a hair more than CASH due to transaction costs, but the borrowing cost should be CASH using futures.

100/900: 1.02
110/810: 1.02
120/720: 1.01
130/630: .98
130/1040 takes it back to 1.01... slightly lower sharpe than for 100/800 and 100/900 but that's just because sharpe falls with more leverage.. the optimum ratio is still 1:8 or 1:9, no matter how much leverage

this is since 1992, longer tests would show lower ratios
Last edited by skierincolorado on Wed Sep 08, 2021 1:14 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 DMoogle »

I'm planning on doing this with my taxable account btw. I haven't figured out exact allocations yet, but I'm thinking about targeting 150/300. I have a very high risk tolerance.

I already have about 125% invested in an array of stocks and ETFs that I've acquired over the years. I have some treasury exposure in there from NTSX. I'm not really looking to liquidate what I have without a reason (e.g. tax loss harvesting), but will instead target a portfolio containing:

150% equities, with all new equity investments being in VT.
Currently using margin now for the 125%, but instead will replace that with box spreads.
300% in ZN futures. I'll account for the current exposure I already have from NTSX.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

DMoogle wrote: Wed Sep 08, 2021 1:13 pm I'm planning on doing this with my taxable account btw. I haven't figured out exact allocations yet, but I'm thinking about targeting 150/300. I have a very high risk tolerance.

I already have about 125% invested in an array of stocks and ETFs that I've acquired over the years. I have some treasury exposure in there from NTSX. I'm not really looking to liquidate what I have without a reason (e.g. tax loss harvesting), but will instead target a portfolio containing:

150% equities, with all new equity investments being in VT.
Currently using margin now for the 125%, but instead will replace that with box spreads.
300% in ZN futures. I'll account for the current exposure I already have from NTSX.
Nice, similar to me but a little more leverage and I have more ZF than ZN. But my AA is across my entire liquid NW, taxable and tax-advantaged. What's your reason for doing only in taxable? The tax treatment of the futures isn't great of course. And in the long-run, we're likely to have large stock gains that would be better off in a Roth.

Taking stock leverage in a traditional IRA/401k might actually be worse than in a brokerage account though if I am thinking about it correctly? For contributions, traditional beats brokerage of course. But if you are going to leverage only brokerage or only traditional, weirdly it might be better to leverage brokerage I think. The extra long-term gains will mostly be taxed at LTCG instead of income tax rates. And in the short-term, you could harvest losses from the extra volatility. There would be some tax drag from dividends though.

Also if the strategy does particularly well, or particularly poorly, I'd like a mix of taxable and tax-advantaged monies rather than zero-ing out or having massive growth concentrated in any one account-type.

Also keep in mind the draw-down for a 6% rate increase is 21% for ZF vs 28% for ZN without leverage (fully funded). If you didn't rebalance, 300% leverage in ZN could zero you out. All the backtests using VFITX are more similar to ZF than to ZN.
Last edited by skierincolorado on Wed Sep 08, 2021 1:41 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 »

DMoogle wrote: Wed Sep 08, 2021 8:36 am On that note, is there any value to diversifying across duration?
There does seem to be. I’m not certain I understand why.

https://www.portfoliovisualizer.com/eff ... teTreasury
60% VUG - 20% VEA - 20% EDV
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

LTCM wrote: Wed Sep 08, 2021 1:28 pm
DMoogle wrote: Wed Sep 08, 2021 8:36 am On that note, is there any value to diversifying across duration?
There does seem to be. I’m not certain I understand why.

https://www.portfoliovisualizer.com/eff ... teTreasury
Any assets with decent sharpe ratios and inter-correlations less than 1 are likely to be included in an efficient portfolio.

The correlation between STT ITT and LTT are all less than 1. So it will take some of all of them, although much less LTT (or none) because the LTT sharpe ratio is so poor.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by klaus14 »

Bentonkb wrote: Wed Sep 08, 2021 10:34 am I think it is interesting to run the asset allocation optimizer at PV for a series of backtests using 5 or 10 year periods. You get a different picture of what an efficient portfolio looked like in a variety of different markets. Running one long backtest that covers 30 or 40 years of historical data gives the impression that there is one "efficient" portfolio.

My objective was to find a portfolio that was not optimized for any particular economic environment, but was a reasonable choice for an arbitrarily chosen environment that is similar to something we have seen in the past.

I settled on 180 stocks/140 treasuries/80 gold. It works pretty well with treasuries in the 10 to 20 year duration range. In most of the backtests, the risk is tilted toward stocks - but sometimes the risk is roughly equal. The gold allocation is, in my opinion, an upper bound for a reasonable portfolio. The treasuries allocation is close to the lower bound.

In practice I am using ZB futures, which currently have a duration of 12 years, and GOVT, which currently has a duration of 6 years. For a effective duration of 11 years. The articles that skierincolorado posted about BAB and yield curve surfing have me rethinking my approach. I might be convinced to shift from ZB to ZN, which would bring my effective duration down to 6 years. I'm not sure if I would go all the way up to 280% treasuries in that case.
i also hold leveraged bonds and gold. I do this:
I normalize my bond holdings to have 22 years duration (this is average of TLT and EDV duration which as similar volatility to gold) and then hold equal amounts of gold.
So I have:
6 ZN contracts -> 800k notional exposure -> 232k notional exposure of a 22y duration bond
Then I hold 232k worth Gold. Some of it through GLDM and some of it through /MGC. As I get get close to my retirement i move from /MGC to GLDM (de-lever)
Last edited by klaus14 on Wed Sep 08, 2021 1:46 pm, edited 2 times in total.
My investment algorithm: https://www.bogleheads.org/forum/viewtopic.php?f=10&t=351899&p=6112869#p6112869
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by EfficientInvestor »

skierincolorado wrote: Wed Sep 08, 2021 11:05 am Is there a ticker I can use in PV for gold back to at least 1991?
Use ^gold. It goes back to May 1968.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by LTCM »

skierincolorado wrote: Wed Sep 08, 2021 1:31 pm
LTCM wrote: Wed Sep 08, 2021 1:28 pm
DMoogle wrote: Wed Sep 08, 2021 8:36 am On that note, is there any value to diversifying across duration?
There does seem to be. I’m not certain I understand why.

https://www.portfoliovisualizer.com/eff ... teTreasury
Any assets with decent sharpe ratios and inter-correlations less than 1 are likely to be included in an efficient portfolio.

The correlation between STT ITT and LTT are all less than 1. So it will take some of all of them, although much less LTT (or none) because the LTT sharpe ratio is so poor.
LTT actually almost totally dominates ITT in the efficient portfolio test. I assume because of the correlation issue you mention.

https://www.portfoliovisualizer.com/eff ... ngTreasury
60% VUG - 20% VEA - 20% EDV
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

EfficientInvestor wrote: Wed Sep 08, 2021 1:41 pm
skierincolorado wrote: Wed Sep 08, 2021 11:05 am Is there a ticker I can use in PV for gold back to at least 1991?
Use ^gold. It goes back to May 1968.
I've been wondering what your opinion on all this is. Have you gotten back into STT or ITT? Do you hold gold? I get a 5% allocation to gold in for the 1972-present efficient portfolio with TSM STT and ITT.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

LTCM wrote: Wed Sep 08, 2021 1:44 pm
skierincolorado wrote: Wed Sep 08, 2021 1:31 pm
LTCM wrote: Wed Sep 08, 2021 1:28 pm
DMoogle wrote: Wed Sep 08, 2021 8:36 am On that note, is there any value to diversifying across duration?
There does seem to be. I’m not certain I understand why.

https://www.portfoliovisualizer.com/eff ... teTreasury
Any assets with decent sharpe ratios and inter-correlations less than 1 are likely to be included in an efficient portfolio.

The correlation between STT ITT and LTT are all less than 1. So it will take some of all of them, although much less LTT (or none) because the LTT sharpe ratio is so poor.
LTT actually almost totally dominates ITT in the efficient portfolio test. I assume because of the correlation issue you mention.

https://www.portfoliovisualizer.com/eff ... ngTreasury
It's not LTT dominating ITT really, it's STT dominating both of them and then holding a little LTT for the correlation <1. But the sharpe of holding ITT instead of STT + a little LTT is nearly identical.


TSM/ITT 32/68: .687
TSM/STT/LTT 24/65/11: .695
TSM/LTT: .664

So the sharpe of TSM/ITT is nearly the same as TSM/STT + a little LTT. Which makes sense, because ITT behaves pretty similarly to STT + a little LTT. But TSM/LTT takes a signficiant hit to the sharpe ratio. Yet again showing why LTT are not good - even after borrowing costs since sharpe subtracts out the risk-free rate.

I'd rather hold 200-300% leverage in ITT, than take 500% leverage in STT + 70% LTT, mostly for practical reasons. Also the transaction costs will be lower I think. And if the cost of leverage is a hair higher, it won't matter as much.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by EfficientInvestor »

skierincolorado wrote: Wed Sep 08, 2021 1:49 pm I've been wondering what your opinion on all this is. Have you gotten back into STT or ITT? Do you hold gold? I get a 5% allocation to gold in for the 1972-present efficient portfolio with TSM STT and ITT.
I've been using longer term treasuries ever since rates dropped. My approach to answering the asset allocation question is to plug my broad forward looking assumptions into the efficient frontier forecasting tool on PV. I assume volatility and correlation will continue to be what they have been in the past, because who am I to assume they will be more or less volatile/correlated? If you want to be more conservative and assume a higher correlation of assets, you can upload your own correlation matrix. Here is a model with my current assumptions:

https://www.portfoliovisualizer.com/eff ... ints=false

Feel free to update the stock assumptions. My assumption of 6% for US stocks is a little more aggressive than the latest Vanguard 10 year projection of 3.4% (https://advisors.vanguard.com/insights/ ... august2021). The bond assumptions are based on current yields for the 2, 5, 10, and 20 year treasuries and I would argue that any assumption outside of that is a form of market timing. The assumed return of gold is based on the FED's 2% inflation target.

As you can see from results, the current yields suggest that you should be on the longer end of the curve. As rates rise and the spread between the risk free rate and the shorter end of the curve increases, I suspect it will make more sense to move back towards the middle to short end of the yield curve.

It's interesting to note that if you remove stocks and gold from the analysis and only run treasuries, it results in a portfolio of almost 100% long term treasuries.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by DMoogle »

skierincolorado wrote: Wed Sep 08, 2021 1:26 pmNice, similar to me but a little more leverage and I have more ZF than ZN. But my AA is across my entire liquid NW, taxable and tax-advantaged. What's your reason for doing only in taxable? The tax treatment of the futures isn't great of course. And in the long-run, we're likely to have large stock gains that would be better off in a Roth.
Already using my Roth for HFEA. I suspect this strategy should be a little more tax efficient than that, so figure it makes sense to pursue this with my taxable account, although I could definitely be wrong there. I think there's some value in strategy diversification here, even if minor.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by klaus14 »

EfficientInvestor wrote: Wed Sep 08, 2021 2:08 pm
skierincolorado wrote: Wed Sep 08, 2021 1:49 pm I've been wondering what your opinion on all this is. Have you gotten back into STT or ITT? Do you hold gold? I get a 5% allocation to gold in for the 1972-present efficient portfolio with TSM STT and ITT.
I've been using longer term treasuries ever since rates dropped. My approach to answering the asset allocation question is to plug my broad forward looking assumptions into the efficient frontier forecasting tool on PV. I assume volatility and correlation will continue to be what they have been in the past, because who am I to assume they will be more or less volatile/correlated? If you want to be more conservative and assume a higher correlation of assets, you can upload your own correlation matrix. Here is a model with my current assumptions:

https://www.portfoliovisualizer.com/eff ... ints=false

Feel free to update the stock assumptions. My assumption of 6% for US stocks is a little more aggressive than the latest Vanguard 10 year projection of 3.4% (https://advisors.vanguard.com/insights/ ... august2021). The bond assumptions are based on current yields for the 2, 5, 10, and 20 year treasuries and I would argue that any assumption outside of that is a form of market timing. The assumed return of gold is based on the FED's 2% inflation target.

As you can see from results, the current yields suggest that you should be on the longer end of the curve. As rates rise and the spread between the risk free rate and the shorter end of the curve increases, I suspect it will make more sense to move back towards the middle to short end of the yield curve.

It's interesting to note that if you remove stocks and gold from the analysis and only run treasuries, it results in a portfolio of almost 100% long term treasuries.
You are using the yield of 5y bond for intermediate. I think using 7 year is more appropriate. (intermediate is 5-10 years). This is different than "average duration" being 5 years.
My investment algorithm: https://www.bogleheads.org/forum/viewtopic.php?f=10&t=351899&p=6112869#p6112869
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

klaus14 wrote: Wed Sep 08, 2021 2:28 pm
EfficientInvestor wrote: Wed Sep 08, 2021 2:08 pm
skierincolorado wrote: Wed Sep 08, 2021 1:49 pm I've been wondering what your opinion on all this is. Have you gotten back into STT or ITT? Do you hold gold? I get a 5% allocation to gold in for the 1972-present efficient portfolio with TSM STT and ITT.
I've been using longer term treasuries ever since rates dropped. My approach to answering the asset allocation question is to plug my broad forward looking assumptions into the efficient frontier forecasting tool on PV. I assume volatility and correlation will continue to be what they have been in the past, because who am I to assume they will be more or less volatile/correlated? If you want to be more conservative and assume a higher correlation of assets, you can upload your own correlation matrix. Here is a model with my current assumptions:

https://www.portfoliovisualizer.com/eff ... ints=false

Feel free to update the stock assumptions. My assumption of 6% for US stocks is a little more aggressive than the latest Vanguard 10 year projection of 3.4% (https://advisors.vanguard.com/insights/ ... august2021). The bond assumptions are based on current yields for the 2, 5, 10, and 20 year treasuries and I would argue that any assumption outside of that is a form of market timing. The assumed return of gold is based on the FED's 2% inflation target.

As you can see from results, the current yields suggest that you should be on the longer end of the curve. As rates rise and the spread between the risk free rate and the shorter end of the curve increases, I suspect it will make more sense to move back towards the middle to short end of the yield curve.

It's interesting to note that if you remove stocks and gold from the analysis and only run treasuries, it results in a portfolio of almost 100% long term treasuries.
You are using the yield of 5y bond for intermediate. I think using 7 year is more appropriate. (intermediate is 5-10 years). This is different than "average duration" being 5 years.
PV defines ITT as the 5 year bond.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by EfficientInvestor »

klaus14 wrote: Wed Sep 08, 2021 2:28 pm You are using the yield of 5y bond for intermediate. I think using 7 year is more appropriate. (intermediate is 5-10 years). This is different than "average duration" being 5 years.
Generally speaking, I would agree that intermediate is more around 5-10 years. However, for the purpose of using the PV tool, the 5 year is more appropriate because the PV historical data for the Intermediate Treasury asset is based on VFITX (current duration of 5.1 yrs) since 1992 and based on the FRED data for the 5-year treasury before that. See, "14. Data Sources for Asset Class Returns" at https://www.portfoliovisualizer.com/faq#.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

EfficientInvestor wrote: Wed Sep 08, 2021 2:08 pm
skierincolorado wrote: Wed Sep 08, 2021 1:49 pm I've been wondering what your opinion on all this is. Have you gotten back into STT or ITT? Do you hold gold? I get a 5% allocation to gold in for the 1972-present efficient portfolio with TSM STT and ITT.
I've been using longer term treasuries ever since rates dropped. My approach to answering the asset allocation question is to plug my broad forward looking assumptions into the efficient frontier forecasting tool on PV. I assume volatility and correlation will continue to be what they have been in the past, because who am I to assume they will be more or less volatile/correlated? If you want to be more conservative and assume a higher correlation of assets, you can upload your own correlation matrix. Here is a model with my current assumptions:

https://www.portfoliovisualizer.com/eff ... ints=false

Feel free to update the stock assumptions. My assumption of 6% for US stocks is a little more aggressive than the latest Vanguard 10 year projection of 3.4% (https://advisors.vanguard.com/insights/ ... august2021). The bond assumptions are based on current yields for the 2, 5, 10, and 20 year treasuries and I would argue that any assumption outside of that is a form of market timing. The assumed return of gold is based on the FED's 2% inflation target.

As you can see from results, the current yields suggest that you should be on the longer end of the curve. As rates rise and the spread between the risk free rate and the shorter end of the curve increases, I suspect it will make more sense to move back towards the middle to short end of the yield curve.

It's interesting to note that if you remove stocks and gold from the analysis and only run treasuries, it results in a portfolio of almost 100% long term treasuries.
This is excellent thank you. I think I've thought of two problems though.

1) You're using YTM I think. I think you should be including return from roll. So for example, the YTM of the 5-yr is 0.8%, but the expected returns are front-loaded to the first couple years of holding the bond. If the yield curve does not change at all, a $1000 5-yr bond today with a 0.8% YTM, in two years it will be a $1011 3-yr bond with a 0.44% YTM. You would have experienced a 1.1% price increase over two years, which would add 0.55% to the 0.82% interest you received. You will have returned 1.32%/year for two years. This assumes no change in the yield curve which isn't quite correct either because changes to the yield curve are implicit in current interest rates which brings me to point #2....

2) Implicit in the current yield curve are expected future changes to the yield curve. So for example, the current 30-y rate is high because the market expects the whole curve to shift upwards, including the 30-y rate. Holding the 30-y to maturity, will of course yield today's current rate of ~1.9%. However, implicit in this rate is the market's expectation that the whole curve will shift upwards and steepen slightly. So the expected return of holding a 30-y bond for the next 3 years is probably less than 1.5%. 3 years from now, if market expectations play out, you'd probably be getting back into the short - intermediate durations. But you didn't realize the 1.9% YTM of the 30-y because you didn't hold to maturity. In a worst case scenario, the curve shifts up more than expected, you lose money on the LTT, and then shift into ITT.

For example, the max-carry strategy often positions on the wrong part of the yield curve. Max-carry is still a good strategy, but it's still true that the terms with the greatest carry often experience interest rate increases and price decreases.

#2 would of course affect #1. We can't assume that the yield curve is unchanged as I did in #1.

Given #1 and #2, I think it's far safer to hold the historically efficient portfolio. Unless you can calculate roll (#1) and future changes to the yield curve that are implicit in current rates (#2). I think it's possible to make both of these calculations. I think I've read papers that have attempted to do so. But it's extremely complicated... and would probably lead us straight back to STT and ITT and away from LTT. One solution would be if there is a financial instrument being traded today on what rates will be 2 or 3 years from now. I don't know of such an instrument though.


TLDR: Interest rates are likely to rise. This is implicit in current interest rates. Your assumptions don't factor this in.
Last edited by skierincolorado on Wed Sep 08, 2021 3:26 pm, edited 3 times in total.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by klaus14 »

EfficientInvestor wrote: Wed Sep 08, 2021 2:36 pm
klaus14 wrote: Wed Sep 08, 2021 2:28 pm You are using the yield of 5y bond for intermediate. I think using 7 year is more appropriate. (intermediate is 5-10 years). This is different than "average duration" being 5 years.
Generally speaking, I would agree that intermediate is more around 5-10 years. However, for the purpose of using the PV tool, the 5 year is more appropriate because the PV historical data for the Intermediate Treasury asset is based on VFITX (current duration of 5.1 yrs) since 1992 and based on the FRED data for the 5-year treasury before that. See, "14. Data Sources for Asset Class Returns" at https://www.portfoliovisualizer.com/faq#.
"Duration" being 5 year doesn't mean 5 year bond. 5 year bond has less than 5 years duration. I would guess ~6 year bond is more closer to 5.1 year duration.
My investment algorithm: https://www.bogleheads.org/forum/viewtopic.php?f=10&t=351899&p=6112869#p6112869
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

klaus14 wrote: Wed Sep 08, 2021 3:00 pm
EfficientInvestor wrote: Wed Sep 08, 2021 2:36 pm
klaus14 wrote: Wed Sep 08, 2021 2:28 pm You are using the yield of 5y bond for intermediate. I think using 7 year is more appropriate. (intermediate is 5-10 years). This is different than "average duration" being 5 years.
Generally speaking, I would agree that intermediate is more around 5-10 years. However, for the purpose of using the PV tool, the 5 year is more appropriate because the PV historical data for the Intermediate Treasury asset is based on VFITX (current duration of 5.1 yrs) since 1992 and based on the FRED data for the 5-year treasury before that. See, "14. Data Sources for Asset Class Returns" at https://www.portfoliovisualizer.com/faq#.
"Duration" being 5 year doesn't mean 5 year bond. 5 year bond has less than 5 years duration. I would guess ~6 year bond is more closer to 5.1 year duration.
Good point. Post 1992 PV is basically using a 6 year bond with 5 year duration. Prior to 1992 they are using 5 year bond with 4.5 year duration. However, currently I think 5.3 YTM = 5.1 duration per the VFITX page.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Bentonkb »

klaus14 wrote: Wed Sep 08, 2021 1:41 pm i also hold leveraged bonds and gold. I do this:
I normalize my bond holdings to have 22 years duration (this is average of TLT and EDV duration which as similar volatility to gold) and then hold equal amounts of gold.
So I have:
6 ZN contracts -> 800k notional exposure -> 232k notional exposure of a 22y duration bond
Then I hold 232k worth Gold. Some of it through GLDM and some of it through /MGC. As I get get close to my retirement i move from /MGC to GLDM (de-lever)
I like your investment algorithm, klaus14. (viewtopic.php?f=10&t=351899&p=6112869#p6112869)
My plan is less detailed, but the macroscopic view is probably similar. I'm looking to retire on about $2.3M at some point, so the notional value of my portfolio is about that now. As I get closer to my goal I will bring down my leverage.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by EfficientInvestor »

skierincolorado wrote: Wed Sep 08, 2021 2:56 pm This is excellent thank you. I think I've thought of two problems though.

1) You're using YTM I think. I think you should be including return from roll. So for example, the YTM of the 5-yr is 0.8%, but the expected returns are front-loaded to the first couple years of holding the bond. If the yield curve does not change at all, a $1000 5-yr bond today with a 0.8% YTM, in two years it will be a $1010 3-yr bond with a 0.44% YTM. You would have experienced a 1.1% price increase over two years, which would add 0.55% to the 0.82% interest you received. You will have returned 1.32% for two years. This assumes no change in the yield curve which isn't quite correct either because changes to the yield curve are implicit in current interest rates which brings me to point #2....

2) Implicit in the current yield curve are expected future changes to the yield curve. So for example, the current 30-y rate is high because the market expects the whole curve to shift upwards, including the 30-y rate. Holding the 30-y to maturity, will of course yield today's current rate of ~1.9%. However, implicit in this rate is the market's expectation that the whole curve will shift upwards and steepen slightly. So the expected return of holding a 30-y bond for the next 3 years is probably less than 1.5%. 3 years from now, if market expectations play out, you'd probably be getting back into the short - intermediate durations. But you didn't realize the 1.9% YTM of the 30-y because you didn't hold to maturity. In a worst case scenario, the curve shifts up more than expected, you lose money on the LTT, and then shift into ITT.

For example, the max-carry strategy often positions on the wrong part of the yield curve. Max-carry is still a good strategy, but it's still true that the terms with the greatest carry often experience interest rate increases and price decreases.

#2 would of course affect #1. We can't assume that the yield curve is unchanged as I did in #1.

Given #1 and #2, I think it's far safer to hold the historically efficient portfolio. Unless you can calculate roll (#1) and future changes to the yield curve that are implicit in current rates (#2). I think it's possible to make both of these calculations. I think I've read papers that have attempted to do so. But it's extremely complicated... and would probably lead us straight back to STT and ITT and away from LTT. One solution would be if there is a financial instrument being traded today on what rates will be 2 or 3 years from now. I don't know of such an instrument though.


TLDR: Interest rates are likely to rise. This is implicit in current interest rates. Your assumptions don't factor this in.
First, I'll say you make some good points. However, I think I'll start by saying I like to think of this portfolio construction in two steps. The first step, which requires the determination of a base asset allocation, is done without the investment vehicles in mind. Therefore, any intricacies involving futures contracts are not included when I run my PV models. But then comes the step of figuring out how much to lever up and how to do it. If my analysis shows that I want to have 90% stocks, 60% LTT bonds, and 20% gold, that doesn't necessarily mean I'm going to use bond futures. Maybe I put 60% of my funds towards TLT and the remaining 40% serves as collateral for the stock and gold futures contracts and the issues you pointed out don't apply as much.

I have thought about #2 a good bit in the past but ultimately determined that I feel like it's a version of market timing to assume that interest rates will rise. But then again, the market itself is trying to say that rates will rise, so is it really timing the market or is it just listening to what the market is saying? I ultimately concluded that for determining what the base asset allocation should be it doesn't really matter whether or not you take the assumed movement of the risk free rate into effect because the base allocation isn't borrowing anything.

I don't fully follow you on #1. My gut reaction is to say that any "return from the roll" is due to the current yield being greater than the implied financing rate (risk free rate). So whether using futures on bonds or futures on stocks right now, you would be getting a positive roll because the current risk free rate is less than the expected yield of bonds and less than the expected dividend of stocks.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by EfficientInvestor »

edit/addition to previous post:
Another thing I forgot to add is the assumption of the no-arbitrage argument. If I just hold VFITX or roll a fully collateralized 5-year treasury contract, I should end up with similar returns in the long run. If they weren't, there would be an arbitrage opportunity. Therefore, whether I'm holding VFITX or rolling 5-year treasuries, it doesn't matter. Sometimes the contract will roll rich and sometimes they will roll cheap, but I like to think they will end up equal in the long run.
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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 »

EfficientInvestor wrote: Wed Sep 08, 2021 3:33 pm
skierincolorado wrote: Wed Sep 08, 2021 2:56 pm This is excellent thank you. I think I've thought of two problems though.

1) You're using YTM I think. I think you should be including return from roll. So for example, the YTM of the 5-yr is 0.8%, but the expected returns are front-loaded to the first couple years of holding the bond. If the yield curve does not change at all, a $1000 5-yr bond today with a 0.8% YTM, in two years it will be a $1010 3-yr bond with a 0.44% YTM. You would have experienced a 1.1% price increase over two years, which would add 0.55% to the 0.82% interest you received. You will have returned 1.32% for two years. This assumes no change in the yield curve which isn't quite correct either because changes to the yield curve are implicit in current interest rates which brings me to point #2....

2) Implicit in the current yield curve are expected future changes to the yield curve. So for example, the current 30-y rate is high because the market expects the whole curve to shift upwards, including the 30-y rate. Holding the 30-y to maturity, will of course yield today's current rate of ~1.9%. However, implicit in this rate is the market's expectation that the whole curve will shift upwards and steepen slightly. So the expected return of holding a 30-y bond for the next 3 years is probably less than 1.5%. 3 years from now, if market expectations play out, you'd probably be getting back into the short - intermediate durations. But you didn't realize the 1.9% YTM of the 30-y because you didn't hold to maturity. In a worst case scenario, the curve shifts up more than expected, you lose money on the LTT, and then shift into ITT.

For example, the max-carry strategy often positions on the wrong part of the yield curve. Max-carry is still a good strategy, but it's still true that the terms with the greatest carry often experience interest rate increases and price decreases.

#2 would of course affect #1. We can't assume that the yield curve is unchanged as I did in #1.

Given #1 and #2, I think it's far safer to hold the historically efficient portfolio. Unless you can calculate roll (#1) and future changes to the yield curve that are implicit in current rates (#2). I think it's possible to make both of these calculations. I think I've read papers that have attempted to do so. But it's extremely complicated... and would probably lead us straight back to STT and ITT and away from LTT. One solution would be if there is a financial instrument being traded today on what rates will be 2 or 3 years from now. I don't know of such an instrument though.


TLDR: Interest rates are likely to rise. This is implicit in current interest rates. Your assumptions don't factor this in.
First, I'll say you make some good points. However, I think I'll start by saying I like to think of this portfolio construction in two steps. The first step, which requires the determination of a base asset allocation, is done without the investment vehicles in mind. Therefore, any intricacies involving futures contracts are not included when I run my PV models. But then comes the step of figuring out how much to lever up and how to do it. If my analysis shows that I want to have 90% stocks, 60% LTT bonds, and 20% gold, that doesn't necessarily mean I'm going to use bond futures. Maybe I put 60% of my funds towards TLT and the remaining 40% serves as collateral for the stock and gold futures contracts and the issues you pointed out don't apply as much.

I have thought about #2 a good bit in the past but ultimately determined that I feel like it's a version of market timing to assume that interest rates will rise. But then again, the market itself is trying to say that rates will rise, so is it really timing the market or is it just listening to what the market is saying? I ultimately concluded that for determining what the base asset allocation should be it doesn't really matter whether or not you take the assumed movement of the risk free rate into effect because the base allocation isn't borrowing anything.

I don't fully follow you on #1. My gut reaction is to say that any "return from the roll" is due to the current yield being greater than the implied financing rate (risk free rate). So whether using futures on bonds or futures on stocks right now, you would be getting a positive roll because the current risk free rate is less than the expected yield of bonds and less than the expected dividend of stocks.
Regarding #2, the market isn't just telling us that the RFR is likely to rise. Implicit in the current yield curve is that long-term rates are likely to rise. The 1.9% YTM of the 30-y bond is backloaded to years 3-27, so it doesn't make sense to hold the 30-y for the first 3 years of its life. If the curve evolves the way the market expects, 3 years from now STT and ITT rates will be higher and it still won't make sense to hold the 30-y.

#1 is really important. What you are thinking of is "carry." "Roll" and "carry" are different concepts. Think through holding a $1000 5-yr bond with a 0.82% coupon and no change in the yield curve. 2 years from now it will be a 3-yr bond with a YTM of 0.44%. Thus the price of the bond (use a bond calculator for this) will be $1011. We experienced a 1.1% capital gain (in 2 years) and collected .82% interest each year. Thus our annualized return was ~ .82 + 1.1/2 = 1.37%. The return of a 5-yr bond is front-loaded because you take more risk in the first 2.5 years of owning the bond than the last 2.5 years.

The return of holding 5 year bonds and rolling them every 2 years (or every year, or every 3 months) is substantially higher than holding 5 year bonds to maturity repeatedly. Thus you can't use the YTM of a 5 year bond as the expected return for a strategy of rolling 5 year bonds. The expected return of rolling 5 year bonds is substantially higher than the expected return of repeatedly holding 5 year bonds to maturity. You've used the latter in your assumptions, but should use the former.
Last edited by skierincolorado on Wed Sep 08, 2021 4:01 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 LTCM »

skierincolorado wrote: Wed Sep 08, 2021 2:56 pm One solution would be if there is a financial instrument being traded today on what rates will be 2 or 3 years from now. I don't know of such an instrument though.
https://www.investopedia.com/terms/f/fi ... orward.asp
A fixed income forward is a derivatives contract to buy or sell fixed-income securities at some date in the future, but at a price accepted today.

https://en.wikipedia.org/wiki/Forward_rate
The forward rate is the future yield on a bond. It is calculated using the yield curve. For example, the yield on a three-month Treasury bill six months from now is a forward rate.
60% VUG - 20% VEA - 20% EDV
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

skierincolorado wrote: Wed Sep 08, 2021 3:58 pm

Regarding #2, the market isn't just telling us that the RFR is likely to rise. Implicit in the current yield curve is that long-term rates are likely to rise. The 1.9% YTM of the 30-y bond is backloaded to years 3-27, so it doesn't make sense to hold the 30-y for the first 3 years of its life. If the curve evolves the way the market expects, 3 years from now STT and ITT rates will be higher and it still won't make sense to hold the 30-y.

#1 is really important. What you are thinking of is "carry." "Roll" and "carry" are different concepts. Think through holding a $1000 5-yr bond with a 0.82% coupon and no change in the yield curve. 2 years from now it will be a 3-yr bond with a YTM of 0.44%. Thus the price of the bond (use a bond calculator for this) will be $1011. We experienced a 1.1% capital gain (in 2 years) and collected .82% interest each year. Thus our annualized return was ~ .82 + 1.1/2 = 1.37%. The return of a 5-yr bond is front-loaded because you take more risk in the first 2.5 years of owning the bond than the last 2.5 years.

The return of holding 5 year bonds and rolling them every 2 years (or every year, or every 3 months) is substantially higher than holding 5 year bonds to maturity repeatedly. Thus you can't use the YTM of a 5 year bond as the expected return for a strategy of rolling 5 year bonds. The expected return of rolling 5 year bonds is substantially higher than the expected return of repeatedly holding 5 year bonds to maturity. You've used the latter in your assumptions, but should use the former.
I can see the effect of roll in my transactions. The interest rates on the day I bought and sold my September ZF were nearly the same. However, I netted ~$440 on the trade per contract. This annualizes to 1.43% - far greater than the 0.8% YTM of the 5 year bond. ZF isn't even a 5 year bond, it's a 4.5 year bond with a YTM of 0.7%. But I got 1.4%. That's the effect of roll. I did get about .25% because interest rates dropped .05%. With no change in the yield curve, I expect the return of ZF to be around 1.2%. Not the 0.8% you have assumed. And ZF is a 4.5 year bond, not 5 years. So bumpt it up to 1.3%.
Last edited by skierincolorado on Wed Sep 08, 2021 4:19 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 EfficientInvestor »

skierincolorado wrote: Wed Sep 08, 2021 3:58 pm
EfficientInvestor wrote: Wed Sep 08, 2021 3:33 pm
skierincolorado wrote: Wed Sep 08, 2021 2:56 pm This is excellent thank you. I think I've thought of two problems though.

1) You're using YTM I think. I think you should be including return from roll. So for example, the YTM of the 5-yr is 0.8%, but the expected returns are front-loaded to the first couple years of holding the bond. If the yield curve does not change at all, a $1000 5-yr bond today with a 0.8% YTM, in two years it will be a $1010 3-yr bond with a 0.44% YTM. You would have experienced a 1.1% price increase over two years, which would add 0.55% to the 0.82% interest you received. You will have returned 1.32% for two years. This assumes no change in the yield curve which isn't quite correct either because changes to the yield curve are implicit in current interest rates which brings me to point #2....

2) Implicit in the current yield curve are expected future changes to the yield curve. So for example, the current 30-y rate is high because the market expects the whole curve to shift upwards, including the 30-y rate. Holding the 30-y to maturity, will of course yield today's current rate of ~1.9%. However, implicit in this rate is the market's expectation that the whole curve will shift upwards and steepen slightly. So the expected return of holding a 30-y bond for the next 3 years is probably less than 1.5%. 3 years from now, if market expectations play out, you'd probably be getting back into the short - intermediate durations. But you didn't realize the 1.9% YTM of the 30-y because you didn't hold to maturity. In a worst case scenario, the curve shifts up more than expected, you lose money on the LTT, and then shift into ITT.

For example, the max-carry strategy often positions on the wrong part of the yield curve. Max-carry is still a good strategy, but it's still true that the terms with the greatest carry often experience interest rate increases and price decreases.

#2 would of course affect #1. We can't assume that the yield curve is unchanged as I did in #1.

Given #1 and #2, I think it's far safer to hold the historically efficient portfolio. Unless you can calculate roll (#1) and future changes to the yield curve that are implicit in current rates (#2). I think it's possible to make both of these calculations. I think I've read papers that have attempted to do so. But it's extremely complicated... and would probably lead us straight back to STT and ITT and away from LTT. One solution would be if there is a financial instrument being traded today on what rates will be 2 or 3 years from now. I don't know of such an instrument though.


TLDR: Interest rates are likely to rise. This is implicit in current interest rates. Your assumptions don't factor this in.
First, I'll say you make some good points. However, I think I'll start by saying I like to think of this portfolio construction in two steps. The first step, which requires the determination of a base asset allocation, is done without the investment vehicles in mind. Therefore, any intricacies involving futures contracts are not included when I run my PV models. But then comes the step of figuring out how much to lever up and how to do it. If my analysis shows that I want to have 90% stocks, 60% LTT bonds, and 20% gold, that doesn't necessarily mean I'm going to use bond futures. Maybe I put 60% of my funds towards TLT and the remaining 40% serves as collateral for the stock and gold futures contracts and the issues you pointed out don't apply as much.

I have thought about #2 a good bit in the past but ultimately determined that I feel like it's a version of market timing to assume that interest rates will rise. But then again, the market itself is trying to say that rates will rise, so is it really timing the market or is it just listening to what the market is saying? I ultimately concluded that for determining what the base asset allocation should be it doesn't really matter whether or not you take the assumed movement of the risk free rate into effect because the base allocation isn't borrowing anything.

I don't fully follow you on #1. My gut reaction is to say that any "return from the roll" is due to the current yield being greater than the implied financing rate (risk free rate). So whether using futures on bonds or futures on stocks right now, you would be getting a positive roll because the current risk free rate is less than the expected yield of bonds and less than the expected dividend of stocks.
Regarding #2, the market isn't just telling us that the RFR is likely to rise. Implicit in the current yield curve is that long-term rates are likely to rise. The 1.9% YTM of the 30-y bond is backloaded to years 3-27, so it doesn't make sense to hold the 30-y for the first 3 years of its life. If the curve evolves the way the market expects, 3 years from now STT and ITT rates will be higher and it still won't make sense to hold the 30-y.

#1 is really important. What you are thinking of is "carry." "Roll" and "carry" are different concepts. Think through holding a $1000 5-yr bond with a 0.82% coupon and no change in the yield curve. 2 years from now it will be a 3-yr bond with a YTM of 0.44%. Thus the price of the bond (use a bond calculator for this) will be $1011. We experienced a 1.1% capital gain (in 2 years) and collected .82% interest each year. Thus our annualized return was ~ .82 + 1.1/2 = 1.37%. The return of a 5-yr bond is front-loaded because you take more risk in the first 2.5 years of owning the bond than the last 2.5 years.

The return of holding 5 year bonds and rolling them every 2 years (or every year, or every 3 months) is substantially higher than holding 5 year bonds to maturity repeatedly. Thus you can't use the YTM of a 5 year bond as the expected return for a strategy of rolling 5 year bonds. The expected return of rolling 5 year bonds is substantially higher than the expected return of repeatedly holding 5 year bonds to maturity. You've used the latter in your assumptions, but should use the former.
Ok. I follow what you are saying now. Perhaps where we are talking past each other a bit then is regarding your last paragraph. I'm not trying to compare rolling futures to holding a bond to maturity. I'm comparing the rolling of futures to the holding of a bond fund that is constantly targeting a certain maturity. So, for instance, whether you roll 5-year futures or hold VFITX, you are continually operating around the same place on the yield curve.

To your point about roll...would it then be your opinion that the optimal solution is to buy bonds just to the right of the steepest part of the yield curve so you can take advantage of the greatest fall in yield in the event that the curve doesn't change?
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

EfficientInvestor wrote: Wed Sep 08, 2021 4:18 pm
skierincolorado wrote: Wed Sep 08, 2021 3:58 pm Regarding #2, the market isn't just telling us that the RFR is likely to rise. Implicit in the current yield curve is that long-term rates are likely to rise. The 1.9% YTM of the 30-y bond is backloaded to years 3-27, so it doesn't make sense to hold the 30-y for the first 3 years of its life. If the curve evolves the way the market expects, 3 years from now STT and ITT rates will be higher and it still won't make sense to hold the 30-y.

#1 is really important. What you are thinking of is "carry." "Roll" and "carry" are different concepts. Think through holding a $1000 5-yr bond with a 0.82% coupon and no change in the yield curve. 2 years from now it will be a 3-yr bond with a YTM of 0.44%. Thus the price of the bond (use a bond calculator for this) will be $1011. We experienced a 1.1% capital gain (in 2 years) and collected .82% interest each year. Thus our annualized return was ~ .82 + 1.1/2 = 1.37%. The return of a 5-yr bond is front-loaded because you take more risk in the first 2.5 years of owning the bond than the last 2.5 years.

The return of holding 5 year bonds and rolling them every 2 years (or every year, or every 3 months) is substantially higher than holding 5 year bonds to maturity repeatedly. Thus you can't use the YTM of a 5 year bond as the expected return for a strategy of rolling 5 year bonds. The expected return of rolling 5 year bonds is substantially higher than the expected return of repeatedly holding 5 year bonds to maturity. You've used the latter in your assumptions, but should use the former.
Ok. I follow what you are saying now. Perhaps where we are talking past each other a bit then is regarding your last paragraph. I'm not trying to compare rolling futures to holding a bond to maturity. I'm comparing the rolling of futures to the holding of a bond fund that is constantly targeting a certain maturity. So, for instance, whether you roll 5-year futures or hold VFITX, you are continually operating around the same place on the yield curve.

To your point about roll...would it then be your opinion that the optimal solution is to buy bonds just to the right of the steepest part of the yield curve so you can take advantage of the greatest fall in yield in the event that the curve doesn't change?
The return of VFITX should be the same or a hair higher than rolling ZFs since the duration of VFITX is a hair longer. Rolling ZFs returns 1.2-1.3% currently with no change in the yield curve. We should use 1.3% in your spreadsheet.

I think max-roll is probably a legitimate bond strategy. We discussed a max-carry strategy a few days ago, which there is strong emprical evidence for in domestic and international bond markets. The max-carry duration is currently ZN we calculated. ZF might have more roll than ZN though. You are correct that max-roll is just to the right of the (or at) the steepest part of the yield curve. Max-carry is a little farther right usually. Historically both max-roll and max-carry strategies are invested in STT or ITT.

Max-roll or max-carry strategies are good ideas I'd be interested in learning more about. They are complicated though so I'm not ready to implement. I'm just point out including return from roll means we should use 1.3% instead of 0.8% in your spreadsheet, which would give the efficient frontier a very strong preference for STT or ITT. The part of the curve with max-carry or max-roll has a tendency to experience less favorable interest rate changes though. So maybe you tone it back to 1.2% or 1.1%. But still 0.8% is not correct and anything above 1.0% switches from LTT to ITT. We definitely cannot use 0.8% because the expected return of rolling 5-yr bonds (whether in a bond ETF or using ZF futures) is substantially greater than 0.8% which is the YTM.

The simplest thing to do and what I still favor is just looking at the historical efficient frontier which is heavily STT or ITT across many time periods and international bond markets. There's really no significant time period in the U.S. bond market where LTT would have been a large part of the efficient frontier. This hold true internationally. There's a good reason for this - beta seeking investors overprice LTT as described in the "Betting against Beta" paper.

Also just wanted to make sure you saw my post on rolling my September ZF. It returned ~$440 -per contract or 1.4% despite almost no change in interest rates (-.05%) from purhcase date to sale date. Good illustration of roll and why you always get more than YTM, unless the curve is inverted.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

Back to my second point on future interest rate changes implicit in the current yield curve.

Here are current forward rates:

https://data.nasdaq.com/data/FED/SVEN1F ... rate-curve

The 1 year forward rate 9 years from now is 2.11%. The market expects the 1-yr bond to yield 2.11% 9 years from now.

Unless the yield curve is inverted 9 years from now, the 30-yr bond will lose money as rates rise from 1.9% to something > 2.11%.

This isn't market timing since this is all based on market data. We could do this for all durations and come up with the optimal bond to hold for the next 9 years, or if we use the 1-yr forward rate 4 years from now, we could do this for 4 years from now. We could theoretically figure out the expected returns at each term for the next year, or 4 years, or 9 years. It will NOT be the same as the current interest rate.

But I suspect this will lead us straight back to STT and ITT.
Last edited by skierincolorado on Wed Sep 08, 2021 5:30 pm, edited 3 times in total.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by klaus14 »

Bentonkb wrote: Wed Sep 08, 2021 3:08 pm
klaus14 wrote: Wed Sep 08, 2021 1:41 pm i also hold leveraged bonds and gold. I do this:
I normalize my bond holdings to have 22 years duration (this is average of TLT and EDV duration which as similar volatility to gold) and then hold equal amounts of gold.
So I have:
6 ZN contracts -> 800k notional exposure -> 232k notional exposure of a 22y duration bond
Then I hold 232k worth Gold. Some of it through GLDM and some of it through /MGC. As I get get close to my retirement i move from /MGC to GLDM (de-lever)
I like your investment algorithm, klaus14. (viewtopic.php?f=10&t=351899&p=6112869#p6112869)
My plan is less detailed, but the macroscopic view is probably similar. I'm looking to retire on about $2.3M at some point, so the notional value of my portfolio is about that now. As I get closer to my goal I will bring down my leverage.
Thanks :happy
I have a similar target. I have all my stocks already bought. I have some leverage with gold and bond futures. I am on a glide path to de-lever them to 1x at retirement.

I am debating to keep some leverage with bond futures though. ITT seems more efficient than LTT but you need leverage.
Last edited by klaus14 on Wed Sep 08, 2021 4:56 pm, edited 1 time in total.
My investment algorithm: https://www.bogleheads.org/forum/viewtopic.php?f=10&t=351899&p=6112869#p6112869
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by EfficientInvestor »

skierincolorado wrote: Wed Sep 08, 2021 4:26 pm
EfficientInvestor wrote: Wed Sep 08, 2021 4:18 pm
skierincolorado wrote: Wed Sep 08, 2021 3:58 pm Regarding #2, the market isn't just telling us that the RFR is likely to rise. Implicit in the current yield curve is that long-term rates are likely to rise. The 1.9% YTM of the 30-y bond is backloaded to years 3-27, so it doesn't make sense to hold the 30-y for the first 3 years of its life. If the curve evolves the way the market expects, 3 years from now STT and ITT rates will be higher and it still won't make sense to hold the 30-y.

#1 is really important. What you are thinking of is "carry." "Roll" and "carry" are different concepts. Think through holding a $1000 5-yr bond with a 0.82% coupon and no change in the yield curve. 2 years from now it will be a 3-yr bond with a YTM of 0.44%. Thus the price of the bond (use a bond calculator for this) will be $1011. We experienced a 1.1% capital gain (in 2 years) and collected .82% interest each year. Thus our annualized return was ~ .82 + 1.1/2 = 1.37%. The return of a 5-yr bond is front-loaded because you take more risk in the first 2.5 years of owning the bond than the last 2.5 years.

The return of holding 5 year bonds and rolling them every 2 years (or every year, or every 3 months) is substantially higher than holding 5 year bonds to maturity repeatedly. Thus you can't use the YTM of a 5 year bond as the expected return for a strategy of rolling 5 year bonds. The expected return of rolling 5 year bonds is substantially higher than the expected return of repeatedly holding 5 year bonds to maturity. You've used the latter in your assumptions, but should use the former.
Ok. I follow what you are saying now. Perhaps where we are talking past each other a bit then is regarding your last paragraph. I'm not trying to compare rolling futures to holding a bond to maturity. I'm comparing the rolling of futures to the holding of a bond fund that is constantly targeting a certain maturity. So, for instance, whether you roll 5-year futures or hold VFITX, you are continually operating around the same place on the yield curve.

To your point about roll...would it then be your opinion that the optimal solution is to buy bonds just to the right of the steepest part of the yield curve so you can take advantage of the greatest fall in yield in the event that the curve doesn't change?
The return of VFITX should be the same or a hair higher than rolling ZFs since the duration of VFITX is a hair longer. Rolling ZFs returns 1.2-1.3% currently with no change in the yield curve. We should use 1.3% in your spreadsheet.

I think max-roll is probably a legitimate bond strategy. We discussed a max-carry strategy a few days ago, which there is strong emprical evidence for in domestic and international bond markets. The max-carry duration is currently ZN we calculated. ZF might have more roll than ZN though. You are correct that max-roll is just to the right of the (or at) the steepest part of the yield curve. Max-carry is a little farther right usually. Historically both max-roll and max-carry strategies are invested in STT or ITT.

Max-roll or max-carry strategies are good ideas I'd be interested in learning more about. They are complicated though so I'm not ready to implement. I'm just point out including return from roll means we should use 1.3% instead of 0.8% in your spreadsheet, which would give the efficient frontier a very strong preference for STT or ITT. The part of the curve with max-carry or max-roll has a tendency to experience less favorable interest rate changes though. So maybe you tone it back to 1.2% or 1.1%. But still 0.8% is not correct and anything above 1.0% switches from LTT to ITT. We definitely cannot use 0.8% because the expected return of rolling 5-yr bonds (whether in a bond ETF or using ZF futures) is substantially greater than 0.8% which is the YTM.

The simplest thing to do and what I still favor is just looking at the historical efficient frontier which is heavily STT or ITT across many time periods and international bond markets. There's really no significant time period in the U.S. bond market where LTT would have been a large part of the efficient frontier. This hold true internationally. There's a good reason for this - beta seeking investors overprice LTT as described in the "Betting against Beta" paper.

Also just wanted to make sure you saw my post on rolling my September ZF. It returned ~$440 -per contract or 1.4% despite almost no change in interest rates (-.05%) from purhcase date to sale date. Good illustration of roll and why you always get more than YTM, unless the curve is inverted.
Good stuff. And yes, I saw the comment about ZF. To your point about it being difficult to implement some of these bond strategies...I often wonder if I should just put about 2/3 in ZF and 1/3 in ZN and call it good enough. What I would really like to do at some point is to gather all historical yield data and develop an algorithm that determines the current optimal point on the curve. So this algorithm would be a function of roll and carry I suppose.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

skierincolorado wrote: Wed Sep 08, 2021 4:49 pm Back to my second point on interest rate changes implicit in the current yield curve.

Here are current forward rates:

https://data.nasdaq.com/data/FED/SVEN1F ... rate-curve

The 1 year forward rate 9 years from now is 2.11%. The market expects the 1-yr bond to yield 2.11% 9 years from now.

Unless the yield curve is inverted 9 years from now, the 30-yr bond will lose money as rates rise from 1.9% to something > 2.11%.

This isn't market timing since this is all based on market data. We could do this for all durations and come up with the optimal bond to hold for the next 9 years, or if we use the 1-yr forward rate 4 years from now, we could do this for 4 years from now. We could theoretically figure out the expected returns at each term for the next year, or 4 years, or 9 years. It will NOT be the same as the current interest rate.

But I suspect this will lead us straight back to STT and ITT.
Based on market forward rates, it looks like the expected return of the 30-yr bond is not much more than zero for the next 10 years. Nominally.
Last edited by skierincolorado on Wed Sep 08, 2021 5:27 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 »

EfficientInvestor wrote: Wed Sep 08, 2021 4:52 pm

Good stuff. And yes, I saw the comment about ZF. To your point about it being difficult to implement some of these bond strategies...I often wonder if I should just put about 2/3 in ZF and 1/3 in ZN and call it good enough. What I would really like to do at some point is to gather all historical yield data and develop an algorithm that determines the current optimal point on the curve. So this algorithm would be a function of roll and carry I suppose.
That's exactly my plan until I come up with something better that's rigorously tested. Such an algorithm would of course be trying to beat the market, which I'm skeptical of but the "max-carry" strategy did seem to exhibit significant alpha, although I'm not sure the alpha was significantly greater than just owning a mix of STT and ITT. I don't consider staying shorter than 10-years to be trying to beat the market or true alpha because there are good reasons for LTT to have lower sharpe ratios explainable within CAPM, and those reasons are likely to persist at least to some extent. Unless something has changed, we should assume those same historical forces are priced into current interest rates (implicit in the 30y interest rate is that the 30y interest rate is likely to rise, and the LTT sharpe ratio will continue to be as lousy as it always has been). The market forward rates seem to confirm this idea.
Last edited by skierincolorado on Wed Sep 08, 2021 5:42 pm, edited 1 time in total.
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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 »

EfficientInvestor wrote: Wed Sep 08, 2021 4:52 pm What I would really like to do at some point is to gather all historical yield data and develop an algorithm that determines the current optimal point on the curve. So this algorithm would be a function of roll and carry I suppose.
That would be very useful!

I liked your efficient portfolio approach listed above. What would you amend the rates to based on this discussion (if anything)?
60% VUG - 20% VEA - 20% EDV
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