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

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klaus14
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by klaus14 »

skierincolorado wrote: Fri Sep 10, 2021 2:39 pm In case anyone missed it, this is my "final" estimate.

.3% ITT
.4% LTT
4.5% domestic stock
5% international stock

The efficient frontier is: 34/22/44 domestic stock / intl stock / ITT

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

***This is extremely sensitive to asssumptions. I suggest simply using the historical efficient frontier.***

I sold all my bond futures today.

Reasoning:
I am not confident that backtests apply to today. I was holding $1M worth of /ZN. ZN is close to 7 years maturity. The real yield on 7 years treasury is -1.5%. This is the median of return expectation for the 7 year time frame. So I'll loose (real) ~$15k (plus futures financing cost minus roll down yield)* every year on the average case. Notice that i am not saying rates will go up or down. This is just the mean expectation. Yes negative correlation with equities may help in the event of a recession. However, unlike past, now this hedge has significant costs compared to potential benefit (which is lower since real yields are at the lowest - less room to go down). I couldn't justify this given my investment horizon is very long (I am mid 30s)

*skierincolorado above did more complex math including roll down yield and forward rate estimates. Using that figure, nominal return expectation: 0.3% ITT => real: -2.8% (using breakeven). And quote is from Sept 7 and real rates are worse today.

So now my only bond holdings are: I Bonds, EE Bonds, an old CD yielding 2.75%
I am planning to buy /ZN when 7 years real yield is positive again.

I wish best of luck to everyone in this thread. I learned a lot here.
My investment algorithm: https://www.bogleheads.org/forum/viewtopic.php?f=10&t=351899&p=6112869#p6112869
Topic Author
skierincolorado
Posts: 2377
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

klaus14 wrote: Mon Nov 15, 2021 4:45 pm
skierincolorado wrote: Fri Sep 10, 2021 2:39 pm In case anyone missed it, this is my "final" estimate.

.3% ITT
.4% LTT
4.5% domestic stock
5% international stock

The efficient frontier is: 34/22/44 domestic stock / intl stock / ITT

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

***This is extremely sensitive to asssumptions. I suggest simply using the historical efficient frontier.***

I sold all my bond futures today.

Reasoning:
I am not confident that backtests apply to today. I was holding $1M worth of /ZN. ZN is close to 7 years maturity. The real yield on 7 years treasury is -1.5%. This is the median of return expectation for the 7 year time frame. So I'll loose (real) ~$15k (plus futures financing cost minus roll down yield)* every year on the average case. Notice that i am not saying rates will go up or down. This is just the mean expectation. Yes negative correlation with equities may help in the event of a recession. However, unlike past, now this hedge has significant costs compared to potential benefit. I couldn't justify this given my investment horizon is very long (I am mid 30s)

*skierincolorado above did more complex math including roll down yield and forward rate estimates. Using that figure, nominal return expectation: 0.3% ITT => real: -2.87 (using breakeven). And quote is from Sept 7 and real rates are worse today.

So now my only bond holdings are: I Bonds, EE Bonds, an old CD yielding 2.75%
I am planning to buy /ZN when 7 years real yield is positive again.

I wish best of luck to everyone in this thread. I learned a lot here.
It's not the real return that matters. The nominal return is expected to be positive. Unless the capital is invested in something else with higher expected returns, the return on that capital that was collateral for ZN is now 0%, or -2.5% real. And holding ZN futures requires very little capital. If we say conservatively each contract requires 5k in capital, and returns .4% on the notional value, that's a $500 return on just 5k in capital committed, or 10%. Arguably ZN futures require near-zero capital because I would not be using the capital for anything else if I weren't buying ZFs and ZNs. I've already maxed out my risk budget for equities, and I'm not interested in gold for example.

Let's say one had already maximized the equity exposure as high as comfortable. Say 180% of net worth. Am I going to be better or worse off I add a 300% ITT exposure on top? Almost certainly better off. The 300% ITT exposure has positive expected return, has negative correlation with my equity exposure, and I don't have to forego a single dollar of my equity exposure to achieve it.

Say I had 1M net worth. What is the expected CAGR of 180/0 vs 180/300? The expected return of the latter is much higher, even assuming .4% nominal return on ITT. Even at 0% nominal return, the expected return is much higher.

Negative real returns on bonds is nothing new. Bonds have frequently had negative real returns and did from most of 2012 onwards. And yet HFEA and mHFEA have had tremendous success over an equities only strategy during that period.

mHFEA and HFEA beat a stock only strategy from 1955-1990, despite substantially negative real returns on bonds.
Last edited by skierincolorado on Mon Nov 15, 2021 5:46 pm, edited 2 times in total.
Hfearless
Posts: 135
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Hfearless »

Unfortunately, IBKR data doesn’t go back far, and I don’t know where else to get futures data without splicing consecutive contracts. Anyway:

ZN

Code: Select all

Dec’19 open 2019-08-23 at $131.61 close 2019-11-22 at $129.45 return -1.64%
Mar’20 open 2019-11-22 at $129.50 close 2020-02-21 at $131.86 return  1.82%
Jun’20 open 2020-02-21 at $131.75 close 2020-05-22 at $139.16 return  5.62%
Sep’20 open 2020-05-22 at $138.89 close 2020-08-25 at $139.31 return  0.30%
Dec’20 open 2020-08-25 at $139.17 close 2020-11-24 at $138.25 return -0.66%
Mar’21 open 2020-11-24 at $137.86 close 2021-02-22 at $135.33 return -1.84%
Jun’21 open 2021-02-22 at $134.23 close 2021-05-25 at $132.98 return -0.93%
Sep’21 open 2021-05-25 at $132.08 close 2021-08-25 at $133.62 return  1.17%
Dec’21 open 2021-08-25 at $133.05 close 2021-11-15 at $130.33 return -2.04%
Total return: +1.6% (all returns shown are over the entire period)
VFITX return: +4.4%
Yahoo spliced data return: −0.5%
SPDJI total return: +2.6%


UB

Code: Select all

Dec’19 open 2019-08-23 at $195.78 close 2019-11-22 at $187.84 return -4.05%
Mar’20 open 2019-11-22 at $187.12 close 2020-02-21 at $197.34 return  5.46%
Jun’20 open 2020-02-21 at $198.16 close 2020-05-22 at $221.53 return  11.80%
Sep’20 open 2020-05-22 at $220.00 close 2020-08-25 at $220.03 return  0.01%
Dec’20 open 2020-08-25 at $223.50 close 2020-11-24 at $216.47 return -3.15%
Mar’21 open 2020-11-24 at $214.81 close 2021-02-22 at $192.06 return -10.59%
Jun’21 open 2021-02-22 at $190.38 close 2021-05-25 at $187.78 return -1.36%
Sep’21 open 2021-05-25 at $185.78 close 2021-08-25 at $197.69 return  6.41%
Dec’21 open 2021-08-25 at $195.97 close 2021-11-15 at $193.56 return -1.23%
Total return: +1.6%
VUSTX return: +5.0%
Investing.com spliced data return: −1.9% (for whatever reason, Yahoo won’t show me /UB data)
SPDJI total return: +3.5% (is this the right one?)

Not quite sure what to make out of it.
Topic Author
skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

Hfearless wrote: Mon Nov 15, 2021 5:26 pm Unfortunately, IBKR data doesn’t go back far, and I don’t know where else to get futures data without splicing consecutive contracts. Anyway:

ZN

Code: Select all

Dec’19 open 2019-08-23 at $131.61 close 2019-11-22 at $129.45 return -1.64%
Mar’20 open 2019-11-22 at $129.50 close 2020-02-21 at $131.86 return  1.82%
Jun’20 open 2020-02-21 at $131.75 close 2020-05-22 at $139.16 return  5.62%
Sep’20 open 2020-05-22 at $138.89 close 2020-08-25 at $139.31 return  0.30%
Dec’20 open 2020-08-25 at $139.17 close 2020-11-24 at $138.25 return -0.66%
Mar’21 open 2020-11-24 at $137.86 close 2021-02-22 at $135.33 return -1.84%
Jun’21 open 2021-02-22 at $134.23 close 2021-05-25 at $132.98 return -0.93%
Sep’21 open 2021-05-25 at $132.08 close 2021-08-25 at $133.62 return  1.17%
Dec’21 open 2021-08-25 at $133.05 close 2021-11-15 at $130.33 return -2.04%
Total return: +1.6% (all returns shown are over the entire period)
VFITX return: +4.4%
Yahoo spliced data return: −0.5%
SPDJI total return: +2.6%


UB

Code: Select all

Dec’19 open 2019-08-23 at $195.78 close 2019-11-22 at $187.84 return -4.05%
Mar’20 open 2019-11-22 at $187.12 close 2020-02-21 at $197.34 return  5.46%
Jun’20 open 2020-02-21 at $198.16 close 2020-05-22 at $221.53 return  11.80%
Sep’20 open 2020-05-22 at $220.00 close 2020-08-25 at $220.03 return  0.01%
Dec’20 open 2020-08-25 at $223.50 close 2020-11-24 at $216.47 return -3.15%
Mar’21 open 2020-11-24 at $214.81 close 2021-02-22 at $192.06 return -10.59%
Jun’21 open 2021-02-22 at $190.38 close 2021-05-25 at $187.78 return -1.36%
Sep’21 open 2021-05-25 at $185.78 close 2021-08-25 at $197.69 return  6.41%
Dec’21 open 2021-08-25 at $195.97 close 2021-11-15 at $193.56 return -1.23%
Total return: +1.6%
VUSTX return: +5.0%
Investing.com spliced data return: −1.9% (for whatever reason, Yahoo won’t show me /UB data)
SPDJI total return: +3.5% (is this the right one?)

Not quite sure what to make out of it.
These were the exact analyses we did earlier in the thread definitely go back and read it particularly the posts by zkn :)
Hfearless
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Hfearless »

skierincolorado wrote: Mon Nov 15, 2021 5:30 pm These were the exact analyses we did earlier in the thread definitely go back and read it particularly the posts by zkn
While I do so, I’d like to admonish you and many other participants for egregious overquoting, which makes this task more difficult than it should be ;-)
Topic Author
skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

Hfearless wrote: Mon Nov 15, 2021 5:33 pm While I do so, I’d like to admonish you and many other participants for egregious overquoting, which makes this task more difficult than it should be ;-)
Haha indeed I can be quite lazy with that.

The conclusion to the whole discussion was basically the zkn posts on page 10 but the back and forth is worth a read too

This is a pretty critical post as well:

viewtopic.php?p=6282355#p6282355
klaus14
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by klaus14 »

skierincolorado wrote: Mon Nov 15, 2021 5:06 pm

It's not the real return that matters. The nominal return is expected to be positive. Unless the capital is invested in something else with higher expected returns, the return on that capital that was collateral for ZN is now 0%, or -2.5% real. And holding ZN futures requires very little capital. If we say conservatively each contract requires 5k in capital, and returns .4% on the notional value, that's a $500 return on just 5k in capital committed, or 10%. Arguably ZN futures require near-zero capital because I would not be using the capital for anything else if I weren't buying ZFs and ZNs. I've already maxed out my risk budget for equities, and I'm not interested in gold for example.

Let's say one had already maximized the equity exposure as high as comfortable. Say 180% of net worth. Am I going to be better or worse off I add a 300% ITT exposure on top? Almost certainly better off. The 300% ITT exposure has positive expected return, has negative correlation with my equity exposure, and I don't have to forego a single dollar of my equity exposure to achieve it.

Say I had 1M net worth. What is the expected CAGR of 180/0 vs 180/300? The expected return of the latter is much higher, even assuming .4% nominal return on ITT. Even at 0% nominal return, the expected return is much higher.

Negative real returns on bonds is nothing new. Bonds have frequently had negative real returns and did from most of 2012 onwards. And yet HFEA and mHFEA have had tremendous success over an equities only strategy during that period.

mHFEA and HFEA beat a stock only strategy from 1955-1990, despite substantially negative real returns on bonds.
you have a point. 0.4% is still uncomfortably close to zero but i think i need to better understand your expected return calculation.
I see forward rates for 1y treasury here. But how do you find out forward rates for 5y treasury ?
My investment algorithm: https://www.bogleheads.org/forum/viewtopic.php?f=10&t=351899&p=6112869#p6112869
Topic Author
skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

klaus14 wrote: Mon Nov 15, 2021 6:02 pm
skierincolorado wrote: Mon Nov 15, 2021 5:06 pm

It's not the real return that matters. The nominal return is expected to be positive. Unless the capital is invested in something else with higher expected returns, the return on that capital that was collateral for ZN is now 0%, or -2.5% real. And holding ZN futures requires very little capital. If we say conservatively each contract requires 5k in capital, and returns .4% on the notional value, that's a $500 return on just 5k in capital committed, or 10%. Arguably ZN futures require near-zero capital because I would not be using the capital for anything else if I weren't buying ZFs and ZNs. I've already maxed out my risk budget for equities, and I'm not interested in gold for example.

Let's say one had already maximized the equity exposure as high as comfortable. Say 180% of net worth. Am I going to be better or worse off I add a 300% ITT exposure on top? Almost certainly better off. The 300% ITT exposure has positive expected return, has negative correlation with my equity exposure, and I don't have to forego a single dollar of my equity exposure to achieve it.

Say I had 1M net worth. What is the expected CAGR of 180/0 vs 180/300? The expected return of the latter is much higher, even assuming .4% nominal return on ITT. Even at 0% nominal return, the expected return is much higher.

Negative real returns on bonds is nothing new. Bonds have frequently had negative real returns and did from most of 2012 onwards. And yet HFEA and mHFEA have had tremendous success over an equities only strategy during that period.

mHFEA and HFEA beat a stock only strategy from 1955-1990, despite substantially negative real returns on bonds.
you have a point. 0.4% is still uncomfortably close to zero but i think i need to better understand your expected return calculation.
I see forward rates for 1y treasury here. But how do you find out forward rates for 5y treasury ?
The problem we found was that those forward rates include a term premium. So the market doesn't actually expect rates that high but the contracts trade at those levels because of the risk involved. Assuming the term premium is positive. But it's no guarantee the term premium is actually positive and there are various ways to estimate. The term premium could actually be negative, and the market really expects rates to be even higher than forward rates indicate in the future. The concept we are really interested in is term premium. Personally I think it's unlikely the term premium is actually negative. One could rely on the fed dot plot.
klaus14
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by klaus14 »

skierincolorado wrote: Mon Nov 15, 2021 6:17 pm
klaus14 wrote: Mon Nov 15, 2021 6:02 pm
skierincolorado wrote: Mon Nov 15, 2021 5:06 pm

It's not the real return that matters. The nominal return is expected to be positive. Unless the capital is invested in something else with higher expected returns, the return on that capital that was collateral for ZN is now 0%, or -2.5% real. And holding ZN futures requires very little capital. If we say conservatively each contract requires 5k in capital, and returns .4% on the notional value, that's a $500 return on just 5k in capital committed, or 10%. Arguably ZN futures require near-zero capital because I would not be using the capital for anything else if I weren't buying ZFs and ZNs. I've already maxed out my risk budget for equities, and I'm not interested in gold for example.

Let's say one had already maximized the equity exposure as high as comfortable. Say 180% of net worth. Am I going to be better or worse off I add a 300% ITT exposure on top? Almost certainly better off. The 300% ITT exposure has positive expected return, has negative correlation with my equity exposure, and I don't have to forego a single dollar of my equity exposure to achieve it.

Say I had 1M net worth. What is the expected CAGR of 180/0 vs 180/300? The expected return of the latter is much higher, even assuming .4% nominal return on ITT. Even at 0% nominal return, the expected return is much higher.

Negative real returns on bonds is nothing new. Bonds have frequently had negative real returns and did from most of 2012 onwards. And yet HFEA and mHFEA have had tremendous success over an equities only strategy during that period.

mHFEA and HFEA beat a stock only strategy from 1955-1990, despite substantially negative real returns on bonds.
you have a point. 0.4% is still uncomfortably close to zero but i think i need to better understand your expected return calculation.
I see forward rates for 1y treasury here. But how do you find out forward rates for 5y treasury ?
The problem we found was that those forward rates include a term premium. So the market doesn't actually expect rates that high but the contracts trade at those levels because of the risk involved. Assuming the term premium is positive. But it's no guarantee the term premium is actually positive and there are various ways to estimate. The term premium could actually be negative, and the market really expects rates to be even higher than forward rates indicate in the future. The concept we are really interested in is term premium. Personally I think it's unlikely the term premium is actually negative. One could rely on the fed dot plot.
thanks. still, what value do you use for the rate of 5y one year hence? Or how do you calculate expected returns?
Last edited by klaus14 on Mon Nov 15, 2021 7:31 pm, edited 1 time in total.
My investment algorithm: https://www.bogleheads.org/forum/viewtopic.php?f=10&t=351899&p=6112869#p6112869
Hfearless
Posts: 135
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Hfearless »

skierincolorado wrote: Mon Nov 15, 2021 5:30 pm These were the exact analyses we did earlier in the thread definitely go back and read it particularly the posts by zkn
Having re-read much of that (which is far from the first time I referred to those highly informative messages), I daresay that the useful research you performed did not include raw, non-spliced futures data. Anyway I simulated the 100% VOO, 200% /ZN portfolio using IBKR data and got this:

Code: Select all

             VOO     ZN Δ        VOO       /ZN
            (adj.)                   (exposure)
2019-08-23  251.83          $100,000  $200,000
2019-11-22  276.32  -1.64%  $106,446  $212,891
2020-02-21  297.91   1.82%  $118,640  $237,280
2020-05-22  265.19   5.62%  $118,943  $237,887
2020-08-25  310.40   0.30%  $139,934  $279,869
2020-11-24  329.01  -0.66%  $146,479  $292,958
2021-02-22  352.17  -1.84%  $151,396  $302,793
2021-05-25  381.96  -0.93%  $161,388  $322,775
2021-08-25  411.28   1.17%  $177,554  $355,107
2021-11-15  429.77  -2.04%  $178,292  $356,583
giving a CAGR of 30%, perfectly matching what PV shows for 33% UPRO, 66% TYD or variations thereof. (I’m pretending that /ZN can be divided into small chunks.) The ZN<VFITX underperformance (about 1 p. p. annualized) must be compensated by LETF expense ratios or borrowing costs.

I’d very much like to do the same for a period where rates were higher, does anybody know where to find unspliced data for interesting periods such as 2006–2007? Nasdaq Data Link seems to have it but requires a $999 subscription :-(
km91
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by km91 »

How can I implement this strategy in my portfolio in a way that requires minimal management on my part? My current portfolio is 100% equities, held as globally diversified index funds. I want to overlay the UST futures to get 90/60 equities/bonds and set it and forget to the extent possible
Hfearless
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Hfearless »

km91 wrote: Mon Nov 15, 2021 7:52 pm How can I implement this strategy in my portfolio in a way that requires minimal management on my part? My current portfolio is 100% equities, held as globally diversified index funds. I want to overlay the UST futures to get 90/60 equities/bonds and set it and forget to the extent possible
That’s literally NTSX. mHFEA would be something like 40% UPRO 60% TYD (or TYA).
km91
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by km91 »

Hfearless wrote: Mon Nov 15, 2021 7:54 pm
km91 wrote: Mon Nov 15, 2021 7:52 pm How can I implement this strategy in my portfolio in a way that requires minimal management on my part? My current portfolio is 100% equities, held as globally diversified index funds. I want to overlay the UST futures to get 90/60 equities/bonds and set it and forget to the extent possible
That’s literally NTSX. mHFEA would be something like 40% UPRO 60% TYD (or TYA).
Is 40% UPRO / 60% TYD preferred over 55% UPRO / 45% TMF?When does it make sense to use futures?
Hfearless
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Hfearless »

km91 wrote: Mon Nov 15, 2021 9:24 pm Is 40% UPRO / 60% TYD preferred over 55% UPRO / 45% TMF?When does it make sense to use futures?
Well, in backtests the former has a better risk-adjusted return. But in absolute terms, the return is slightly lower so it needs to be leveraged more. But if you’re doing this with all your net worth (a risky proposition for sure), you don’t have any more room for leveraging using ETFs so you need futures.

This is basically a tl;dr, read the thread for lots of technical detail.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

DMoogle wrote: Sun Nov 14, 2021 10:58 am At a glance, however, I see two downsides:
  • It's far lower volume than the non-micro treasuries, i.e. probably bigger spreads/less efficiency (although maybe this isn't that big of a deal).
  • The expiration schedule is monthly, not quarterly. Since practically all the volume is with the nearest month, this means you'll have to roll over monthly. Little bit of a hassle.
Interesting to hear they're launching a "nano" size contract. Curious to see if that takes off.
"The expiration schedule is monthly, not quarterly." - Thanks for reminding me. It's a deal-breaker for me. They tried to keep retail investors really busy. Meanwhile, the pros who already sit at their computer terminals every day, get the quarterly futures. Hard to understand.
Last edited by comeinvest on Tue Nov 16, 2021 5:11 pm, edited 1 time in total.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

Hfearless wrote: Mon Nov 15, 2021 6:54 pm I’d very much like to do the same for a period where rates were higher, does anybody know where to find unspliced data for interesting periods such as 2006–2007? Nasdaq Data Link seems to have it but requires a $999 subscription :-(
I think there are some places on the internet with free historical futures data, but I think the bigger problem is getting historical futures duration data for backtesting duration-matched strategies.
Last edited by comeinvest on Tue Nov 16, 2021 5:12 pm, edited 1 time in total.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Sat Nov 13, 2021 10:33 am
DMoogle wrote: Fri Nov 12, 2021 6:49 pm The net value of the portfolio I'm doing this with is $480k. Current allocation is around $700k in equities and around $1.2M in ZN (9 contracts). I have a very high risk tolerance. ZN got fairly wrecked the past quarter (my portion on it is down $27k since I started on it), but whatevs - I agree with the fundamental concepts behind this strategy, and it's not for the faint of heart.

So when I roll over my futures in the coming month, current thought is to (based on the contract prices above) liquidate the ZN contracts for maybe:
5 contracts ZF ($484k)
3 contracts ZN ($390k)
1 contract TN ($145k)
1 contract ZB ($161k)
For a total of $1.18M exposure (similar to now), and probably keep my current equities (or tax loss harvest if I can).
I think this is equal risk in ZB as ZF. I think the weighted duration would be just over 8 years.

Even during periods of flattening when the 8 year rate dropped more than the 5 year rate, the 5 year rate has significantly outperformed. I'd try to keep the weighted duration somewhat close to 5. During periods of non-flattening, the outperformance of 5 year has been even greater...
But I think the weighted duration of his proposed portfolio is about 6.5 years, not 8 years. If by "weighted duration" you meant "duration-weighted duration", I'm not sure how meaningful that definition would be :) If you look at his proposed portfolio, the notional values are already very much tilted towards the shorter durations. Further bias to the shorter durations would make the effect of the longer durations as diversifiers rather meaningless, should the relative performance of treasuries of the different durations ever vary.
In summary, I'm still not sure if duration-adjusted distribution across the maturity range makes sense, or should it be risk-adjusted or by notional value, or somewhere in between (something that probably only a risk-adjusted backtest would answer); but I definitely struggle with the concept of duration-weighted duration.
zkn
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by zkn »

New blog post on tax efficiency of futures based bond funds by Simplify (responsible for TYA):
https://www.simplify.us/blog/can-future ... efficiency

The key message for me is that they assume the "hypothetical futures-based U.S. Treasury funds" are taxed like futures under Section 1256. I was wondering if Simplify would be able to pull off some trick to convert interest into long term capital gains (like swap-based TMF/TYD), but this does not seem to be the case if their assumptions here apply to TYA. With no tax benefit, I am not aware of any reason except convenience to use TYA instead of futures directly, unless using futures directly is not an option.

Otherwise the article shows the tax efficiency of bond futures versus holding bonds directly or in an ETF.
DMoogle
Posts: 549
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by DMoogle »

comeinvest wrote: Tue Nov 16, 2021 5:53 am
skierincolorado wrote: Sat Nov 13, 2021 10:33 am
DMoogle wrote: Fri Nov 12, 2021 6:49 pm The net value of the portfolio I'm doing this with is $480k. Current allocation is around $700k in equities and around $1.2M in ZN (9 contracts). I have a very high risk tolerance. ZN got fairly wrecked the past quarter (my portion on it is down $27k since I started on it), but whatevs - I agree with the fundamental concepts behind this strategy, and it's not for the faint of heart.

So when I roll over my futures in the coming month, current thought is to (based on the contract prices above) liquidate the ZN contracts for maybe:
5 contracts ZF ($484k)
3 contracts ZN ($390k)
1 contract TN ($145k)
1 contract ZB ($161k)
For a total of $1.18M exposure (similar to now), and probably keep my current equities (or tax loss harvest if I can).
I think this is equal risk in ZB as ZF. I think the weighted duration would be just over 8 years.

Even during periods of flattening when the 8 year rate dropped more than the 5 year rate, the 5 year rate has significantly outperformed. I'd try to keep the weighted duration somewhat close to 5. During periods of non-flattening, the outperformance of 5 year has been even greater...
But I think the weighted duration of his proposed portfolio is about 6.5 years, not 8 years. If by "weighted duration" you meant "duration-weighted duration", I'm not sure how meaningful that definition would be :) If you look at his proposed portfolio, the notional values are already very much tilted towards the shorter durations. Further bias to the shorter durations would make the effect of the longer durations as diversifiers rather meaningless, should the relative performance of treasuries of the different durations ever vary.
In summary, I'm still not sure if duration-adjusted distribution across the maturity range makes sense, or should it be risk-adjusted or by notional value, or somewhere in between (something that probably only a risk-adjusted backtest would answer); but I definitely struggle with the concept of duration-weighted duration.
OK correct me if any of this is wrong:
Contract | Approx.Duration
ZF | 5
ZN | 8
TN | 10
ZB | 20

Sumproducting the # of contracts I chose would equal 79 (meaningless number), divide that by total number of contracts (10) equals a weighted average duration of 7.9.
Topic Author
skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Tue Nov 16, 2021 5:53 am
skierincolorado wrote: Sat Nov 13, 2021 10:33 am
DMoogle wrote: Fri Nov 12, 2021 6:49 pm The net value of the portfolio I'm doing this with is $480k. Current allocation is around $700k in equities and around $1.2M in ZN (9 contracts). I have a very high risk tolerance. ZN got fairly wrecked the past quarter (my portion on it is down $27k since I started on it), but whatevs - I agree with the fundamental concepts behind this strategy, and it's not for the faint of heart.

So when I roll over my futures in the coming month, current thought is to (based on the contract prices above) liquidate the ZN contracts for maybe:
5 contracts ZF ($484k)
3 contracts ZN ($390k)
1 contract TN ($145k)
1 contract ZB ($161k)
For a total of $1.18M exposure (similar to now), and probably keep my current equities (or tax loss harvest if I can).
I think this is equal risk in ZB as ZF. I think the weighted duration would be just over 8 years.

Even during periods of flattening when the 8 year rate dropped more than the 5 year rate, the 5 year rate has significantly outperformed. I'd try to keep the weighted duration somewhat close to 5. During periods of non-flattening, the outperformance of 5 year has been even greater...
But I think the weighted duration of his proposed portfolio is about 6.5 years, not 8 years. If by "weighted duration" you meant "duration-weighted duration", I'm not sure how meaningful that definition would be :) If you look at his proposed portfolio, the notional values are already very much tilted towards the shorter durations. Further bias to the shorter durations would make the effect of the longer durations as diversifiers rather meaningless, should the relative performance of treasuries of the different durations ever vary.
In summary, I'm still not sure if duration-adjusted distribution across the maturity range makes sense, or should it be risk-adjusted or by notional value, or somewhere in between (something that probably only a risk-adjusted backtest would answer); but I definitely struggle with the concept of duration-weighted duration.
When you think of it as equal risk/return in zb as zf in his portfolio, it seems too long to me. I think that is what duration weighted duration represents. I would not want half my risk and return from the part of the curve with historically low risk adjusted returns and where the current curve is pretty flat. Maybe a little would be ok for diversification. But I think he’d find a lot of the daily moves were coming from the zb. Part of the problem is the notional value is so high for that contract.

Either way, I see the bigger problem being switching from zn to something longer. Having suffered through the last few months of Zn I would not want to be making big changes to my Aa now. I would go for a more subtle diversification.
hdas
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by hdas »

hhhhhh
Last edited by hdas on Tue Nov 23, 2021 12:33 pm, edited 1 time in total.
....
Topic Author
skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

hdas wrote: Tue Nov 16, 2021 9:12 am
skierincolorado wrote: Tue Nov 16, 2021 8:33 am Having suffered through the last few months of Zn I would not want to be making big changes to my Aa now. I would go for a more subtle diversification.
You didn't have to suffer, if you had looked at the data and realized that the out-under performance of this scheme is totally attributed to the flattening/steepening cycle, i.e the term premium. Just create a term premium series using 5/30 curve and run the regression.

Image
We’ve been over this. I challenge you to come up with a rules based backtest that outperforms buy and hold. For example, I’m highly skeptical that any rules based approach could have predicted the strong ITT returns from 2010 to 2015. And even if it did it was likely just data mining and overfit.

You’ve picked 2018 as the endpoint for a switch. What if COViD happened in 2017?

Pick a rule and test it. If the rule is simple and the test robust I would seriously consider following it.
hdas
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by hdas »

hhhhhhh
Last edited by hdas on Tue Nov 23, 2021 12:34 pm, edited 1 time in total.
....
Topic Author
skierincolorado
Posts: 2377
Joined: Sat Mar 21, 2020 10:56 am

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

Post by skierincolorado »

hdas wrote: Tue Nov 16, 2021 9:41 am
skierincolorado wrote: Tue Nov 16, 2021 9:13 am I’m highly skeptical that any rules based approach could have predicted the strong ITT returns from 2010 to 2015.
This statement is baffling, in 2010 the term premium was screaming BUY!!!!!!!!!. Highest ever since we have good data (late 80's)
skierincolorado wrote: Tue Nov 16, 2021 9:13 am You’ve picked 2018 as the endpoint for a switch. What if COViD happened in 2017?
Why do you keep dismissing the valuable information you get from the curve?.........Anybody can see that the attractiveness of LTT over ITT is different if the spread is 3% or 0.2%. What is so difficult to understand?. Since you are such a fan of backtests, have you tested the relative performance of LTT vs ITT CONDITIONAL on the spread level?
Again, come up with a rules based strategy and test it, or this is all talk. I've read several papers that have attempted this sort of dynamic rules based strategy, and there is some slight outperformance - but not the type of outperformance you seem to think and there is no guarantee it's not simply data mining and overfitting. The idea that you're going to get dramatic outperformance from such a simple strategy is simply contrary to EMH. I don’t have to backtest it - other people already have - and EMH tells us the type of outperformance you are talking about is unlikely.
Last edited by skierincolorado on Tue Nov 16, 2021 10:54 am, edited 2 times in total.
Lock
Posts: 98
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Lock »

klaus14 wrote: Mon Nov 15, 2021 4:45 pm
skierincolorado wrote: Fri Sep 10, 2021 2:39 pm In case anyone missed it, this is my "final" estimate.

.3% ITT
.4% LTT
4.5% domestic stock
5% international stock

The efficient frontier is: 34/22/44 domestic stock / intl stock / ITT

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

***This is extremely sensitive to asssumptions. I suggest simply using the historical efficient frontier.***

I sold all my bond futures today.

Reasoning:
I am not confident that backtests apply to today. I was holding $1M worth of /ZN. ZN is close to 7 years maturity. The real yield on 7 years treasury is -1.5%. This is the median of return expectation for the 7 year time frame. So I'll loose (real) ~$15k (plus futures financing cost minus roll down yield)* every year on the average case. Notice that i am not saying rates will go up or down. This is just the mean expectation. Yes negative correlation with equities may help in the event of a recession. However, unlike past, now this hedge has significant costs compared to potential benefit (which is lower since real yields are at the lowest - less room to go down). I couldn't justify this given my investment horizon is very long (I am mid 30s)

*skierincolorado above did more complex math including roll down yield and forward rate estimates. Using that figure, nominal return expectation: 0.3% ITT => real: -2.8% (using breakeven). And quote is from Sept 7 and real rates are worse today.

So now my only bond holdings are: I Bonds, EE Bonds, an old CD yielding 2.75%
I am planning to buy /ZN when 7 years real yield is positive again.

I wish best of luck to everyone in this thread. I learned a lot here.
Why not just go short (i.e. sell contracts)? YTD the stock/bond correlation has been positive so you can re-create a negative correlation asset.

Disclaimer: I've been running a risk parity portfolio for about 3 years and this year I sold ZN contracts for the first time.
Topic Author
skierincolorado
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Joined: Sat Mar 21, 2020 10:56 am

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

Post by skierincolorado »

Lock wrote: Tue Nov 16, 2021 10:29 am
klaus14 wrote: Mon Nov 15, 2021 4:45 pm
skierincolorado wrote: Fri Sep 10, 2021 2:39 pm In case anyone missed it, this is my "final" estimate.

.3% ITT
.4% LTT
4.5% domestic stock
5% international stock

The efficient frontier is: 34/22/44 domestic stock / intl stock / ITT

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

***This is extremely sensitive to asssumptions. I suggest simply using the historical efficient frontier.***

I sold all my bond futures today.

Reasoning:
I am not confident that backtests apply to today. I was holding $1M worth of /ZN. ZN is close to 7 years maturity. The real yield on 7 years treasury is -1.5%. This is the median of return expectation for the 7 year time frame. So I'll loose (real) ~$15k (plus futures financing cost minus roll down yield)* every year on the average case. Notice that i am not saying rates will go up or down. This is just the mean expectation. Yes negative correlation with equities may help in the event of a recession. However, unlike past, now this hedge has significant costs compared to potential benefit (which is lower since real yields are at the lowest - less room to go down). I couldn't justify this given my investment horizon is very long (I am mid 30s)

*skierincolorado above did more complex math including roll down yield and forward rate estimates. Using that figure, nominal return expectation: 0.3% ITT => real: -2.8% (using breakeven). And quote is from Sept 7 and real rates are worse today.

So now my only bond holdings are: I Bonds, EE Bonds, an old CD yielding 2.75%
I am planning to buy /ZN when 7 years real yield is positive again.

I wish best of luck to everyone in this thread. I learned a lot here.
Why not just go short (i.e. sell contracts)? YTD the stock/bond correlation has been positive so you can re-create a negative correlation asset.

Disclaimer: I've been running a risk parity portfolio for about 3 years and this year I sold ZN contracts for the first time.
1)Because the expected return of zn is still likely positive for the long position and negative for the short.

2)I would guess the correlation was also positive in 2018 and 2019 leaving you caught red handed in 2020.

3)The difference between a +.05 and -.05 correlation is trivial and both would more accurately be described as uncorrelated. The strategy works not because the correlation between stocks and bonds has ever truly been significantly negative, but because we are able to take more risk in each bucket without increasing our overall risk because the buckets are uncorrelated. And the return of each bucket is positive.
comeinvest
Posts: 2669
Joined: Mon Mar 12, 2012 6:57 pm

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

Post by comeinvest »

skierincolorado wrote: Tue Nov 16, 2021 10:50 am
Lock wrote: Tue Nov 16, 2021 10:29 am
klaus14 wrote: Mon Nov 15, 2021 4:45 pm
skierincolorado wrote: Fri Sep 10, 2021 2:39 pm In case anyone missed it, this is my "final" estimate.

.3% ITT
.4% LTT
4.5% domestic stock
5% international stock

The efficient frontier is: 34/22/44 domestic stock / intl stock / ITT

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

***This is extremely sensitive to asssumptions. I suggest simply using the historical efficient frontier.***

I sold all my bond futures today.

Reasoning:
I am not confident that backtests apply to today. I was holding $1M worth of /ZN. ZN is close to 7 years maturity. The real yield on 7 years treasury is -1.5%. This is the median of return expectation for the 7 year time frame. So I'll loose (real) ~$15k (plus futures financing cost minus roll down yield)* every year on the average case. Notice that i am not saying rates will go up or down. This is just the mean expectation. Yes negative correlation with equities may help in the event of a recession. However, unlike past, now this hedge has significant costs compared to potential benefit (which is lower since real yields are at the lowest - less room to go down). I couldn't justify this given my investment horizon is very long (I am mid 30s)

*skierincolorado above did more complex math including roll down yield and forward rate estimates. Using that figure, nominal return expectation: 0.3% ITT => real: -2.8% (using breakeven). And quote is from Sept 7 and real rates are worse today.

So now my only bond holdings are: I Bonds, EE Bonds, an old CD yielding 2.75%
I am planning to buy /ZN when 7 years real yield is positive again.

I wish best of luck to everyone in this thread. I learned a lot here.
Why not just go short (i.e. sell contracts)? YTD the stock/bond correlation has been positive so you can re-create a negative correlation asset.

Disclaimer: I've been running a risk parity portfolio for about 3 years and this year I sold ZN contracts for the first time.
1)Because the expected return of zn is still likely positive for the long position and negative for the short.

2)I would guess the correlation was also positive in 2018 and 2019 leaving you caught red handed in 2020.

3)The difference between a +.05 and -.05 correlation is trivial and both would more accurately be described as uncorrelated. The strategy works not because the correlation between stocks and bonds has ever truly been significantly negative, but because we are able to take more risk in each bucket without increasing our overall risk because the buckets are uncorrelated. And the return of each bucket is positive.
But the expected returns of all treasury futures are currently negative if we believe the ACM model. I know I said the same about 2 pages upthread, and your answer was that your confidence in the ACM model is not that high, or you think it's too pessimistic. I must admit I don't really understand the ACM model, but it seems like somebody put way more thought into estimating term premia than I ever did. Although it seems to at least partially based on surveys, so I'm not sure about its confidence level. However it doesn't strike me as pessimistic, considering that the real returns are hugely negative for all treasury bonds, i.e. investors in treasuries knowingly transfer wealth to somebody else - why would anybody do that? On the other hand one could argue it's pessimistic, considering that most of the developed world has more negative yields. Investors that make the market must assume that all or most assets have negative returns in the future, and that there is no good way to park larger amounts of money for free. Weird world. I don't find Klaus' decision necessarily irrational, but his reasoning and supporting math was definitely wrong.
comeinvest
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Joined: Mon Mar 12, 2012 6:57 pm

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

Post by comeinvest »

DMoogle wrote: Tue Nov 16, 2021 8:25 am
comeinvest wrote: Tue Nov 16, 2021 5:53 am
skierincolorado wrote: Sat Nov 13, 2021 10:33 am
DMoogle wrote: Fri Nov 12, 2021 6:49 pm The net value of the portfolio I'm doing this with is $480k. Current allocation is around $700k in equities and around $1.2M in ZN (9 contracts). I have a very high risk tolerance. ZN got fairly wrecked the past quarter (my portion on it is down $27k since I started on it), but whatevs - I agree with the fundamental concepts behind this strategy, and it's not for the faint of heart.

So when I roll over my futures in the coming month, current thought is to (based on the contract prices above) liquidate the ZN contracts for maybe:
5 contracts ZF ($484k)
3 contracts ZN ($390k)
1 contract TN ($145k)
1 contract ZB ($161k)
For a total of $1.18M exposure (similar to now), and probably keep my current equities (or tax loss harvest if I can).
I think this is equal risk in ZB as ZF. I think the weighted duration would be just over 8 years.

Even during periods of flattening when the 8 year rate dropped more than the 5 year rate, the 5 year rate has significantly outperformed. I'd try to keep the weighted duration somewhat close to 5. During periods of non-flattening, the outperformance of 5 year has been even greater...
But I think the weighted duration of his proposed portfolio is about 6.5 years, not 8 years. If by "weighted duration" you meant "duration-weighted duration", I'm not sure how meaningful that definition would be :) If you look at his proposed portfolio, the notional values are already very much tilted towards the shorter durations. Further bias to the shorter durations would make the effect of the longer durations as diversifiers rather meaningless, should the relative performance of treasuries of the different durations ever vary.
In summary, I'm still not sure if duration-adjusted distribution across the maturity range makes sense, or should it be risk-adjusted or by notional value, or somewhere in between (something that probably only a risk-adjusted backtest would answer); but I definitely struggle with the concept of duration-weighted duration.
OK correct me if any of this is wrong:
Contract | Approx.Duration
ZF | 5
ZN | 8
TN | 10
ZB | 20

Sumproducting the # of contracts I chose would equal 79 (meaningless number), divide that by total number of contracts (10) equals a weighted average duration of 7.9.
ZM currently has a duration of about 6.17.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Tue Nov 16, 2021 8:33 am
comeinvest wrote: Tue Nov 16, 2021 5:53 am
skierincolorado wrote: Sat Nov 13, 2021 10:33 am
DMoogle wrote: Fri Nov 12, 2021 6:49 pm The net value of the portfolio I'm doing this with is $480k. Current allocation is around $700k in equities and around $1.2M in ZN (9 contracts). I have a very high risk tolerance. ZN got fairly wrecked the past quarter (my portion on it is down $27k since I started on it), but whatevs - I agree with the fundamental concepts behind this strategy, and it's not for the faint of heart.

So when I roll over my futures in the coming month, current thought is to (based on the contract prices above) liquidate the ZN contracts for maybe:
5 contracts ZF ($484k)
3 contracts ZN ($390k)
1 contract TN ($145k)
1 contract ZB ($161k)
For a total of $1.18M exposure (similar to now), and probably keep my current equities (or tax loss harvest if I can).
I think this is equal risk in ZB as ZF. I think the weighted duration would be just over 8 years.

Even during periods of flattening when the 8 year rate dropped more than the 5 year rate, the 5 year rate has significantly outperformed. I'd try to keep the weighted duration somewhat close to 5. During periods of non-flattening, the outperformance of 5 year has been even greater...
But I think the weighted duration of his proposed portfolio is about 6.5 years, not 8 years. If by "weighted duration" you meant "duration-weighted duration", I'm not sure how meaningful that definition would be :) If you look at his proposed portfolio, the notional values are already very much tilted towards the shorter durations. Further bias to the shorter durations would make the effect of the longer durations as diversifiers rather meaningless, should the relative performance of treasuries of the different durations ever vary.
In summary, I'm still not sure if duration-adjusted distribution across the maturity range makes sense, or should it be risk-adjusted or by notional value, or somewhere in between (something that probably only a risk-adjusted backtest would answer); but I definitely struggle with the concept of duration-weighted duration.
When you think of it as equal risk/return in zb as zf in his portfolio, it seems too long to me. I think that is what duration weighted duration represents. I would not want half my risk and return from the part of the curve with historically low risk adjusted returns and where the current curve is pretty flat. Maybe a little would be ok for diversification. But I think he’d find a lot of the daily moves were coming from the zb. Part of the problem is the notional value is so high for that contract.
I am totally lost with your reasoning. "Duration weighted duration" almost sounds like a parody to me. ZF has duration of about 4.5 if I remember right; ZB has about 11.5. So his 484:161 ratio is already *more* than a duration-adjusted allocation, i.e. his ZF position has already more duration risk than his ZB allocation. And that is setting aside the fact that, as you discovered in the course of this thread, the actual relative risks as you move along the maturities are less than what a strict duration based risk model would suggest, because the interest rates of shorter durations fluctuate more. But regardless of the specific model, his treasury portfolio interest rate sensitivity wold be about 6.5, not 8. Weighting durations by duration to come up with a weighted average duration makes zero sense to me. It's like double dipping. And what would be the meaning of that number.

Let's also look at it from another angle. Say in a given hypothetical future time period, the curve flattens and interest rates generally increase - stagflation with decreasing term premia because of little demand for capital - a tail risk scenario that we want to hedge by diversifying across the yield curve. Say ZF returns -10%, and ZB returns -1% during that period. With $484k in ZF and $161 in ZB, your treasury portfolio return would be -7.8%. An equi-distribution based on notional values would have a treasury portfolio return of -5.5%, a significantly smaller drawdown. By the way, your equities tank during that hypothetical period because of stagflation. All this is just one example. ZB could also increase in value all the while ZF drops, which is what happened in the past 6 months.
I know, my equi-distribution based on notional values has lower expected return based on your historical backtests. But it is more diversified. What you are suggesting would make the diversification effect minuscule if not irrelevant. ZF and ZN are very close to each other, and even with DMoogle's proposal would already have 3/4 of the assets. Do you move 75% or more, maybe 90% of your equities to Australia, just because the Australian stock market had the highest risk-adjusted returns historically?
Might be interesting to actually backtest a diversified-ITT (ZF/ZN/TN/ZB with either duration-adjusted or notional value based weights) vs. a short-maturity-ITT portfolio during a historical rising rate plus flattening period, or compare returns and drawdowns over a full cycle.
samwise_fool
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Joined: Tue Nov 16, 2021 2:13 pm

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

Post by samwise_fool »

This is a great thread! Finally got me to sign up for a BH account after lurking here for years so I could ask a (hopefully not too foolish!) question.

Has anyone taken a look at the micro yield futures that the CME started offering back in August? They're pretty thinly traded as they launched back in August (though Tastytrade's Small Exchange has had a similar product for a while now with lowish volume as well).There's not much data to backtest these on yet, but conceptually should you be able to substitute these for treasury futures in smaller accounts by selling contracts? I only have a smaller account at IBKR, and the size of treasury futures is too rich for me if I still want to hit my target leverage ratio in my IRA.

Intuitively I guess my worry is that shorting yields directly would capture the "interest rate risk" part of treasuries without capturing the actual roll yield etc. If that's the case though one would be able to long bond futures and short yield futures so it seems like they should even out...?

The contracts are 2YY, 5YY, 10Y, and 30Y on IBKR if you want to take a look.
Topic Author
skierincolorado
Posts: 2377
Joined: Sat Mar 21, 2020 10:56 am

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

Post by skierincolorado »

comeinvest wrote: Tue Nov 16, 2021 2:38 pm
skierincolorado wrote: Tue Nov 16, 2021 8:33 am
comeinvest wrote: Tue Nov 16, 2021 5:53 am
skierincolorado wrote: Sat Nov 13, 2021 10:33 am
DMoogle wrote: Fri Nov 12, 2021 6:49 pm The net value of the portfolio I'm doing this with is $480k. Current allocation is around $700k in equities and around $1.2M in ZN (9 contracts). I have a very high risk tolerance. ZN got fairly wrecked the past quarter (my portion on it is down $27k since I started on it), but whatevs - I agree with the fundamental concepts behind this strategy, and it's not for the faint of heart.

So when I roll over my futures in the coming month, current thought is to (based on the contract prices above) liquidate the ZN contracts for maybe:
5 contracts ZF ($484k)
3 contracts ZN ($390k)
1 contract TN ($145k)
1 contract ZB ($161k)
For a total of $1.18M exposure (similar to now), and probably keep my current equities (or tax loss harvest if I can).
I think this is equal risk in ZB as ZF. I think the weighted duration would be just over 8 years.

Even during periods of flattening when the 8 year rate dropped more than the 5 year rate, the 5 year rate has significantly outperformed. I'd try to keep the weighted duration somewhat close to 5. During periods of non-flattening, the outperformance of 5 year has been even greater...
But I think the weighted duration of his proposed portfolio is about 6.5 years, not 8 years. If by "weighted duration" you meant "duration-weighted duration", I'm not sure how meaningful that definition would be :) If you look at his proposed portfolio, the notional values are already very much tilted towards the shorter durations. Further bias to the shorter durations would make the effect of the longer durations as diversifiers rather meaningless, should the relative performance of treasuries of the different durations ever vary.
In summary, I'm still not sure if duration-adjusted distribution across the maturity range makes sense, or should it be risk-adjusted or by notional value, or somewhere in between (something that probably only a risk-adjusted backtest would answer); but I definitely struggle with the concept of duration-weighted duration.
When you think of it as equal risk/return in zb as zf in his portfolio, it seems too long to me. I think that is what duration weighted duration represents. I would not want half my risk and return from the part of the curve with historically low risk adjusted returns and where the current curve is pretty flat. Maybe a little would be ok for diversification. But I think he’d find a lot of the daily moves were coming from the zb. Part of the problem is the notional value is so high for that contract.
I am totally lost with your reasoning. "Duration weighted duration" almost sounds like a parody to me. ZF has duration of about 4.5 if I remember right; ZB has about 11.5. So his 484:161 ratio is already *more* than a duration-adjusted allocation, i.e. his ZF position has already more duration risk than his ZB allocation. And that is setting aside the fact that, as you discovered in the course of this thread, the actual relative risks as you move along the maturities are less than what a strict duration based risk model would suggest, because the interest rates of shorter durations fluctuate more. But regardless of the specific model, his treasury portfolio interest rate sensitivity wold be about 6.5, not 8. Weighting durations by duration to come up with a weighted average duration makes zero sense to me. It's like double dipping. And what would be the meaning of that number.

Let's also look at it from another angle. Say in a given hypothetical future time period, the curve flattens and interest rates generally increase - stagflation with decreasing term premia because of little demand for capital - a tail risk scenario that we want to hedge by diversifying across the yield curve. Say ZF returns -10%, and ZB returns -1% during that period. With $484k in ZF and $161 in ZB, your treasury portfolio return would be -7.8%. An equi-distribution based on notional values would have a treasury portfolio return of -5.5%, a significantly smaller drawdown. By the way, your equities tank during that hypothetical period because of stagflation. All this is just one example. ZB could also increase in value all the while ZF drops, which is what happened in the past 6 months.
I know, my equi-distribution based on notional values has lower expected return based on your historical backtests. But it is more diversified. What you are suggesting would make the diversification effect minuscule if not irrelevant. ZF and ZN are very close to each other, and even with DMoogle's proposal would already have 3/4 of the assets. Do you move 75% of your equities to Australia, just because the Australian stock market had the highest risk-adjusted returns historically?
Might be interesting to actually backtest a diversified-ITT (ZF/ZN/TN/ZB with either duration-adjusted or notional value based weights) vs. a short-maturity-ITT portfolio during a historical rising rate plus flattening period, or compare returns and drawdowns over a full cycle.
The situation you have described for its diversificatoin benefit - a 10% drop in ZF and a 1% drop in ZB.. would amount to a 2.5% rate increase for ZF and a .1% rate increase for ZB. The yield curve would be insanely inverted with 4.5 year rates of 3.75% and 11.5 year rates of 1.8%. Totally unheard of even in the early 80s.

Note that the 11.5 year rate increased 25x more than the 4.5 year rate (2.5% vs .1%).

Let's try the reverse scenario. What if the 11.5 year rate increases 25x more than the 4.5 year rate. The ZB would lose 23%. ZF would lose 0.5%. But the return of the portfolio would be completely dominated by the single ZB contract. In your nightmare scenario we lost 48k from all the ZFs. In my nightmare scenario we lost 37k from a single ZB. Nearly as much. The non-linearness helped a bit. This is what I mean you are taking nearly equal risk in ZB as in ZF. Your risk profile is half 4.5 and half 11.5. Why would you want half your risk at the duration with much lower risk-adjusted returns? I understand taking some risk at that duration for diversificaiton, but half?? No thank you.

While both scenarios (yours and mine) are extremely unlikely bordering on impossible, I'd still argue the second mine more likely than the yours since a 2.5-3% spread between 11y vs 4.5y has actually happened before (the spread was nearly that wide as recently as 2010) while a 2% inversion has not. In what universe would the 11.5 year yield 1.8% while the 4.5 year yielded 3.8%?


How about a more realistic scenario where 4.5 year rates increase 3% and 11.5 year rates increase 2.5%. The yield curve would still be inverted. But one would of course have been much better off in the shorter durations 1) because we can have less duration risk (I'd replace each ZB with 1.5 ZFs) and 2) unless this happened overnight we'd be getting the much better roll and carry of the shorter durations every single day that interest rates didn't rise
Last edited by skierincolorado on Tue Nov 16, 2021 3:26 pm, edited 1 time in total.
comeinvest
Posts: 2669
Joined: Mon Mar 12, 2012 6:57 pm

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

Post by comeinvest »

skierincolorado wrote: Tue Nov 16, 2021 3:02 pm
comeinvest wrote: Tue Nov 16, 2021 2:38 pm I am totally lost with your reasoning. "Duration weighted duration" almost sounds like a parody to me. ZF has duration of about 4.5 if I remember right; ZB has about 11.5. So his 484:161 ratio is already *more* than a duration-adjusted allocation, i.e. his ZF position has already more duration risk than his ZB allocation. And that is setting aside the fact that, as you discovered in the course of this thread, the actual relative risks as you move along the maturities are less than what a strict duration based risk model would suggest, because the interest rates of shorter durations fluctuate more. But regardless of the specific model, his treasury portfolio interest rate sensitivity wold be about 6.5, not 8. Weighting durations by duration to come up with a weighted average duration makes zero sense to me. It's like double dipping. And what would be the meaning of that number.

Let's also look at it from another angle. Say in a given hypothetical future time period, the curve flattens and interest rates generally increase - stagflation with decreasing term premia because of little demand for capital - a tail risk scenario that we want to hedge by diversifying across the yield curve. Say ZF returns -10%, and ZB returns -1% during that period. With $484k in ZF and $161 in ZB, your treasury portfolio return would be -7.8%. An equi-distribution based on notional values would have a treasury portfolio return of -5.5%, a significantly smaller drawdown. By the way, your equities tank during that hypothetical period because of stagflation. All this is just one example. ZB could also increase in value all the while ZF drops, which is what happened in the past 6 months.
I know, my equi-distribution based on notional values has lower expected return based on your historical backtests. But it is more diversified. What you are suggesting would make the diversification effect minuscule if not irrelevant. ZF and ZN are very close to each other, and even with DMoogle's proposal would already have 3/4 of the assets. Do you move 75% of your equities to Australia, just because the Australian stock market had the highest risk-adjusted returns historically?
Might be interesting to actually backtest a diversified-ITT (ZF/ZN/TN/ZB with either duration-adjusted or notional value based weights) vs. a short-maturity-ITT portfolio during a historical rising rate plus flattening period, or compare returns and drawdowns over a full cycle.
The situation you have described for its diversificatoin benefit - a 10% drop in ZF and a 1% drop in ZB.. would amount to a 2.5% rate increase for ZF and a .1% rate increase for ZB. The yield curve would be insanely inverted with 4.5 year rates of 3.75% and 11.5 year rates of 1.8%.

Note that the 11.5 year rate increased 25x more than the 4.5 year rate (2.5% vs .1%).

Let's try the reverse scenario. What if the 11.5 year rate increases 25x more than the 4.5 year rate. The ZB would lose 23%. ZF would lose 0.5%. But the return of the portfolio would be completely dominated by the single ZB contract.

While both scenarios are extremely unlikely bordering on impossible, I'd still argue the second is more likely than the former since a 2.5-3% spread between 11y vs 4.5y has actually happened before while a 2% inversion has not.
My example was just an ad hoc example to demonstrate the benefit of diversification. Tweak the numbers to your liking or make them more realistic.
The return in a steepening or flattening scenario will always be dominated by the maturity where the rate changed more. That effect is a wash.
Although I think the theoretical rationale is shaky, I could follow your argument for a weighting based on duration risk (which would be based on an assumption of an equal probability of steepening vs. flattening by the same nominal interest rate change), or at least based on "modified" duration risk that reflects the bigger fluctuations of rates at shorter maturities. But I'm lost with your concept of going beyond that.
You also sometimes tend to allude to mean reversion based on current valuations, as in "this can only continue so long"; while other times you say you only consider strict rules based allocations based on simple rules. I would generally not disagree with either one approach. But firstly, you have to reflect drawdowns based on temporary dislocations in your risk model, even if they "can only continue so long". Secondly, there are not only theoretical, but also real scenarios that are happening in other parts of the world - permanent flattening -, where longer maturities would benefit, and as a result, diversification might benefit vs putting all your eggs in one basket.
Topic Author
skierincolorado
Posts: 2377
Joined: Sat Mar 21, 2020 10:56 am

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

Post by skierincolorado »

comeinvest wrote: Tue Nov 16, 2021 3:23 pm
skierincolorado wrote: Tue Nov 16, 2021 3:02 pm
comeinvest wrote: Tue Nov 16, 2021 2:38 pm I am totally lost with your reasoning. "Duration weighted duration" almost sounds like a parody to me. ZF has duration of about 4.5 if I remember right; ZB has about 11.5. So his 484:161 ratio is already *more* than a duration-adjusted allocation, i.e. his ZF position has already more duration risk than his ZB allocation. And that is setting aside the fact that, as you discovered in the course of this thread, the actual relative risks as you move along the maturities are less than what a strict duration based risk model would suggest, because the interest rates of shorter durations fluctuate more. But regardless of the specific model, his treasury portfolio interest rate sensitivity wold be about 6.5, not 8. Weighting durations by duration to come up with a weighted average duration makes zero sense to me. It's like double dipping. And what would be the meaning of that number.

Let's also look at it from another angle. Say in a given hypothetical future time period, the curve flattens and interest rates generally increase - stagflation with decreasing term premia because of little demand for capital - a tail risk scenario that we want to hedge by diversifying across the yield curve. Say ZF returns -10%, and ZB returns -1% during that period. With $484k in ZF and $161 in ZB, your treasury portfolio return would be -7.8%. An equi-distribution based on notional values would have a treasury portfolio return of -5.5%, a significantly smaller drawdown. By the way, your equities tank during that hypothetical period because of stagflation. All this is just one example. ZB could also increase in value all the while ZF drops, which is what happened in the past 6 months.
I know, my equi-distribution based on notional values has lower expected return based on your historical backtests. But it is more diversified. What you are suggesting would make the diversification effect minuscule if not irrelevant. ZF and ZN are very close to each other, and even with DMoogle's proposal would already have 3/4 of the assets. Do you move 75% of your equities to Australia, just because the Australian stock market had the highest risk-adjusted returns historically?
Might be interesting to actually backtest a diversified-ITT (ZF/ZN/TN/ZB with either duration-adjusted or notional value based weights) vs. a short-maturity-ITT portfolio during a historical rising rate plus flattening period, or compare returns and drawdowns over a full cycle.
The situation you have described for its diversificatoin benefit - a 10% drop in ZF and a 1% drop in ZB.. would amount to a 2.5% rate increase for ZF and a .1% rate increase for ZB. The yield curve would be insanely inverted with 4.5 year rates of 3.75% and 11.5 year rates of 1.8%.

Note that the 11.5 year rate increased 25x more than the 4.5 year rate (2.5% vs .1%).

Let's try the reverse scenario. What if the 11.5 year rate increases 25x more than the 4.5 year rate. The ZB would lose 23%. ZF would lose 0.5%. But the return of the portfolio would be completely dominated by the single ZB contract.

While both scenarios are extremely unlikely bordering on impossible, I'd still argue the second is more likely than the former since a 2.5-3% spread between 11y vs 4.5y has actually happened before while a 2% inversion has not.
My example was just an ad hoc example to demonstrate the benefit of diversification. Tweak the numbers to your liking or make them more realistic.
The return in a steepening or flattening scenario will always be dominated by the maturity where the rate changed more. That effect is a wash.
Although I think the theoretical rationale is shaky, I could follow your argument for a weighting based on duration risk (which would be based on an assumption of an equal probability of steepening vs. flattening by the same nominal interest rate change), or at least based on "modified" duration risk that reflects the bigger fluctuations of rates at shorter maturities. But I'm lost with your concept of going beyond that.
You also sometimes tend to allude to mean reversion based on current valuations, as in "this can only continue so long"; while other times you say you only consider strict rules based allocations based on simple rules. I would generally not disagree with either one approach. But firstly, you have to reflect drawdowns based on temporary dislocations in your risk model, even if they "can only continue so long". Secondly, there are not only theoretical, but also real scenarios that are happening in other parts of the world - permanent flattening -, where longer maturities would benefit, and as a result, diversification would benefit vs putting all your eggs in one basket.
I edited to include the fact that the loss on the ZB in my 2.5% widening was nearly as large on all those ZFs in your 2.5% inversioning (I won't even call that a flattening haha so I am making up a word). This is what I mean by he has equal risk at each duration.

Ignoring the fact that a 2.5% widening is probably more likely than a 2.5% inversioning, we still should tilt towards the lower duration because the roll and carry is better. If there is no flattening or widening, the ZF wins substantially. Only if we believe flattening/inversioning will be rapid at high probability would we want equal risk. That's the breakeven. Otherwise we tilt to the one with the better roll and carry and historical returns.

If widening/flattening was a normal distribution centered at zero... we would pick ZF and zero TN or ZB. It's not centered at zero though.. slight flattening is probably a bit more likely than widening. But not enough to push us into equal risk in ZB.

How about a more realistic scenario where 4.5 year rates increase 3% and 11.5 year rates increase 2.5%. The yield curve would still be inverted. But one would of course have been much better off in the shorter durations 1) because we can have less duration risk (I'd replace each ZB with 1.5 ZFs) and 2) unless this happened overnight we'd be getting the much better roll and carry of the shorter durations every single day that interest rates didn't rise
Lock
Posts: 98
Joined: Sat Oct 05, 2019 8:52 pm

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

Post by Lock »

skierincolorado wrote: Tue Nov 16, 2021 10:50 am
Lock wrote: Tue Nov 16, 2021 10:29 am
klaus14 wrote: Mon Nov 15, 2021 4:45 pm
skierincolorado wrote: Fri Sep 10, 2021 2:39 pm In case anyone missed it, this is my "final" estimate.

.3% ITT
.4% LTT
4.5% domestic stock
5% international stock

The efficient frontier is: 34/22/44 domestic stock / intl stock / ITT

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

***This is extremely sensitive to asssumptions. I suggest simply using the historical efficient frontier.***

I sold all my bond futures today.

Reasoning:
I am not confident that backtests apply to today. I was holding $1M worth of /ZN. ZN is close to 7 years maturity. The real yield on 7 years treasury is -1.5%. This is the median of return expectation for the 7 year time frame. So I'll loose (real) ~$15k (plus futures financing cost minus roll down yield)* every year on the average case. Notice that i am not saying rates will go up or down. This is just the mean expectation. Yes negative correlation with equities may help in the event of a recession. However, unlike past, now this hedge has significant costs compared to potential benefit (which is lower since real yields are at the lowest - less room to go down). I couldn't justify this given my investment horizon is very long (I am mid 30s)

*skierincolorado above did more complex math including roll down yield and forward rate estimates. Using that figure, nominal return expectation: 0.3% ITT => real: -2.8% (using breakeven). And quote is from Sept 7 and real rates are worse today.

So now my only bond holdings are: I Bonds, EE Bonds, an old CD yielding 2.75%
I am planning to buy /ZN when 7 years real yield is positive again.

I wish best of luck to everyone in this thread. I learned a lot here.
Why not just go short (i.e. sell contracts)? YTD the stock/bond correlation has been positive so you can re-create a negative correlation asset.

Disclaimer: I've been running a risk parity portfolio for about 3 years and this year I sold ZN contracts for the first time.
1)Because the expected return of zn is still likely positive for the long position and negative for the short.

2)I would guess the correlation was also positive in 2018 and 2019 leaving you caught red handed in 2020.

3)The difference between a +.05 and -.05 correlation is trivial and both would more accurately be described as uncorrelated. The strategy works not because the correlation between stocks and bonds has ever truly been significantly negative, but because we are able to take more risk in each bucket without increasing our overall risk because the buckets are uncorrelated. And the return of each bucket is positive.
I'm really loving this thread - the calculation of future rates is outstanding and the theory is great. Skier you have a super interesting perspective on modern portfolio craft.

Can we step back for a minute and talk about why people invest in assets at all? The Occam's razor of investing boils down to the idea that you are putting money into a vehicle that will be at least as valuable (and redeemable) at some date in the future. That's fundamentally the idea of positive expected return and those are the assets we seek to hold via modern portfolio theory. Does going long intermediate bonds right now really match this basic premise on a real returns basis?

The point of risk parity/modern portfolio theory is to better distribute risk - does a 125 equity/ 150 bond (or even 200) portfolio really distribute risk? It may get great historical returns - which I agree is awesome and got me interested - but are you really solving for modern portfolio theory at the current moment in the current environment?
Topic Author
skierincolorado
Posts: 2377
Joined: Sat Mar 21, 2020 10:56 am

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

Post by skierincolorado »

Lock wrote: Tue Nov 16, 2021 3:51 pm
skierincolorado wrote: Tue Nov 16, 2021 10:50 am
Lock wrote: Tue Nov 16, 2021 10:29 am
klaus14 wrote: Mon Nov 15, 2021 4:45 pm
skierincolorado wrote: Fri Sep 10, 2021 2:39 pm In case anyone missed it, this is my "final" estimate.

.3% ITT
.4% LTT
4.5% domestic stock
5% international stock

The efficient frontier is: 34/22/44 domestic stock / intl stock / ITT

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

***This is extremely sensitive to asssumptions. I suggest simply using the historical efficient frontier.***

I sold all my bond futures today.

Reasoning:
I am not confident that backtests apply to today. I was holding $1M worth of /ZN. ZN is close to 7 years maturity. The real yield on 7 years treasury is -1.5%. This is the median of return expectation for the 7 year time frame. So I'll loose (real) ~$15k (plus futures financing cost minus roll down yield)* every year on the average case. Notice that i am not saying rates will go up or down. This is just the mean expectation. Yes negative correlation with equities may help in the event of a recession. However, unlike past, now this hedge has significant costs compared to potential benefit (which is lower since real yields are at the lowest - less room to go down). I couldn't justify this given my investment horizon is very long (I am mid 30s)

*skierincolorado above did more complex math including roll down yield and forward rate estimates. Using that figure, nominal return expectation: 0.3% ITT => real: -2.8% (using breakeven). And quote is from Sept 7 and real rates are worse today.

So now my only bond holdings are: I Bonds, EE Bonds, an old CD yielding 2.75%
I am planning to buy /ZN when 7 years real yield is positive again.

I wish best of luck to everyone in this thread. I learned a lot here.
Why not just go short (i.e. sell contracts)? YTD the stock/bond correlation has been positive so you can re-create a negative correlation asset.

Disclaimer: I've been running a risk parity portfolio for about 3 years and this year I sold ZN contracts for the first time.
1)Because the expected return of zn is still likely positive for the long position and negative for the short.

2)I would guess the correlation was also positive in 2018 and 2019 leaving you caught red handed in 2020.

3)The difference between a +.05 and -.05 correlation is trivial and both would more accurately be described as uncorrelated. The strategy works not because the correlation between stocks and bonds has ever truly been significantly negative, but because we are able to take more risk in each bucket without increasing our overall risk because the buckets are uncorrelated. And the return of each bucket is positive.
I'm really loving this thread - the calculation of future rates is outstanding and the theory is great. Skier you have a super interesting perspective on modern portfolio craft.

Can we step back for a minute and talk about why people invest in assets at all? The Occam's razor of investing boils down to the idea that you are putting money into a vehicle that will be at least as valuable (and redeemable) at some date in the future. That's fundamentally the idea of positive expected return and those are the assets we seek to hold via modern portfolio theory. Does going long intermediate bonds right now really match this basic premise on a real returns basis?

The point of risk parity/modern portfolio theory is to better distribute risk - does a 125 equity/ 150 bond (or even 200) portfolio really distribute risk? It may get great historical returns - which I agree is awesome and got me interested - but are you really solving for modern portfolio theory at the current moment in the current environment?
I’d object to the above formulation for two reasons.

1) the investment must only be more valuable in the future than the money we exchanged for the investment will be in the future. If inflation is 3% and my investment is 1% and cash is 0%, my investment was still good assuming no other better options.

2) I can invest on borrowed money in which case my investment must only be redeemable for more than what I must repay. Anything with a nominal return satisfies this condition. In a negative rate environment, investments with negative returns satisfy this condition if the negative return is less negative than the negative interest on the borrowed money. Of course putting the borrowed money in hard cash would be even better but this is usually not possible.

Both points get back to the fact that it is the nominal return of the investment minus borrowing cost that makes a good investment.

Try it in the pv efficient frontier. Enter a bond return below inflation and stock return above inflation. The maximum risk adjusted return will still include substantial bonds. The inflation rate doesn’t even enter into the picture.
comeinvest
Posts: 2669
Joined: Mon Mar 12, 2012 6:57 pm

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

Post by comeinvest »

skierincolorado wrote: Tue Nov 16, 2021 3:36 pm
comeinvest wrote: Tue Nov 16, 2021 3:23 pm
skierincolorado wrote: Tue Nov 16, 2021 3:02 pm
comeinvest wrote: Tue Nov 16, 2021 2:38 pm I am totally lost with your reasoning. "Duration weighted duration" almost sounds like a parody to me. ZF has duration of about 4.5 if I remember right; ZB has about 11.5. So his 484:161 ratio is already *more* than a duration-adjusted allocation, i.e. his ZF position has already more duration risk than his ZB allocation. And that is setting aside the fact that, as you discovered in the course of this thread, the actual relative risks as you move along the maturities are less than what a strict duration based risk model would suggest, because the interest rates of shorter durations fluctuate more. But regardless of the specific model, his treasury portfolio interest rate sensitivity wold be about 6.5, not 8. Weighting durations by duration to come up with a weighted average duration makes zero sense to me. It's like double dipping. And what would be the meaning of that number.

Let's also look at it from another angle. Say in a given hypothetical future time period, the curve flattens and interest rates generally increase - stagflation with decreasing term premia because of little demand for capital - a tail risk scenario that we want to hedge by diversifying across the yield curve. Say ZF returns -10%, and ZB returns -1% during that period. With $484k in ZF and $161 in ZB, your treasury portfolio return would be -7.8%. An equi-distribution based on notional values would have a treasury portfolio return of -5.5%, a significantly smaller drawdown. By the way, your equities tank during that hypothetical period because of stagflation. All this is just one example. ZB could also increase in value all the while ZF drops, which is what happened in the past 6 months.
I know, my equi-distribution based on notional values has lower expected return based on your historical backtests. But it is more diversified. What you are suggesting would make the diversification effect minuscule if not irrelevant. ZF and ZN are very close to each other, and even with DMoogle's proposal would already have 3/4 of the assets. Do you move 75% of your equities to Australia, just because the Australian stock market had the highest risk-adjusted returns historically?
Might be interesting to actually backtest a diversified-ITT (ZF/ZN/TN/ZB with either duration-adjusted or notional value based weights) vs. a short-maturity-ITT portfolio during a historical rising rate plus flattening period, or compare returns and drawdowns over a full cycle.
The situation you have described for its diversificatoin benefit - a 10% drop in ZF and a 1% drop in ZB.. would amount to a 2.5% rate increase for ZF and a .1% rate increase for ZB. The yield curve would be insanely inverted with 4.5 year rates of 3.75% and 11.5 year rates of 1.8%.

Note that the 11.5 year rate increased 25x more than the 4.5 year rate (2.5% vs .1%).

Let's try the reverse scenario. What if the 11.5 year rate increases 25x more than the 4.5 year rate. The ZB would lose 23%. ZF would lose 0.5%. But the return of the portfolio would be completely dominated by the single ZB contract.

While both scenarios are extremely unlikely bordering on impossible, I'd still argue the second is more likely than the former since a 2.5-3% spread between 11y vs 4.5y has actually happened before while a 2% inversion has not.
My example was just an ad hoc example to demonstrate the benefit of diversification. Tweak the numbers to your liking or make them more realistic.
The return in a steepening or flattening scenario will always be dominated by the maturity where the rate changed more. That effect is a wash.
Although I think the theoretical rationale is shaky, I could follow your argument for a weighting based on duration risk (which would be based on an assumption of an equal probability of steepening vs. flattening by the same nominal interest rate change), or at least based on "modified" duration risk that reflects the bigger fluctuations of rates at shorter maturities. But I'm lost with your concept of going beyond that.
You also sometimes tend to allude to mean reversion based on current valuations, as in "this can only continue so long"; while other times you say you only consider strict rules based allocations based on simple rules. I would generally not disagree with either one approach. But firstly, you have to reflect drawdowns based on temporary dislocations in your risk model, even if they "can only continue so long". Secondly, there are not only theoretical, but also real scenarios that are happening in other parts of the world - permanent flattening -, where longer maturities would benefit, and as a result, diversification would benefit vs putting all your eggs in one basket.
I edited to include the fact that the loss on the ZB in my 2.5% widening was nearly as large on all those ZFs in your 2.5% inversioning (I won't even call that a flattening haha so I am making up a word). This is what I mean by he has equal risk at each duration.

Ignoring the fact that a 2.5% widening is probably more likely than a 2.5% inversioning, we still should tilt towards the lower duration because the roll and carry is better. If there is no flattening or widening, the ZF wins substantially. Only if we believe flattening/inversioning will be rapid at high probability would we want equal risk. That's the breakeven. Otherwise we tilt to the one with the better roll and carry and historical returns.

If widening/flattening was a normal distribution centered at zero... we would pick ZF and zero TN or ZB. It's not centered at zero though.. slight flattening is probably a bit more likely than widening. But not enough to push us into equal risk in ZB.

How about a more realistic scenario where 4.5 year rates increase 3% and 11.5 year rates increase 2.5%. The yield curve would still be inverted. But one would of course have been much better off in the shorter durations 1) because we can have less duration risk (I'd replace each ZB with 1.5 ZFs) and 2) unless this happened overnight we'd be getting the much better roll and carry of the shorter durations every single day that interest rates didn't rise
Again I don't generally disagree, but I would also question, or at least not blindly follow, the approach to estimating expected returns and risk based on simplistic interest rates models and simplistic relationships. It's a nice and valuable exercise, but in the end, we are dealing with financial markets, which are governed by preferences of market participants, some of which theoretically have the same information or more information than we have. The BAB effect is hard to quantify, and it may or may not persist. (Just like "value" risk-adjusted outperformance persisted for decades in the U.S. stock market, until it didn't for 2+ decades.)

"we would pick ZF and zero TN or ZB" - makes only sense if you think you can forecast the future with 100% accuracy in that ZF will outperform by virtue of its carry, and give 0% chance to alternate scenarios.

If we assume that whatever biases lead to ITT outperformance will persist, then I think the Simplify chart is one of the most valuable supporting an ITT based strategy. I am re-posting it. The chart shows the "carry", which I interpret to be an estimator of returns after removing the effect of changes in interest rate (which can only persist so long until they reverse).

The outperformance of ITT was on average ca. 2.5% in the 5-7 year range. If I understand the assumptions right that Simplify made, the chart does not reflect the futures slippage of ca. 0.2%, but then they use the 1-year treasury rate as funding rate and not a 3-month funding, so it might be a wash. But I think we might want to adjust the expected future outperformance or ITT vs LTT by dividing it by a "compression factor" of maybe 2 or 3 to reflect the generally lower interest rate level at the long end of maturities compared to history, that I think must eventually result in lower term premiums across the yield curve, as we have less "vertical space" on the y-axis of the yield curve to work with.

Also note that the chart is based on duration-adjusted allocations, not risk-adjusted allocations that we determined to be somewhat lower.

https://www.simplify.us/blog/efficient- ... -investing

Image
Topic Author
skierincolorado
Posts: 2377
Joined: Sat Mar 21, 2020 10:56 am

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

Post by skierincolorado »

comeinvest wrote: Tue Nov 16, 2021 4:42 pm
skierincolorado wrote: Tue Nov 16, 2021 3:36 pm
comeinvest wrote: Tue Nov 16, 2021 3:23 pm
skierincolorado wrote: Tue Nov 16, 2021 3:02 pm
comeinvest wrote: Tue Nov 16, 2021 2:38 pm I am totally lost with your reasoning. "Duration weighted duration" almost sounds like a parody to me. ZF has duration of about 4.5 if I remember right; ZB has about 11.5. So his 484:161 ratio is already *more* than a duration-adjusted allocation, i.e. his ZF position has already more duration risk than his ZB allocation. And that is setting aside the fact that, as you discovered in the course of this thread, the actual relative risks as you move along the maturities are less than what a strict duration based risk model would suggest, because the interest rates of shorter durations fluctuate more. But regardless of the specific model, his treasury portfolio interest rate sensitivity wold be about 6.5, not 8. Weighting durations by duration to come up with a weighted average duration makes zero sense to me. It's like double dipping. And what would be the meaning of that number.

Let's also look at it from another angle. Say in a given hypothetical future time period, the curve flattens and interest rates generally increase - stagflation with decreasing term premia because of little demand for capital - a tail risk scenario that we want to hedge by diversifying across the yield curve. Say ZF returns -10%, and ZB returns -1% during that period. With $484k in ZF and $161 in ZB, your treasury portfolio return would be -7.8%. An equi-distribution based on notional values would have a treasury portfolio return of -5.5%, a significantly smaller drawdown. By the way, your equities tank during that hypothetical period because of stagflation. All this is just one example. ZB could also increase in value all the while ZF drops, which is what happened in the past 6 months.
I know, my equi-distribution based on notional values has lower expected return based on your historical backtests. But it is more diversified. What you are suggesting would make the diversification effect minuscule if not irrelevant. ZF and ZN are very close to each other, and even with DMoogle's proposal would already have 3/4 of the assets. Do you move 75% of your equities to Australia, just because the Australian stock market had the highest risk-adjusted returns historically?
Might be interesting to actually backtest a diversified-ITT (ZF/ZN/TN/ZB with either duration-adjusted or notional value based weights) vs. a short-maturity-ITT portfolio during a historical rising rate plus flattening period, or compare returns and drawdowns over a full cycle.
The situation you have described for its diversificatoin benefit - a 10% drop in ZF and a 1% drop in ZB.. would amount to a 2.5% rate increase for ZF and a .1% rate increase for ZB. The yield curve would be insanely inverted with 4.5 year rates of 3.75% and 11.5 year rates of 1.8%.

Note that the 11.5 year rate increased 25x more than the 4.5 year rate (2.5% vs .1%).

Let's try the reverse scenario. What if the 11.5 year rate increases 25x more than the 4.5 year rate. The ZB would lose 23%. ZF would lose 0.5%. But the return of the portfolio would be completely dominated by the single ZB contract.

While both scenarios are extremely unlikely bordering on impossible, I'd still argue the second is more likely than the former since a 2.5-3% spread between 11y vs 4.5y has actually happened before while a 2% inversion has not.
My example was just an ad hoc example to demonstrate the benefit of diversification. Tweak the numbers to your liking or make them more realistic.
The return in a steepening or flattening scenario will always be dominated by the maturity where the rate changed more. That effect is a wash.
Although I think the theoretical rationale is shaky, I could follow your argument for a weighting based on duration risk (which would be based on an assumption of an equal probability of steepening vs. flattening by the same nominal interest rate change), or at least based on "modified" duration risk that reflects the bigger fluctuations of rates at shorter maturities. But I'm lost with your concept of going beyond that.
You also sometimes tend to allude to mean reversion based on current valuations, as in "this can only continue so long"; while other times you say you only consider strict rules based allocations based on simple rules. I would generally not disagree with either one approach. But firstly, you have to reflect drawdowns based on temporary dislocations in your risk model, even if they "can only continue so long". Secondly, there are not only theoretical, but also real scenarios that are happening in other parts of the world - permanent flattening -, where longer maturities would benefit, and as a result, diversification would benefit vs putting all your eggs in one basket.
I edited to include the fact that the loss on the ZB in my 2.5% widening was nearly as large on all those ZFs in your 2.5% inversioning (I won't even call that a flattening haha so I am making up a word). This is what I mean by he has equal risk at each duration.

Ignoring the fact that a 2.5% widening is probably more likely than a 2.5% inversioning, we still should tilt towards the lower duration because the roll and carry is better. If there is no flattening or widening, the ZF wins substantially. Only if we believe flattening/inversioning will be rapid at high probability would we want equal risk. That's the breakeven. Otherwise we tilt to the one with the better roll and carry and historical returns.

If widening/flattening was a normal distribution centered at zero... we would pick ZF and zero TN or ZB. It's not centered at zero though.. slight flattening is probably a bit more likely than widening. But not enough to push us into equal risk in ZB.

How about a more realistic scenario where 4.5 year rates increase 3% and 11.5 year rates increase 2.5%. The yield curve would still be inverted. But one would of course have been much better off in the shorter durations 1) because we can have less duration risk (I'd replace each ZB with 1.5 ZFs) and 2) unless this happened overnight we'd be getting the much better roll and carry of the shorter durations every single day that interest rates didn't rise
Again I don't generally disagree, but I would also question, or at least not blindly follow, the approach to estimating expected returns and risk based on simplistic interest rates models and simplistic relationships. It's a nice and valuable exercise, but in the end, we are dealing with financial markets, which are governed by preferences of market participants, some of which theoretically have the same information or more information than we have. The BAB effect is hard to quantify, and it may or may not persist. (Just like "value" risk-adjusted outperformance persisted for decades in the U.S. stock market, until it didn't for 2+ decades.)

If we assume that whatever biases lead to ITT outperformance will persist, then I think the Simplify chart is one of the most valuable supporting an ITT based strategy. I am re-posting it. The chart shows the "carry", which I interpret to be an estimator of returns after removing the effect of changes in interest rate (which can only persist so long until they reverse).

The outperformance of ITT was on average ca. 2.5% in the 5-7 year range. If I understand the assumptions right that Simplify made, the chart does not reflect the futures slippage of ca. 0.2%, but then they use the 1-year treasury rate as funding rate and not a 3-month funding, so it might be a wash. But I think we might want to adjust the expected future outperformance or ITT vs LTT by dividing it by a "compression factor" of maybe 2 or 3 to reflect the generally lower interest rate level at the long end of maturities compared to history, that I think must eventually result in lower term premiums across the yield curve, as we have less "vertical space" on the y-axis of the yield curve to work with.

Also note that the chart is based on duration-adjusted allocations, not risk-adjusted allocations that we determined to be somewhat lower.

https://www.simplify.us/blog/efficient- ... -investing

Image
I agree this is mostly premised on BAB but the downside of bab being gone is I eat a very small loss as the curve flattens out between 0 and 15. The itt don’t outperform in the short run due to the flattening, and then in the long run all bonds are dead because the curve is flat and stays flat.

The upside is limitless because it’s a long term strategy. If at some point bab dies it will have been a small price to pay.

I can definitely see the appeal of investing in zb to diversify against a further flattening between 5 and 11. But I just think half ones risk is far too much.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

Lock wrote: Tue Nov 16, 2021 3:51 pm
skierincolorado wrote: Tue Nov 16, 2021 10:50 am
Lock wrote: Tue Nov 16, 2021 10:29 am
klaus14 wrote: Mon Nov 15, 2021 4:45 pm
skierincolorado wrote: Fri Sep 10, 2021 2:39 pm In case anyone missed it, this is my "final" estimate.

.3% ITT
.4% LTT
4.5% domestic stock
5% international stock

The efficient frontier is: 34/22/44 domestic stock / intl stock / ITT

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

***This is extremely sensitive to asssumptions. I suggest simply using the historical efficient frontier.***

I sold all my bond futures today.

Reasoning:
I am not confident that backtests apply to today. I was holding $1M worth of /ZN. ZN is close to 7 years maturity. The real yield on 7 years treasury is -1.5%. This is the median of return expectation for the 7 year time frame. So I'll loose (real) ~$15k (plus futures financing cost minus roll down yield)* every year on the average case. Notice that i am not saying rates will go up or down. This is just the mean expectation. Yes negative correlation with equities may help in the event of a recession. However, unlike past, now this hedge has significant costs compared to potential benefit (which is lower since real yields are at the lowest - less room to go down). I couldn't justify this given my investment horizon is very long (I am mid 30s)

*skierincolorado above did more complex math including roll down yield and forward rate estimates. Using that figure, nominal return expectation: 0.3% ITT => real: -2.8% (using breakeven). And quote is from Sept 7 and real rates are worse today.

So now my only bond holdings are: I Bonds, EE Bonds, an old CD yielding 2.75%
I am planning to buy /ZN when 7 years real yield is positive again.

I wish best of luck to everyone in this thread. I learned a lot here.
Why not just go short (i.e. sell contracts)? YTD the stock/bond correlation has been positive so you can re-create a negative correlation asset.

Disclaimer: I've been running a risk parity portfolio for about 3 years and this year I sold ZN contracts for the first time.
1)Because the expected return of zn is still likely positive for the long position and negative for the short.

2)I would guess the correlation was also positive in 2018 and 2019 leaving you caught red handed in 2020.

3)The difference between a +.05 and -.05 correlation is trivial and both would more accurately be described as uncorrelated. The strategy works not because the correlation between stocks and bonds has ever truly been significantly negative, but because we are able to take more risk in each bucket without increasing our overall risk because the buckets are uncorrelated. And the return of each bucket is positive.
I'm really loving this thread - the calculation of future rates is outstanding and the theory is great. Skier you have a super interesting perspective on modern portfolio craft.

Can we step back for a minute and talk about why people invest in assets at all? The Occam's razor of investing boils down to the idea that you are putting money into a vehicle that will be at least as valuable (and redeemable) at some date in the future. That's fundamentally the idea of positive expected return and those are the assets we seek to hold via modern portfolio theory. Does going long intermediate bonds right now really match this basic premise on a real returns basis?

The point of risk parity/modern portfolio theory is to better distribute risk - does a 125 equity/ 150 bond (or even 200) portfolio really distribute risk? It may get great historical returns - which I agree is awesome and got me interested - but are you really solving for modern portfolio theory at the current moment in the current environment?
I think it all comes down to the question, how sustainable are negative real and even negative nominal interest rates, i.e. people giving away their money with almost certain knowledge of getting back less in the future. Is this a temporary dislocation, or can this persist. If the former, then there is the risk of a sudden return to "normal", which wouldn't be pretty for mHFEA. But given how long this situation has lasted in Europe for example, some of us have been conditioned to the possibility that this is the "new normal". The problem is that nobody knows the future. That's why I think many in this thread started mHFEA half-heartedly i.e. with a reduced bond allocation, possibly bumping it up if and when rates are more "normal".
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Tue Nov 16, 2021 10:23 am
hdas wrote: Tue Nov 16, 2021 9:41 am
skierincolorado wrote: Tue Nov 16, 2021 9:13 am I’m highly skeptical that any rules based approach could have predicted the strong ITT returns from 2010 to 2015.
This statement is baffling, in 2010 the term premium was screaming BUY!!!!!!!!!. Highest ever since we have good data (late 80's)
skierincolorado wrote: Tue Nov 16, 2021 9:13 am You’ve picked 2018 as the endpoint for a switch. What if COViD happened in 2017?
Why do you keep dismissing the valuable information you get from the curve?.........Anybody can see that the attractiveness of LTT over ITT is different if the spread is 3% or 0.2%. What is so difficult to understand?. Since you are such a fan of backtests, have you tested the relative performance of LTT vs ITT CONDITIONAL on the spread level?
Again, come up with a rules based strategy and test it, or this is all talk. I've read several papers that have attempted this sort of dynamic rules based strategy, and there is some slight outperformance - but not the type of outperformance you seem to think and there is no guarantee it's not simply data mining and overfitting. The idea that you're going to get dramatic outperformance from such a simple strategy is simply contrary to EMH. I don’t have to backtest it - other people already have - and EMH tells us the type of outperformance you are talking about is unlikely.
I agree we have to be careful to not do data mining and overfitting; but I wouldn't rush too early into dismissing possible sources of strategic alpha simply by pointing to EMH. Any market could be biased in some way that we might exploit, as we are trying to do with ITT/LTT. Markets are governed by parties with various interests, among others by the Fed that dictates short-term rates and affects the rest of the yield curve.
Here's a paper relevant to yield curve premia, that examines the slope of the yield curve, among other things: https://spinup-000d1a-wp-offload-media. ... Premia.pdf
A paper about the carry and BAB strategies: https://www.efmaefm.org/0EFMAMEETINGS/E ... lpaper.pdf
Last edited by comeinvest on Tue Nov 16, 2021 6:46 pm, edited 1 time in total.
Lock
Posts: 98
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Lock »

skierincolorado wrote: Tue Nov 16, 2021 4:05 pm
Lock wrote: Tue Nov 16, 2021 3:51 pm
skierincolorado wrote: Tue Nov 16, 2021 10:50 am
Lock wrote: Tue Nov 16, 2021 10:29 am
klaus14 wrote: Mon Nov 15, 2021 4:45 pm


I sold all my bond futures today.

Reasoning:
I am not confident that backtests apply to today. I was holding $1M worth of /ZN. ZN is close to 7 years maturity. The real yield on 7 years treasury is -1.5%. This is the median of return expectation for the 7 year time frame. So I'll loose (real) ~$15k (plus futures financing cost minus roll down yield)* every year on the average case. Notice that i am not saying rates will go up or down. This is just the mean expectation. Yes negative correlation with equities may help in the event of a recession. However, unlike past, now this hedge has significant costs compared to potential benefit (which is lower since real yields are at the lowest - less room to go down). I couldn't justify this given my investment horizon is very long (I am mid 30s)

*skierincolorado above did more complex math including roll down yield and forward rate estimates. Using that figure, nominal return expectation: 0.3% ITT => real: -2.8% (using breakeven). And quote is from Sept 7 and real rates are worse today.

So now my only bond holdings are: I Bonds, EE Bonds, an old CD yielding 2.75%
I am planning to buy /ZN when 7 years real yield is positive again.

I wish best of luck to everyone in this thread. I learned a lot here.
Why not just go short (i.e. sell contracts)? YTD the stock/bond correlation has been positive so you can re-create a negative correlation asset.

Disclaimer: I've been running a risk parity portfolio for about 3 years and this year I sold ZN contracts for the first time.
1)Because the expected return of zn is still likely positive for the long position and negative for the short.

2)I would guess the correlation was also positive in 2018 and 2019 leaving you caught red handed in 2020.

3)The difference between a +.05 and -.05 correlation is trivial and both would more accurately be described as uncorrelated. The strategy works not because the correlation between stocks and bonds has ever truly been significantly negative, but because we are able to take more risk in each bucket without increasing our overall risk because the buckets are uncorrelated. And the return of each bucket is positive.
I'm really loving this thread - the calculation of future rates is outstanding and the theory is great. Skier you have a super interesting perspective on modern portfolio craft.

Can we step back for a minute and talk about why people invest in assets at all? The Occam's razor of investing boils down to the idea that you are putting money into a vehicle that will be at least as valuable (and redeemable) at some date in the future. That's fundamentally the idea of positive expected return and those are the assets we seek to hold via modern portfolio theory. Does going long intermediate bonds right now really match this basic premise on a real returns basis?

The point of risk parity/modern portfolio theory is to better distribute risk - does a 125 equity/ 150 bond (or even 200) portfolio really distribute risk? It may get great historical returns - which I agree is awesome and got me interested - but are you really solving for modern portfolio theory at the current moment in the current environment?
I’d object to the above formulation for two reasons.

1) the investment must only be more valuable in the future than the money we exchanged for the investment will be in the future. If inflation is 3% and my investment is 1% and cash is 0%, my investment was still good assuming no other better options.

2) I can invest on borrowed money in which case my investment must only be redeemable for more than what I must repay. Anything with a nominal return satisfies this condition. In a negative rate environment, investments with negative returns satisfy this condition if the negative return is less negative than the negative interest on the borrowed money. Of course putting the borrowed money in hard cash would be even better but this is usually not possible.

Both points get back to the fact that it is the nominal return of the investment minus borrowing cost that makes a good investment.

Try it in the pv efficient frontier. Enter a bond return below inflation and stock return above inflation. The maximum risk adjusted return will still include substantial bonds. The inflation rate doesn’t even enter into the picture.
Thanks for the reply.

The problem with 1) is that's great and makes a ton of sense if we're just talking about being forced into a bond or cash option (do you want to lose money fast or slow :D) . But I would argue there are better options with a better expected return. We can financially engineer any product we want with futures.

2. I'm with you on this part, but if cash is supposed to have a greater expected return, according to modern portfolio theory the appropriate response it to delever.

Regarding PV - if you do efficient frontier forecast (4% stock return, -2% bond), upload your own correlations (for instance I did this exercise with a correlation of 0.2 between stocks and bonds - which isn't implausible in a fiscal policy environment), you'll see that the whole efficient frontier falters. I think this is because PV can't factor in a negative (short allocation). It gives the tangency portfolio as 100% stocks and if you actually trace the tangent point the portfolio has a negative expected return.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Tue Nov 16, 2021 9:13 am
hdas wrote: Tue Nov 16, 2021 9:12 am
skierincolorado wrote: Tue Nov 16, 2021 8:33 am Having suffered through the last few months of Zn I would not want to be making big changes to my Aa now. I would go for a more subtle diversification.
You didn't have to suffer, if you had looked at the data and realized that the out-under performance of this scheme is totally attributed to the flattening/steepening cycle, i.e the term premium. Just create a term premium series using 5/30 curve and run the regression.

Image
We’ve been over this. I challenge you to come up with a rules based backtest that outperforms buy and hold. For example, I’m highly skeptical that any rules based approach could have predicted the strong ITT returns from 2010 to 2015. And even if it did it was likely just data mining and overfit.

You’ve picked 2018 as the endpoint for a switch. What if COViD happened in 2017?

Pick a rule and test it. If the rule is simple and the test robust I would seriously consider following it.
hdas' table looks convincing and I was intrigued, but when you bring up the chart, not so much. The inverted 30y5y as a switch signal would have failed in 2018. It came very close to inverting, but missed it.

How about using the 2% and 1% levels as a trigger. I know, now we are data mining. Also examine if this would be subsumed by the carry strategy.

Interesting how every recession period was accompanied by curve steepening, no exception, including the 80ies. A long ITT / short LTT (curve steepener) component to the portfolio might be a perfect negatively correlated diversifier to equities, with positive expected returns.

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

Post by hdas »

hhhhhhh
Last edited by hdas on Tue Nov 23, 2021 12:34 pm, edited 1 time in total.
....
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Tue Nov 16, 2021 3:36 pm I edited to include the fact that the loss on the ZB in my 2.5% widening was nearly as large on all those ZFs in your 2.5% inversioning (I won't even call that a flattening haha so I am making up a word). This is what I mean by he has equal risk at each duration.

Ignoring the fact that a 2.5% widening is probably more likely than a 2.5% inversioning, we still should tilt towards the lower duration because the roll and carry is better. If there is no flattening or widening, the ZF wins substantially. Only if we believe flattening/inversioning will be rapid at high probability would we want equal risk. That's the breakeven. Otherwise we tilt to the one with the better roll and carry and historical returns.

If widening/flattening was a normal distribution centered at zero... we would pick ZF and zero TN or ZB. It's not centered at zero though.. slight flattening is probably a bit more likely than widening. But not enough to push us into equal risk in ZB.

How about a more realistic scenario where 4.5 year rates increase 3% and 11.5 year rates increase 2.5%. The yield curve would still be inverted. But one would of course have been much better off in the shorter durations 1) because we can have less duration risk (I'd replace each ZB with 1.5 ZFs) and 2) unless this happened overnight we'd be getting the much better roll and carry of the shorter durations every single day that interest rates didn't rise
But what is so bad about equal risk in ZF as in ZB. It means your allocation would be agnostic to 5y12y steepening or flattening. All the while you would be collecting the higher carry returns from your ZF with 70%+ of your treasury portfolio (> 75% in DMoogle's proposal). If we assume a 0.75% risk-adjusted outperformance of ZF vs ZB, you would be giving up 0.75% * 0.25 = 0.1875% CAGR for the benefit of being shielded from 5y12y flattening risk. (I got the 0.75% by eyeballing the Simplify charts, and reducing the factor for the higher risk of shorter maturities than strict duration matching would suggest, for compressed yield curve, and for uncertainties around persistence of anomalies.) I get your point and would not argue for or against it, but trying to quantify things. Seems like small return differences for small diversification and risk improvements.

We have to be cognizant that several return and risk factors are at play - duration, carry, steepening, flattening -, and everything is probabilistic and sensitive to input assumptions.
klaus14
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by klaus14 »

Lock wrote: Tue Nov 16, 2021 10:29 am
klaus14 wrote: Mon Nov 15, 2021 4:45 pm
skierincolorado wrote: Fri Sep 10, 2021 2:39 pm In case anyone missed it, this is my "final" estimate.

.3% ITT
.4% LTT
4.5% domestic stock
5% international stock

The efficient frontier is: 34/22/44 domestic stock / intl stock / ITT

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

***This is extremely sensitive to asssumptions. I suggest simply using the historical efficient frontier.***

I sold all my bond futures today.

Reasoning:
I am not confident that backtests apply to today. I was holding $1M worth of /ZN. ZN is close to 7 years maturity. The real yield on 7 years treasury is -1.5%. This is the median of return expectation for the 7 year time frame. So I'll loose (real) ~$15k (plus futures financing cost minus roll down yield)* every year on the average case. Notice that i am not saying rates will go up or down. This is just the mean expectation. Yes negative correlation with equities may help in the event of a recession. However, unlike past, now this hedge has significant costs compared to potential benefit (which is lower since real yields are at the lowest - less room to go down). I couldn't justify this given my investment horizon is very long (I am mid 30s)

*skierincolorado above did more complex math including roll down yield and forward rate estimates. Using that figure, nominal return expectation: 0.3% ITT => real: -2.8% (using breakeven). And quote is from Sept 7 and real rates are worse today.

So now my only bond holdings are: I Bonds, EE Bonds, an old CD yielding 2.75%
I am planning to buy /ZN when 7 years real yield is positive again.

I wish best of luck to everyone in this thread. I learned a lot here.
Why not just go short (i.e. sell contracts)? YTD the stock/bond correlation has been positive so you can re-create a negative correlation asset.

Disclaimer: I've been running a risk parity portfolio for about 3 years and this year I sold ZN contracts for the first time.
That would only make sense if nominal return expectation was negative AND correlation to equities is positive.
I don't know how to do the math myself unfortunately but skierincolorado posted +0.3 or +0.4 above which is too small for me to justify a position but still positive.
My investment algorithm: https://www.bogleheads.org/forum/viewtopic.php?f=10&t=351899&p=6112869#p6112869
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

hdas wrote: Tue Nov 16, 2021 7:30 pm
comeinvest wrote: Tue Nov 16, 2021 6:58 pm
How about using the 2% and 1% levels as a trigger. I know, now we are data mining. Also examine if this would be subsumed by the carry strategy.

Interesting how every recession period was accompanied by curve steepening, no exception, including the 80ies. A long ITT / short LTT (curve steepener) component to the portfolio might be a perfect negatively correlated diversifier to equities, with positive expected returns.
The funny thing is that even if we have some shock that makes interest rates go down, Mr. Skier doesn't have enough ZF to match what LTT would do in such scenario. Furthermore, using the ad hoc constant leverage that is touted in this thread, it's very likely that even if the curve steepens, an allocation to EDV,GOVZ,ZROZ would do better....like it has been the case since Oct/2019.
It all depends on what ITT and LTT would actually do during a shock. It looks like in Spring 2020 the 5y30y steepened. Also look at diagrams like the one I posted here viewtopic.php?p=6323051#p6323051 . Also consider that skier has a lot more ITT than you would have LTT.

ITT outperformed duration-adjusted since Oct 2019 (and was a slightly better shock absorber duration-adjusted in Spring 2020), but there was a slight steepening between then and now, which favored ITT. Risk-adjusted, not sure which outperformed. I let skier speak to that one :)
https://www.portfoliovisualizer.com/bac ... on3_1=-230
klaus14
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by klaus14 »

comeinvest wrote: Tue Nov 16, 2021 2:07 pm
skierincolorado wrote: Tue Nov 16, 2021 10:50 am
Lock wrote: Tue Nov 16, 2021 10:29 am
klaus14 wrote: Mon Nov 15, 2021 4:45 pm I sold all my bond futures today.

Reasoning:
I am not confident that backtests apply to today. I was holding $1M worth of /ZN. ZN is close to 7 years maturity. The real yield on 7 years treasury is -1.5%. This is the median of return expectation for the 7 year time frame. So I'll loose (real) ~$15k (plus futures financing cost minus roll down yield)* every year on the average case. Notice that i am not saying rates will go up or down. This is just the mean expectation. Yes negative correlation with equities may help in the event of a recession. However, unlike past, now this hedge has significant costs compared to potential benefit (which is lower since real yields are at the lowest - less room to go down). I couldn't justify this given my investment horizon is very long (I am mid 30s)

*skierincolorado above did more complex math including roll down yield and forward rate estimates. Using that figure, nominal return expectation: 0.3% ITT => real: -2.8% (using breakeven). And quote is from Sept 7 and real rates are worse today.

So now my only bond holdings are: I Bonds, EE Bonds, an old CD yielding 2.75%
I am planning to buy /ZN when 7 years real yield is positive again.

I wish best of luck to everyone in this thread. I learned a lot here.
Why not just go short (i.e. sell contracts)? YTD the stock/bond correlation has been positive so you can re-create a negative correlation asset.

Disclaimer: I've been running a risk parity portfolio for about 3 years and this year I sold ZN contracts for the first time.
1)Because the expected return of zn is still likely positive for the long position and negative for the short.

2)I would guess the correlation was also positive in 2018 and 2019 leaving you caught red handed in 2020.

3)The difference between a +.05 and -.05 correlation is trivial and both would more accurately be described as uncorrelated. The strategy works not because the correlation between stocks and bonds has ever truly been significantly negative, but because we are able to take more risk in each bucket without increasing our overall risk because the buckets are uncorrelated. And the return of each bucket is positive.
But the expected returns of all treasury futures are currently negative if we believe the ACM model. I know I said the same about 2 pages upthread, and your answer was that your confidence in the ACM model is not that high, or you think it's too pessimistic. I must admit I don't really understand the ACM model, but it seems like somebody put way more thought into estimating term premia than I ever did. Although it seems to at least partially based on surveys, so I'm not sure about its confidence level. However it doesn't strike me as pessimistic, considering that the real returns are hugely negative for all treasury bonds, i.e. investors in treasuries knowingly transfer wealth to somebody else - why would anybody do that? On the other hand one could argue it's pessimistic, considering that most of the developed world has more negative yields. Investors that make the market must assume that all or most assets have negative returns in the future, and that there is no good way to park larger amounts of money for free. Weird world. I don't find Klaus' decision necessarily irrational, but his reasoning and supporting math was definitely wrong.
I may be wrong. Maybe we should use nominal returns. But, i find it uncanny to say: "As a long time investor, If I had a million dollars, i wouldn't invest in treasuries because their real return expectation is negative. However, I would happily assume the same exposure if i can do it with $50k capital". This just doesn't feel right. I understand the point about negative correlation or the lack of it but it is not really a strong point. Correlations have been changing lately and there is a logical argument for it (the reason growth stocks are highly valued is the low yields)
My investment algorithm: https://www.bogleheads.org/forum/viewtopic.php?f=10&t=351899&p=6112869#p6112869
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

klaus14 wrote: Tue Nov 16, 2021 8:31 pm I may be wrong. Maybe we should use nominal returns. But, i find it uncanny to say: "As a long time investor, If I had a million dollars, i wouldn't invest in treasuries because their real return expectation is negative. However, I would happily assume the same exposure if i can do it with $50k capital". This just doesn't feel right. I understand the point about negative correlation or the lack of it but it is not really a strong point. Correlations have been changing lately and there is a logical argument for it (the reason growth stocks are highly valued is the low yields)
If one assumes that inflation is 2%, that the cash funding rates stay below inflation (say -1% real in the medium run), and that I have good alternate investments like the equity market that I expect to return significantly above inflation (say 3% real), then it makes a lot of difference. Your discount rate of your treasury allocation in nominal terms would be 1% in case of cash funding (i.e. borrowing), but 5% in case of "equities funding" when you constrain yourself to a max 100% pie i.e. no borrowing, so to speak. But this logic has nothing to do with whether bond returns are negative or positive. It has everything to do with the fact that in the long run, equities are likely to outperform bonds exponentially, and the exponential function always "wins" if you wait long enough. That means if you have a pie of 100%, you might want to allocate it to equities only, if you can wait long enough. Not so if you have more than 100% to distribute.
Last edited by comeinvest on Tue Nov 16, 2021 8:51 pm, edited 2 times in total.
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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 »

klaus14 wrote: Tue Nov 16, 2021 8:31 pm
comeinvest wrote: Tue Nov 16, 2021 2:07 pm
skierincolorado wrote: Tue Nov 16, 2021 10:50 am
Lock wrote: Tue Nov 16, 2021 10:29 am
klaus14 wrote: Mon Nov 15, 2021 4:45 pm I sold all my bond futures today.

Reasoning:
I am not confident that backtests apply to today. I was holding $1M worth of /ZN. ZN is close to 7 years maturity. The real yield on 7 years treasury is -1.5%. This is the median of return expectation for the 7 year time frame. So I'll loose (real) ~$15k (plus futures financing cost minus roll down yield)* every year on the average case. Notice that i am not saying rates will go up or down. This is just the mean expectation. Yes negative correlation with equities may help in the event of a recession. However, unlike past, now this hedge has significant costs compared to potential benefit (which is lower since real yields are at the lowest - less room to go down). I couldn't justify this given my investment horizon is very long (I am mid 30s)

*skierincolorado above did more complex math including roll down yield and forward rate estimates. Using that figure, nominal return expectation: 0.3% ITT => real: -2.8% (using breakeven). And quote is from Sept 7 and real rates are worse today.

So now my only bond holdings are: I Bonds, EE Bonds, an old CD yielding 2.75%
I am planning to buy /ZN when 7 years real yield is positive again.

I wish best of luck to everyone in this thread. I learned a lot here.
Why not just go short (i.e. sell contracts)? YTD the stock/bond correlation has been positive so you can re-create a negative correlation asset.

Disclaimer: I've been running a risk parity portfolio for about 3 years and this year I sold ZN contracts for the first time.
1)Because the expected return of zn is still likely positive for the long position and negative for the short.

2)I would guess the correlation was also positive in 2018 and 2019 leaving you caught red handed in 2020.

3)The difference between a +.05 and -.05 correlation is trivial and both would more accurately be described as uncorrelated. The strategy works not because the correlation between stocks and bonds has ever truly been significantly negative, but because we are able to take more risk in each bucket without increasing our overall risk because the buckets are uncorrelated. And the return of each bucket is positive.
But the expected returns of all treasury futures are currently negative if we believe the ACM model. I know I said the same about 2 pages upthread, and your answer was that your confidence in the ACM model is not that high, or you think it's too pessimistic. I must admit I don't really understand the ACM model, but it seems like somebody put way more thought into estimating term premia than I ever did. Although it seems to at least partially based on surveys, so I'm not sure about its confidence level. However it doesn't strike me as pessimistic, considering that the real returns are hugely negative for all treasury bonds, i.e. investors in treasuries knowingly transfer wealth to somebody else - why would anybody do that? On the other hand one could argue it's pessimistic, considering that most of the developed world has more negative yields. Investors that make the market must assume that all or most assets have negative returns in the future, and that there is no good way to park larger amounts of money for free. Weird world. I don't find Klaus' decision necessarily irrational, but his reasoning and supporting math was definitely wrong.
I may be wrong. Maybe we should use nominal returns. But, i find it uncanny to say: "As a long time investor, If I had a million dollars, i wouldn't invest in treasuries because their real return expectation is negative. However, I would happily assume the same exposure if i can do it with $50k capital". This just doesn't feel right. I understand the point about negative correlation or the lack of it but it is not really a strong point. Correlations have been changing lately and there is a logical argument for it (the reason growth stocks are highly valued is the low yields)
If my risk tolerance were low, I absolutely would take an unleveraged cash position in treasuries and it would be totally rational to do so as long as the nominal return is expected to be positive OR if we believe bonds would rise in an equity crash.
Last edited by skierincolorado on Tue Nov 16, 2021 8:58 pm, edited 1 time in total.
Topic Author
skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

hdas wrote: Tue Nov 16, 2021 7:30 pm
comeinvest wrote: Tue Nov 16, 2021 6:58 pm
How about using the 2% and 1% levels as a trigger. I know, now we are data mining. Also examine if this would be subsumed by the carry strategy.

Interesting how every recession period was accompanied by curve steepening, no exception, including the 80ies. A long ITT / short LTT (curve steepener) component to the portfolio might be a perfect negatively correlated diversifier to equities, with positive expected returns.
The funny thing is that even if we have some shock that makes interest rates go down, Mr. Skier doesn't have enough ZF to match what LTT would do in such scenario. Furthermore, using the ad hoc constant leverage that is touted in this thread, it's very likely that even if the curve steepens, an allocation to EDV,GOVZ,ZROZ would do better....like it has been the case since Oct/2019.
And yet somehow buy and hold ITT has dramatically outperformed buy and hold LTT historically. Perhaps because baring a dramatic flattening (inversioning) or decrease in rates my “arbitrary” amount of ITT would beat LTT in every other scenario. Any rising rate scenario.. gradual decrease in rates scenario... any steepening scenario... and any slow flattening scenario.

Again I suggest you come up with a rules based strategy and backtest it.
Topic Author
skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Tue Nov 16, 2021 7:48 pm
skierincolorado wrote: Tue Nov 16, 2021 3:36 pm I edited to include the fact that the loss on the ZB in my 2.5% widening was nearly as large on all those ZFs in your 2.5% inversioning (I won't even call that a flattening haha so I am making up a word). This is what I mean by he has equal risk at each duration.

Ignoring the fact that a 2.5% widening is probably more likely than a 2.5% inversioning, we still should tilt towards the lower duration because the roll and carry is better. If there is no flattening or widening, the ZF wins substantially. Only if we believe flattening/inversioning will be rapid at high probability would we want equal risk. That's the breakeven. Otherwise we tilt to the one with the better roll and carry and historical returns.

If widening/flattening was a normal distribution centered at zero... we would pick ZF and zero TN or ZB. It's not centered at zero though.. slight flattening is probably a bit more likely than widening. But not enough to push us into equal risk in ZB.

How about a more realistic scenario where 4.5 year rates increase 3% and 11.5 year rates increase 2.5%. The yield curve would still be inverted. But one would of course have been much better off in the shorter durations 1) because we can have less duration risk (I'd replace each ZB with 1.5 ZFs) and 2) unless this happened overnight we'd be getting the much better roll and carry of the shorter durations every single day that interest rates didn't rise
But what is so bad about equal risk in ZF as in ZB. It means your allocation would be agnostic to 5y12y steepening or flattening. All the while you would be collecting the higher carry returns from your ZF with 70%+ of your treasury portfolio (> 75% in DMoogle's proposal). If we assume a 0.75% risk-adjusted outperformance of ZF vs ZB, you would be giving up 0.75% * 0.25 = 0.1875% CAGR for the benefit of being shielded from 5y12y flattening risk. (I got the 0.75% by eyeballing the Simplify charts, and reducing the factor for the higher risk of shorter maturities than strict duration matching would suggest, for compressed yield curve, and for uncertainties around persistence of anomalies.) I get your point and would not argue for or against it, but trying to quantify things. Seems like small return differences for small diversification and risk improvements.

We have to be cognizant that several return and risk factors are at play - duration, carry, steepening, flattening -, and everything is probabilistic and sensitive to input assumptions.
Good math. But I view that as a lot of cagr especially when levered 2x to nearly .4%, for a risk I’m not terribly concerned about mitigating. If the 5y12y gets even flatter than it is currently or inverts it’s no big deal the relative outperformance of zb would be quite small. It’s the rising rate scenario that is the real risk for this strategy. And in that scenario I would rather have 1.5x as much zf instead of zb.
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