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

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

Post by hdas »

hhhhhh
Last edited by hdas on Wed Nov 24, 2021 3:45 pm, edited 1 time 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 »

hdas wrote: Wed Nov 24, 2021 2:51 pm
skierincolorado wrote: Wed Nov 24, 2021 1:27 pm I can say that I am not down nearly as much as you suggest on my bond position, and I doubt others are either unless they had the misfortune of entering this strategy on the worst possible day of the last decade or have more leverage. I am down under 3%.
Good to hear. What this means is that you are only down ~ 13-15% in relative terms. You must factor the counterfactual!. Perhaps it also means you don't have enough ZF so when some shock happens, you could underperform LTT also in the way up!!

How long will it take for you to recover so your position is not underwater RELATIVE to having same exposure in LTT?

For people that deviate from the good path (myself included), it's always good to compare our real life performance with a composite of benchmarks. A composite of benchmarks for you would at least include:

1. A target date fund that matches your investing horizon.
2. A leveraged portfolio mimicking your your current leverage and asset allocation. Including international equities. This benchmark should include a bond fund with the duration that matches your investment horizon. From your comments seems like you should be in EDV, ZROZ, GOVT et.al.
skierincolorado wrote: Wed Nov 24, 2021 1:27 pm Comeinvest had some success market timing the switch, but I’m not entirely convinced it’s reproduceable.
He abandoned the UB ship a long time ago, so one can hardly call that "some success".

I can find many reasons to expect the curve to continue flattening, and perhaps invert. It could be useful to frame your expectations:

1. Can you find good reasons for persistent steepening, besides hoping for another COVID or a war?
2. Are you expecting the FED to reverse course and announce a slowdown or stop on the path to normalization?
3. Do you think the current best market estimate of long term inflation is wrong?
4. Do the short term inflation concerns, coupled with secular trends of deflation in the long term support a secular steepening of the curve?

At the time of this message the 5/30 spread is 0.625%

A image for the visually inclined, starting with a 500k allocation (as of 11/22/21):

Image
I’m also down 2000% relative to GME. Your other points are market timing and I don’t have an opinion on them, at least not an opinion I am confident enough in to be actionable.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

I had some luck as long as I had UB and before skier convinced me, never called it market timing or even a strategy - just luck :) Now it looks like I "should" have held it longer, but it would be foolish to judge a strategy by a 6-months performance. Skier did a lot of work going back 75-100 years, and examined mHFEA under most conceivable scenarios. Like any other investment strategy, there is still no 100% guarantee that it works, not even in the medium-long run - with no risk there would probably be no possible return. I outlined a few possible adverse scenarios in some of my posts in this thread and in the HFEA thread.

I currently took short positions in TN and UB, and very long ZN as a tactical relative value play overlay to mHFEA, as an experiment. Unfortunately my analytic data capabilities are not as good as I wish - particularly historic futures durations and such. But I estimated my risk and return under reasonable worst case scenarios. I read an opinion piece that the 20y-30y inversion is an exploitable anomaly, but unfortunately there is no 20y future. Although I'm still learning, I don't have high confidence in dynamic strategies yet. mHFEA is very sound.
Last edited by comeinvest on Thu Nov 25, 2021 6:48 am, edited 1 time in total.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by oldcomputerguy »

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

Post by zkn »

hdas wrote: Sat Nov 20, 2021 1:34 pm [..cut...]

All your "backtests" include look ahead bias, they are a naive interpolations. Follow this exercise: Imagine that your are sitting on Jan-2010 and you decided to implement this strategy. Your run the backtest up to the present (Dec-2009) and get this:

VUSTX > CAGR 7.67, STD 9.11, Sharpe 0.47
VFINX > CARG 6.78, STD 5.21, Sharpe 0.61

You say, GREAT!, I can leverage VFINX and do better than VUSTX, based on the information of the last 20 years. Let's leverage VFINX up to the level that matches the volatility VUSTX. Look at the beautiful backtest: By leveraging VFINX 1.78x, you match the volatility of VUSTX and get an extra 1.3% of CAGR, great!!. Now let's see how that played out in reality:

Image

[..cut...]
I am assuming all instances of "VFINX" (SP500) here should have been "VFITX" (ITTs).

This may be conceived as an issue of position sizing rather than underperformance. VFITX actually outperforms VUSTX during the second period in terms of Sharpe (.59 for VFITX versus .52 for VUSTX). The problem was that the investor who selected their position size based on the SD of VFITX during 1992 to 2009 (inclusive) would have been under-positioned (or under-leveraged) as the riskiness of VFITX plummeted. A VFITX investor who was better positioned for risk would have outperformed a VUSTX investor during the second period.

Perhaps a better question is whether position sizing is easier with longer duration treasuries than shorter duration. That is, maybe the risk of longer duration treasuries is more consistent over time, allowing for better results in the real world even if Sharpe is lower because investors would have better position sizes in practice.

I looked at this using the data from Simba's dataset. I am not sure how great the data is, but some data is better than no data. The data is spliced and yearly. This is how the data is documented:

LTT
1871-1941 Longinvest's bond fund simulator (30-10 model) (crude mapping, by lack of LT interest rates history in this time period)
1942-1972 Longinvest's bond fund simulator (30-10 model)
1973-2009 Bloomberg Barclays US Treasury Long TR USD
2010+ Vanguard Long-Term Treasury Index Fund (VLGSX)

ITT
1871-2002 Longinvest's bond fund simulator (10-3 model)
2003-2009 Bloomberg Barclays US Treasury 3-10 Yr TR USD
2010+ Vanguard Intermediate-Term Treasury Index Fund (VSIGX)

STT
1871-1975 Longinvest's bond fund simulator (3-1 model)
1976-2009 Bloomberg Barclays Treasury 1-3 Yr TR USD
2010+ Vanguard Short-Term Treasury Index Fund (VSBSX)

I calculated the standard deviation of the previous 10 years of annual percentage returns:

Image

The rolling SDs for LTTs are a lot more variable, but this is not a fair comparison because we would be leveraging shorter duration treasuries. Here is the same standard deviation series, but divided by the overall SD for the full series of annual percentage returns for each type of treasuries, on a log scale:

Image

The ratio describes the experienced risk (as defined as the standard deviation over the previous 10 year returns) relative to the risk of the entire time period. For example, a hypothetical ITT investor who was invested with a fixed proportion for the entire time period would have experienced only 20% of the average risk during 1935-1944 and 200% of the average risk during 1978-1987.

My take-aways...
  • The SD of the bond returns is very variable, suggesting it is difficult to forecast future SD (and therefore optimal positioning) based on historical data.
  • Bond returns of all maturities were very variable, suggesting that using LTT does not help us here. In fact, the SD of the log ratios is all about the same, suggesting that LTT/ITT/STT investors will experience about the same variation in their realized vs target risk.
  • I am not economic historian but it is notable that the lowest SDs were experienced while the FOMC was directly controlling the Treasury yield curve in the 40s (see paper). The highest SDs were experienced when rates peaked in early 1980s (FRED). Then for some reason we see a divergence where SD of LTT remained above the historical average but STT dropped below its historical average.
  • It is the anomaly of LTT SDs remaining elevated while ITT SDs reverted to their historical mean in the 2010s that explains hdas' results for better returns from LTT during that period despite lower Sharpe. But an LTT investor using a historical SD from a larger backtest to select position sizing would have exceeded their target SD/risk during this period.
  • Using only more readily available data (e.g., post-1980) would lead to observing larger differences in STT/ITT/LTT risk profiles than in Simba's data from 1871 and hence promote larger leverage ratios for STT and ITT to match the risk of LTT. This may be relevant when interpreting (e.g., PortfolioVisualizer-based) backtests.
Ultimately hdas does have a point that in lieu of look-ahead bias, position sizing probably will not be optimal for the future. A conservative investor who assumes risk may be realized in the higher percentiles in history and positions accordingly then should expect lower returns as risk is likely to be lower than expected. But the question about LTT vs ITT (or STT) is probably irrelevant to this point as they all show similar variability in risk over time, so investing in LTT does not help to get position sizing right. Also I don't see that the position sizes in mHFEA specifically have been closely optimized to the data that would necessarily introduce large look-ahead bias in the results anyway.
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millennialmillions
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by millennialmillions »

DMoogle wrote: Wed Nov 24, 2021 11:44 am
millennialmillions wrote: Sun Nov 21, 2021 11:48 amTo roll the contracts from December to March, I am planning to use a calendar spread order to ensure I sell the December contract and buy March at the same time. Here is a walkthrough of how to do that in TWS, but it is also very intuitive in the mobile app under "Future Spread Combo", which is what I'm planning to use.
Where is the Future Spread Combo in the mobile app? Kept poking around and couldn't find it. Probably just going to sell DEC position and buy next quarter's separately.
Go to trade -> quote -> ZF -> Future Spread Combo and then you will have a nice interface to choose the front and back of your roll. However, note that I (along with some others here) got errors when trying to do limit orders on mobile. I just ended up placing market orders during trading hours.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by DMoogle »

millennialmillions wrote: Fri Nov 26, 2021 10:55 amGo to trade -> quote -> ZF -> Future Spread Combo and then you will have a nice interface to choose the front and back of your roll. However, note that I (along with some others here) got errors when trying to do limit orders on mobile. I just ended up placing market orders during trading hours.
Thanks, don't know how I missed that since it's basically the same for options/setting up a box spread. I ended up doing market orders on Wednesday.

Got unlucky in the timing, given I moved a good chunk from ZN to ZF on Wednesday and bonds are way up today, but balanced out by being lazy and not increasing my exposure to stocks until today. Evens out, I suppose. :beer
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by zkn »

comeinvest wrote: Tue Nov 23, 2021 7:16 pm
[...]

50/150: I think if you have a longer horizon, 50/150 would arguably be more risky to achieving your investment goals than 135/200 or something, considering that the future returns from treasuries are highly questionable even whether they will be positive or negative based on current valuations. The stock market is arguably more predictable to be positive at least over medium or longer time horizons, and then the treasuries are the icing on the cake, if they ever turn out to add to my returns. That's my thinking.

We do have to account for the possibility that the term premium will never be positive again, even if it sounds absurd. Times change. For example, whoever invests in German 30-year treasuries right now, is guaranteed a loss for 30 years of -2% p.a. if inflation is 2% over that time period, and I think inflation expectations implied from derivatives are around 2%, at least for the next 10 years or so. I know the term premium might still be slightly positive even with negative real returns, but even that is not guaranteed. Absurd does not mean impossible.

The equity risk premium will probably be lower than historically, but it was initially a lot higher than the term premium. So it might be that in the future, only equities can generate positive returns over investors' lifetimes. Likewise, unlike the past, I think the returns of the equity allocation might dominate the overall outcome in the future.
The main point I was trying to make is the principles described in this thread, such as allocating a larger proportion of risk to bonds and tilting bonds to lower maturities, would make just as much sense to someone not interested in a high-risk portfolio. Maybe something like a "half mHFEA" 62.5/135 would have been a better example. There was a comment in another thread suggesting that using leverage to manage risk is a facade and people are only using leverage to increase risk. I don't agree, leverage can be used to achieve time diversification (lifecycle investing), portfolio optimization (no need to overlook/underweight high Sharpe but low-risk assets when leverage is available), and BAB factor tilts. Yet I can see how people could come to the conclusion that all the discussions of leverage are reflecting speculative fervor (and maybe they are).

Anyway my original example does betray my bias towards higher allocations to bonds towards risk parity weighting. I have been trying to catch up to previous discussions on the robustness of the term premium, which has obvious implications on whether it makes sense to hold bonds at all let alone dedicate a large proportion of risk to bonds. I understand models such as ACM estimate negative term premiums. Here are some hypotheses:

1) The composition of bond market participants has changed to be dominated by actors that do not require term premiums, such as pension funds with long-term liabilities. So bonds are priced according to unbiased expectations theory and no term premium exists. This makes sense, but I am not aware of evidence that the market composition has changed from recent history when there was a term premium.
2) The models are wrong. The models are probably ball-park correct that the term premium has been decreasing and close to zero but they may not be exact. I'd have to do a lot more work to intelligently critique the models, but it did stand out to me that ACM and KW models assume that rates are normally distributed. This seems unreasonable if the market expects central banks to enforce the zero bound, which implies a non-symmetric distribution that is maybe or maybe not truncated at zero. There is literature on this point but it is technical and it would be a lot of effort to get on top of that (and this is not my job).
3) The bond market is wrong. Well, maybe. But this is Bogleheads after all and trying to out-smart the market tends not to work out. I am confident that the consensus of professional bond traders know better than me.
4) The term premium is low, zero or even negative but bond holders are compensated in some other way. The obvious reason is hedging. The term premium may be decreasing due to increased hedging demands and greater expectation of negative stock-bond correlation. There are a lot of papers on this (e.g.,) Hedging is not just for reducing risk, as a rebalanced portfolio with mean-reverting negatively correlated assets can have a greater expected (arithmetic) return than the weighted average return of the two assets. In theory a stock-bond portfolio with zero return on the bonds can have a greater return than a 100% stock portfolio due to this effect. Furthermore, even without this effect so the expected return is not boosted (lets say stocks and bonds are not mean reverting), variance of the portfolio is decreased, and hence CAGR, safe withdrawal rate, and Kelly criterion can be increased. So negative correlation is a reward as well any return premium.

The other side of the equation is the equity risk premium. Are equities such a great deal right now with the SP500 CAPE at 39? Equities have a great historical record, especially in US data, but we cannot guarantee the future will look like the past. The historical record has a more than doubling of stock valuations, presumably due to a repricing of the equity risk premium lower as investors priced in better regulations, lower fees/taxes, "the Fed put", better access to diversification, etc. as well as possibly unexpected degree of economic growth in the US. Furthermore, US stocks are not immune to the more dramatic crashes and drawdowns experienced by Japan post-1990 and the various countries that were devastated by the world wars just because there are no sequences that bad in the US data. In contrast to stocks and their increasing valuations, long run data on US bonds would probably more fairly forecast future returns for bonds as rates went the full cycle, not just down. It is not so much that bonds are so great - they did get destroyed in the rising rate cycle - but maybe we should not be so confident stocks are so great either.

4 is a key point here. If the market was expecting a higher and positive stock-bond correlation, we would probably have a higher term premium. But would that necessarily mean we should allocate more to bonds? I am not so sure -- the market is saying the greater term premium is a fair trade for the higher correlation, so maybe we should not change the allocation. In relation to confirming that the bond market is pricing in a negative stock-bond correlation right now, my working model is that stocks and bonds are repriced in the same direction as expectations of inflation change and in different directions as expectations of growth change. Thus a positive stock-bond correlation is realized in periods where inflation expectations are more volatile than growth expectations. So we should be most concerned about positive stock-bond correlations when uncertainty about inflation is high. The market uncertainty about inflation is currently less than what it was in 2013 (based on the standard deviation of the probability density function derived from CPI options, via this tool). So I am not worried about the correlation flipping positive for an extended period right now. My working model of the stock-bond correlation assumes that the Fed reacts to market pressures to mediate the relationship between rates with growth and inflation. This is not always true but I'll leave the macroeconomic theorizing out.

So in sum it is not so obvious to me that something so dramatic has changed that makes holding bonds a bad deal.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by LTCM »

hdas wrote: Wed Nov 24, 2021 2:51 pm 1. Can you find good reasons for persistent steepening, besides hoping for another COVID or a war?
wikipedia wrote:The [Omicron] variant was first reported to the World Health Organization (WHO) from South Africa on 24 November 2021.
Impeccable timing. :beer
60% VUG - 20% VEA - 20% EDV
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

zkn wrote: Sat Nov 27, 2021 4:59 pm
comeinvest wrote: Tue Nov 23, 2021 7:16 pm
[...]

50/150: I think if you have a longer horizon, 50/150 would arguably be more risky to achieving your investment goals than 135/200 or something, considering that the future returns from treasuries are highly questionable even whether they will be positive or negative based on current valuations. The stock market is arguably more predictable to be positive at least over medium or longer time horizons, and then the treasuries are the icing on the cake, if they ever turn out to add to my returns. That's my thinking.

We do have to account for the possibility that the term premium will never be positive again, even if it sounds absurd. Times change. For example, whoever invests in German 30-year treasuries right now, is guaranteed a loss for 30 years of -2% p.a. if inflation is 2% over that time period, and I think inflation expectations implied from derivatives are around 2%, at least for the next 10 years or so. I know the term premium might still be slightly positive even with negative real returns, but even that is not guaranteed. Absurd does not mean impossible.

The equity risk premium will probably be lower than historically, but it was initially a lot higher than the term premium. So it might be that in the future, only equities can generate positive returns over investors' lifetimes. Likewise, unlike the past, I think the returns of the equity allocation might dominate the overall outcome in the future.
The main point I was trying to make is the principles described in this thread, such as allocating a larger proportion of risk to bonds and tilting bonds to lower maturities, would make just as much sense to someone not interested in a high-risk portfolio. Maybe something like a "half mHFEA" 62.5/135 would have been a better example. There was a comment in another thread suggesting that using leverage to manage risk is a facade and people are only using leverage to increase risk. I don't agree, leverage can be used to achieve time diversification (lifecycle investing), portfolio optimization (no need to overlook/underweight high Sharpe but low-risk assets when leverage is available), and BAB factor tilts. Yet I can see how people could come to the conclusion that all the discussions of leverage are reflecting speculative fervor (and maybe they are).

Anyway my original example does betray my bias towards higher allocations to bonds towards risk parity weighting. I have been trying to catch up to previous discussions on the robustness of the term premium, which has obvious implications on whether it makes sense to hold bonds at all let alone dedicate a large proportion of risk to bonds. I understand models such as ACM estimate negative term premiums. Here are some hypotheses:

1) The composition of bond market participants has changed to be dominated by actors that do not require term premiums, such as pension funds with long-term liabilities. So bonds are priced according to unbiased expectations theory and no term premium exists. This makes sense, but I am not aware of evidence that the market composition has changed from recent history when there was a term premium.
2) The models are wrong. The models are probably ball-park correct that the term premium has been decreasing and close to zero but they may not be exact. I'd have to do a lot more work to intelligently critique the models, but it did stand out to me that ACM and KW models assume that rates are normally distributed. This seems unreasonable if the market expects central banks to enforce the zero bound, which implies a non-symmetric distribution that is maybe or maybe not truncated at zero. There is literature on this point but it is technical and it would be a lot of effort to get on top of that (and this is not my job).
3) The bond market is wrong. Well, maybe. But this is Bogleheads after all and trying to out-smart the market tends not to work out. I am confident that the consensus of professional bond traders know better than me.
4) The term premium is low, zero or even negative but bond holders are compensated in some other way. The obvious reason is hedging. The term premium may be decreasing due to increased hedging demands and greater expectation of negative stock-bond correlation. There are a lot of papers on this (e.g.,) Hedging is not just for reducing risk, as a rebalanced portfolio with mean-reverting negatively correlated assets can have a greater expected (arithmetic) return than the weighted average return of the two assets. In theory a stock-bond portfolio with zero return on the bonds can have a greater return than a 100% stock portfolio due to this effect. Furthermore, even without this effect so the expected return is not boosted (lets say stocks and bonds are not mean reverting), variance of the portfolio is decreased, and hence CAGR, safe withdrawal rate, and Kelly criterion can be increased. So negative correlation is a reward as well any return premium.

The other side of the equation is the equity risk premium. Are equities such a great deal right now with the SP500 CAPE at 39? Equities have a great historical record, especially in US data, but we cannot guarantee the future will look like the past. The historical record has a more than doubling of stock valuations, presumably due to a repricing of the equity risk premium lower as investors priced in better regulations, lower fees/taxes, "the Fed put", better access to diversification, etc. as well as possibly unexpected degree of economic growth in the US. Furthermore, US stocks are not immune to the more dramatic crashes and drawdowns experienced by Japan post-1990 and the various countries that were devastated by the world wars just because there are no sequences that bad in the US data. In contrast to stocks and their increasing valuations, long run data on US bonds would probably more fairly forecast future returns for bonds as rates went the full cycle, not just down. It is not so much that bonds are so great - they did get destroyed in the rising rate cycle - but maybe we should not be so confident stocks are so great either.

4 is a key point here. If the market was expecting a higher and positive stock-bond correlation, we would probably have a higher term premium. But would that necessarily mean we should allocate more to bonds? I am not so sure -- the market is saying the greater term premium is a fair trade for the higher correlation, so maybe we should not change the allocation. In relation to confirming that the bond market is pricing in a negative stock-bond correlation right now, my working model is that stocks and bonds are repriced in the same direction as expectations of inflation change and in different directions as expectations of growth change. Thus a positive stock-bond correlation is realized in periods where inflation expectations are more volatile than growth expectations. So we should be most concerned about positive stock-bond correlations when uncertainty about inflation is high. The market uncertainty about inflation is currently less than what it was in 2013 (based on the standard deviation of the probability density function derived from CPI options, via this tool). So I am not worried about the correlation flipping positive for an extended period right now. My working model of the stock-bond correlation assumes that the Fed reacts to market pressures to mediate the relationship between rates with growth and inflation. This is not always true but I'll leave the macroeconomic theorizing out.

So in sum it is not so obvious to me that something so dramatic has changed that makes holding bonds a bad deal.
Your analysis is a lot more sophisticated than mine. However, let's take a step back and see what makes sense. I think almost all your points would equally apply to the European situation. However, would you use an asset with -2% estimated real return for 30 years as part of your multi-asset rebalancing strategy? I know, maybe there is a sudden drop of inflation in years 10-30 (I don't know if inflation estimates are available beyond 10y). But maybe there is a sudden rise in inflation somewhere before year 30. Who knows. Besides, the German 10y bond has almost the same negative real return, guaranteed, and the inflation numbers are from tradable derivatives, so -2% is what you get if you assume no-arbitrage. Show me an asset allocation, rebalanced or not, that benefits from an asset with a "guaranteed" -2% p.a. real return for 10 years. Or look how much German bonds benefitted from the Covid crisis: not very much. I know, we are talking about the U.S., not Germany. But what I'm trying to say, you have to draw some line where you stop trusting models from historic backtests and efficient markets, don't you?

The U.S. stock market valuations are high, but by magnitudes lower than those of Japan at their peak. The stock market returns will be the sum of dividend growth (or earnings growth) plus variations in valuation. The former is exponential in the long run; the latter are hard to predict but are somewhat mean-reverting by nature, i.e. the variations will offset in the long run, and become negligible compared to the exponential growth part. That's my understanding. Treasury returns, by contrast, can be very accurately predicted from the current yields. They also have a valuation part to performance between now and maturity, which is mean-reverting by nature, and interest rates "kind of" have a lower bound of zero or near zero. In summary, even though nobody knows nothing about the future, and even though it's difficult to build quantitative models for an unprecedented situation, I can kind of see why many mHFEA people in this thread use a "muted" treasury allocation.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by zkn »

comeinvest wrote: Tue Nov 23, 2021 7:16 pm Your analysis is a lot more sophisticated than mine. However, let's take a step back and see what makes sense. I think almost all your points would equally apply to the European situation. However, would you use an asset with -2% estimated real return for 30 years as part of your multi-asset rebalancing strategy? I know, maybe there is a sudden drop of inflation in years 10-30 (I don't know if inflation estimates are available beyond 10y). But maybe there is a sudden rise in inflation somewhere before year 30. Who knows. Besides, the German 10y bond has almost the same negative real return, guaranteed, and the inflation numbers are from tradable derivatives, so -2% is what you get if you assume no-arbitrage. Show me an asset allocation, rebalanced or not, that benefits from an asset with a "guaranteed" -2% p.a. real return for 10 years. Or look how much German bonds benefitted from the Covid crisis: not very much. I know, we are talking about the U.S., not Germany. But what I'm trying to say, you have to draw some line where you stop trusting models from historic backtests and efficient markets, don't you?

The U.S. stock market valuations are high, but by magnitudes lower than those of Japan at their peak. The stock market returns will be the sum of dividend growth (or earnings growth) plus variations in valuation. The former is exponential in the long run; the latter are hard to predict but are somewhat mean-reverting by nature, i.e. the variations will offset in the long run, and become negligible compared to the exponential growth part. That's my understanding. In summary, even though nobody knows nothing about the future, I can kind of see why many mHFEA people in this thread use a "muted" treasury allocation.
My thinking is this: if we take the tautology that all asset returns are the sum of the risk-free rate and a risk premium, negative expected or even guaranteed negative returns are not so immediately relevant if the negative return is reflecting a negative risk-free rate and not a negative risk premium. When selecting the portfolio that has maximal returns for a unit of risk, the risk-free rate is irrelevant. When the goal of optimization is to maximize expected returns for a given level of risk, the risk-free rate is still irrelevant, because the optimal solution would be to lever the risk-return optimized portfolio to the given level of risk. However, it is relevant if the goal of optimization is a given value of CAGR or expected return, or a given % chance of reaching some final portfolio balance, because more leverage would be required for lower risk-free rates. But in all of these cases, the optimal weighting of stocks vs bonds is unchanged by the risk-free rate going negative.

In line with this, I would take an asset that has a -2% annual real return if the cost to carry that asset was significantly less than that to compensate for the risk of holding that asset, i.e., the risk premium was fair. It is not obvious to me why negative bond returns should imply a negative term risk premium, but maybe the term premium is zero or even negative right now as you have suggested may be the case and the ACM model implies. Maybe that is related to the rates being negative or maybe that is something else entirely. I would draw a line when prices (and the probabilities implied by the prices etc.) are outside my range of plausibility, the composition of market participants had significantly changed in a way that suggests the historical risk premium may be gone, and/or the market participants had significantly different preferences to me. The example of German bonds is certainly challenging. (Anyway, comeinvest, I thought you held European bonds?) I'm sure a compelling argument can be made that we are on the wrong side of the line for US bonds, but I am not sure we are there yet for the reasons I noted in my previous post.

I find your argument in the second paragraph appealing. Maybe stocks require less faith in models. Stocks are ownership in real companies that have real earning growth but bonds are just securitized agreements and are less "real". On the other hand, the high stock valuations may be suggesting all that earning growth is already priced in for the immediate future. That is, that stock returns are also suppressed by a low, negative real risk-free rate like bond returns.

There is no escape from models; any forecasted expected return must come from a model. But all the models are bad. That's actually my preference for risk-parity weighting, because it follows in my view from the simplest and weakest modelling assumptions.
Hfearless
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Hfearless »

zkn wrote: Mon Nov 29, 2021 5:50 pm In line with this, I would take an asset that has a -2% annual real return if the cost to carry that asset was significantly less than that to compensate for the risk of holding that asset, i.e., the risk premium was fair.
So in ELI5 terms—you would happily hold an asset with a negative return if you were sufficiently confident it would surge in time of crisis and thus permit you to leverage your equities higher than you would be able to otherwise, compensating for the drag of said asset?

By the way, another thing that grows most of the time and surges in time of crisis is a short position in developing countries’ currencies. I’m trying to wrap my head around whether that’s somehow a trap.
DMoogle
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by DMoogle »

Hfearless wrote: Mon Nov 29, 2021 6:12 pmSo in ELI5 terms—you would happily hold an asset with a negative return if you were sufficiently confident it would surge in time of crisis and thus permit you to leverage your equities higher than you would be able to otherwise, compensating for the drag of said asset?
This is a perfectly logical position. Think of an extreme theoretical scenario: say there's a volatile asset A with 7% expected return, and another asset B with -3% expected return, but when an equal position is taken with both assets, all volatility is neutralized. Your average return is 2%, but due to 0 volatility, you could leverage infinitely for infinite profit.

Reality isn't like extreme scenarios, but the concept still exists - achieving a better risk-adjusted return may involve including assets with negative expected return.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by zkn »

DMoogle wrote: Mon Nov 29, 2021 6:19 pm
Hfearless wrote: Mon Nov 29, 2021 6:12 pmSo in ELI5 terms—you would happily hold an asset with a negative return if you were sufficiently confident it would surge in time of crisis and thus permit you to leverage your equities higher than you would be able to otherwise, compensating for the drag of said asset?
This is a perfectly logical position. Think of an extreme theoretical scenario: say there's a volatile asset A with 7% expected return, and another asset B with -3% expected return, but when an equal position is taken with both assets, all volatility is neutralized. Your average return is 2%, but due to 0 volatility, you could leverage infinitely for infinite profit.

Reality isn't like extreme scenarios, but the concept still exists - achieving a better risk-adjusted return may involve including assets with negative expected return.
I agree with the logic. But you really need to have a strong case for the negative correlation to lever up a portfolio after adding a risk asset. If the correlation turns positive, you could end up with a portfolio way more risky than you had targeted.

Something to consider on being short the carry trade: High-interest currencies are often correlated with commodity prices (and hence inflation). Adding a short carry trade position to a stock-bond portfolio with US treasuries might result in doubling up on deflationary shock protection while adding more vulnerability to inflation.
Hfearless
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Hfearless »

zkn wrote: Mon Nov 29, 2021 8:44 pm Something to consider on being short the carry trade: High-interest currencies are often correlated with commodity prices (and hence inflation). Adding a short carry trade position to a stock-bond portfolio with US treasuries might result in doubling up on deflationary shock protection while adding more vulnerability to inflation.
Isn’t that risk as easily hedged with futures? Add e. g. gold futures to the mix and suddenly it’s as though you own gold but it’s yielding 10%.
DMoogle
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by DMoogle »

zkn wrote: Mon Nov 29, 2021 8:44 pm I agree with the logic. But you really need to have a strong case for the negative correlation to lever up a portfolio after adding a risk asset. If the correlation turns positive, you could end up with a portfolio way more risky than you had targeted.
True, it can, but just because assets are positively correlated doesn't mean there isn't a benefit - basically any correlation below 1 has a benefit in diversification, even if it's above 0 (with the exception being systematic risk that theoretically cannot be diversified away). Most stocks are positively correlated with each other, but there's still a benefit to holding multiple stocks vs. only one.

But yeah, have to be careful for sure. Just like with the original HFEA, this isn't for the faint of heart.

I'm not going to comment on the currency aspect, because it's something I know practically nothing about.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

zkn wrote: Mon Nov 29, 2021 8:44 pm
DMoogle wrote: Mon Nov 29, 2021 6:19 pm
Hfearless wrote: Mon Nov 29, 2021 6:12 pmSo in ELI5 terms—you would happily hold an asset with a negative return if you were sufficiently confident it would surge in time of crisis and thus permit you to leverage your equities higher than you would be able to otherwise, compensating for the drag of said asset?
This is a perfectly logical position. Think of an extreme theoretical scenario: say there's a volatile asset A with 7% expected return, and another asset B with -3% expected return, but when an equal position is taken with both assets, all volatility is neutralized. Your average return is 2%, but due to 0 volatility, you could leverage infinitely for infinite profit.

Reality isn't like extreme scenarios, but the concept still exists - achieving a better risk-adjusted return may involve including assets with negative expected return.
I agree with the logic. But you really need to have a strong case for the negative correlation to lever up a portfolio after adding a risk asset. If the correlation turns positive, you could end up with a portfolio way more risky than you had targeted.

Something to consider on being short the carry trade: High-interest currencies are often correlated with commodity prices (and hence inflation). Adding a short carry trade position to a stock-bond portfolio with US treasuries might result in doubling up on deflationary shock protection while adding more vulnerability to inflation.
After reading several papers on the subject of carry trades, my understanding is that positive returns can be generated with carry trades, at the expense of rather rare, but sudden and relatively significant drawdowns. The question is what is the tail risk of very rare events that are hard to model with backtesting. Maybe you earn a positive return with carry trades, but what is the risk-adjusted return... is it still positive... that is the more difficult question.
With a negative position in carry trades, you would do the opposite - pay for insurance in the long run. Research has shown that in the long run, the simple solution (equities + treasuries) wins over almost any and all more sophisticated (and often fee-bearing) solutions.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

DMoogle wrote: Mon Nov 29, 2021 9:06 pm
zkn wrote: Mon Nov 29, 2021 8:44 pm I agree with the logic. But you really need to have a strong case for the negative correlation to lever up a portfolio after adding a risk asset. If the correlation turns positive, you could end up with a portfolio way more risky than you had targeted.
True, it can, but just because assets are positively correlated doesn't mean there isn't a benefit - basically any correlation below 1 has a benefit in diversification, even if it's above 0 (with the exception being systematic risk that theoretically cannot be diversified away). Most stocks are positively correlated with each other, but there's still a benefit to holding multiple stocks vs. only one.

But yeah, have to be careful for sure. Just like with the original HFEA, this isn't for the faint of heart.

I'm not going to comment on the currency aspect, because it's something I know practically nothing about.
I think the rebalancing bonus, if we are optimistic, is about 0.5% p.a. if I remember right from way back in the HFEA thread. So that wouldn't move the needle with an asset returning -2% p.a. Setting aside the fact that German government bonds had already negative interest rates before the Covid crisis, and did not help much with the equities drawdown in Spring 2020.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

zkn wrote: Mon Nov 29, 2021 5:50 pm
comeinvest wrote: Tue Nov 23, 2021 7:16 pm Your analysis is a lot more sophisticated than mine. However, let's take a step back and see what makes sense. I think almost all your points would equally apply to the European situation. However, would you use an asset with -2% estimated real return for 30 years as part of your multi-asset rebalancing strategy? I know, maybe there is a sudden drop of inflation in years 10-30 (I don't know if inflation estimates are available beyond 10y). But maybe there is a sudden rise in inflation somewhere before year 30. Who knows. Besides, the German 10y bond has almost the same negative real return, guaranteed, and the inflation numbers are from tradable derivatives, so -2% is what you get if you assume no-arbitrage. Show me an asset allocation, rebalanced or not, that benefits from an asset with a "guaranteed" -2% p.a. real return for 10 years. Or look how much German bonds benefitted from the Covid crisis: not very much. I know, we are talking about the U.S., not Germany. But what I'm trying to say, you have to draw some line where you stop trusting models from historic backtests and efficient markets, don't you?

The U.S. stock market valuations are high, but by magnitudes lower than those of Japan at their peak. The stock market returns will be the sum of dividend growth (or earnings growth) plus variations in valuation. The former is exponential in the long run; the latter are hard to predict but are somewhat mean-reverting by nature, i.e. the variations will offset in the long run, and become negligible compared to the exponential growth part. That's my understanding. In summary, even though nobody knows nothing about the future, I can kind of see why many mHFEA people in this thread use a "muted" treasury allocation.
My thinking is this: if we take the tautology that all asset returns are the sum of the risk-free rate and a risk premium, negative expected or even guaranteed negative returns are not so immediately relevant if the negative return is reflecting a negative risk-free rate and not a negative risk premium. When selecting the portfolio that has maximal returns for a unit of risk, the risk-free rate is irrelevant. When the goal of optimization is to maximize expected returns for a given level of risk, the risk-free rate is still irrelevant, because the optimal solution would be to lever the risk-return optimized portfolio to the given level of risk. However, it is relevant if the goal of optimization is a given value of CAGR or expected return, or a given % chance of reaching some final portfolio balance, because more leverage would be required for lower risk-free rates. But in all of these cases, the optimal weighting of stocks vs bonds is unchanged by the risk-free rate going negative.

In line with this, I would take an asset that has a -2% annual real return if the cost to carry that asset was significantly less than that to compensate for the risk of holding that asset, i.e., the risk premium was fair. It is not obvious to me why negative bond returns should imply a negative term risk premium, but maybe the term premium is zero or even negative right now as you have suggested may be the case and the ACM model implies. Maybe that is related to the rates being negative or maybe that is something else entirely. I would draw a line when prices (and the probabilities implied by the prices etc.) are outside my range of plausibility, the composition of market participants had significantly changed in a way that suggests the historical risk premium may be gone, and/or the market participants had significantly different preferences to me. The example of German bonds is certainly challenging. (Anyway, comeinvest, I thought you held European bonds?) I'm sure a compelling argument can be made that we are on the wrong side of the line for US bonds, but I am not sure we are there yet for the reasons I noted in my previous post.

I find your argument in the second paragraph appealing. Maybe stocks require less faith in models. Stocks are ownership in real companies that have real earning growth but bonds are just securitized agreements and are less "real". On the other hand, the high stock valuations may be suggesting all that earning growth is already priced in for the immediate future. That is, that stock returns are also suppressed by a low, negative real risk-free rate like bond returns.

There is no escape from models; any forecasted expected return must come from a model. But all the models are bad. That's actually my preference for risk-parity weighting, because it follows in my view from the simplest and weakest modelling assumptions.
I don't disagree with almost anything you are saying, but purely intuitively I have a feeling that when government bonds are at -2% real return (taking the example of Germany to make the argument more obvious), term premia have a much bigger likelihood of being nil or negative, than if government bonds were at, say, 4% or 6% real or nominal yields. There should be some lower bound of interest rates, although we cannot pinpoint it. So the risk/reward seems asymmetric.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

zkn wrote: Mon Nov 29, 2021 5:50 pm (Anyway, comeinvest, I thought you held European bonds?)
I happen to have a *short* position in German government bonds via the 2-year future (GBS) for a while. The German yield curve formed a trough in the 2-3y area for several months this year, which seemed too enticing to pass, but it's more playing than a proven strategy. I hope to hedge a scenario of a global rise of inflation and interest rates at zero or very little carry cost and risk that way, and perhaps benefit from the USD/EUR carry trade in bond yields. I also have the USD ITTs as part of my mHFEA.
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