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 2:45 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 1:51 pm
skierincolorado wrote: Wed Nov 24, 2021 12:27 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 12:27 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.
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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 5:48 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 12:34 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 10:44 am
millennialmillions wrote: Sun Nov 21, 2021 10:48 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 9:55 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 6:16 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 1:51 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
55% VUG - 20% VEA - 20% EDV - 5% BNDX
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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 3:59 pm
comeinvest wrote: Tue Nov 23, 2021 6:16 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 6:16 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 4:50 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 5:12 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.
zkn
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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 5:19 pm
Hfearless wrote: Mon Nov 29, 2021 5:12 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 7:44 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 7:44 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.
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: Mon Nov 29, 2021 7:44 pm
DMoogle wrote: Mon Nov 29, 2021 5:19 pm
Hfearless wrote: Mon Nov 29, 2021 5:12 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 8:06 pm
zkn wrote: Mon Nov 29, 2021 7:44 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.
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: Mon Nov 29, 2021 4:50 pm
comeinvest wrote: Tue Nov 23, 2021 6:16 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 4:50 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.
zkn
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by zkn »

comeinvest wrote: Mon Nov 29, 2021 8:20 pm 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.
It's not intuitive to me that an asymmetric or negatively skewed return distribution implies a lower term premium. For example, selling puts on the SP500 is extremely asymmetric, but has a larger risk premium than buying the SP500. Similarly, negatively skewed stocks tend to outperform positively skewed ones (value over growth).

We might find that there is a boundary on the other side, too, as the amount of debt prevents central banks from raising rates much.
comeinvest wrote: Mon Nov 29, 2021 8:24 pm
zkn wrote: Mon Nov 29, 2021 4:50 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.
Let us know how it goes.
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: Tue Nov 30, 2021 7:46 am
comeinvest wrote: Mon Nov 29, 2021 8:20 pm 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.
It's not intuitive to me that an asymmetric or negatively skewed return distribution implies a lower term premium. For example, selling puts on the SP500 is extremely asymmetric, but has a larger risk premium than buying the SP500. Similarly, negatively skewed stocks tend to outperform positively skewed ones (value over growth).

We might find that there is a boundary on the other side, too, as the amount of debt prevents central banks from raising rates much.
I think the 2 things have almost nothing in common - an assumption that interest rates are limited at somewhere around -1%, and skewness of return distributions of put write strategies or of value stocks. But in all cases it all depends what probabilities you assign to certain scenarios, which in the case of interest rates not even experts who are much smarter than I and who do this for a living can agree. I guess all I can do is make up my mind and stick to my modeI, or at least don't switch back and forth too often. My model is that interest rates are in the -1% to +4% range in my lifetime, and that the risk reward is somewhat asymmetric when rates approach either bound. I'm a quantitative guy, but I have no quantitative justification, and maybe it's impossible or doesn't even make sense to try to quantify that model, given the high sensitivity to input assumptions. Nor do I believe that you can justify any better your model of sticking to historical backtesting agnostic of unprecedented levels of interest rates. My assumptions may or may not hold. Maybe German rates are -2% nominal next year, and U.S. rates increase and don't come down all the while the stock market crashes, and I'm screwed. But I have to start somewhere. I implemented mHFEA with a "muted" bond allocation similar to what Skier proposed, much less than the original HFEA. I will increase the bond allocation when interest rates and expected term premia are measurably higher. I would probably decrease or eliminate my treasuries allocation if interest rates were negative like in Germany.

I do know that German pension funds and life insurance companies are forced to buy government bonds, and I pray for them ;) I myself take the opposite side, however :)

I may be wrong, but I think put write strategies and value tilting are hard to model, as the results depend heavily on assumptions of tail risk that are hard to model from backtesting. That's maybe why there is so much controversy.
adamhg
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by adamhg »

skierincolorado wrote: Wed Nov 10, 2021 2:44 pm If we assume yields aren't going to rise at all, then something that yields .45% with financing of .55% is a net -.1%. Leveraging it 10x would be -1%. That's a big oversimplification though. In reality we have two other factors to consider 1) market based expectations of interest rate increases 2) rolll yield. The former isn't market timing since these expectations are already baked into the yield curve. 2 year bonds yield .45% (higher today) *because* interest rates are expected to rise. The rational investor in 2 year bonds should expect some interest rate increases, which the .55% yield should help compensate them for. We can get a sense of market expected interest rate increases from interest rate forwards contracts. Interest rates are expected to increase nearly 0.5% in the next year, which would knock nearly 1% off the price of a 2 year bond. On the other hand, you have roll yield which is adding around .5% to your return. So on net SHY is expected to return around 0.1% in the next year. Minus the .55% financing and you have a -.45% expected return. Leveraged 10x and you get -4.5%.

The breakeven is pretty close to 0.2% rate increase. If rates increase less than 0.2% you'll make money, if they increase more than 0.2% you'll lose money. Right now the market expects around 0.5%. If rates somehow don't increase at all, you'd make close to 1% on the underlying after roll yield. After financing this would be .45%. Leveraged 10x this would be a 4.5% return. But the odds of rates not increasing at all are very very low according to the market.


I don't think your implied financing changes day to day. You're just making or losing money. The implied financing is an abstraction on the day of purchase based on how much you are overpaying if the underlying returned nothing. You've locked in those costs unless you are able to sell to somebody else willing to incur similar costs. We could repeat the calculation based on today's trading price for the option and underlying. Are you saying that if I were to buy one today I'd have higher implied financing than you did buying a few days ago?

You are probably right that options could have an added benefit as a hedge due to the IV. It would be interesting to backtest. I still very much doubt it's worth it though because the only reason you're getting even semi-reasonable financing costs on SHY is because the expected return is so low. On anything with more expected return like IEF (or SHY in the future when expected return is higher), the implied financing cost is going to be much higher. Also I'm not sure how much IV we would capture being so DITM. The fact that there is essentially zero IV at this strike price is how we could justify call all of the costs "implied financing" rather than a premium we paid for IV. From the IEF I looked at there wasn't much IV until we got within ~$8 of the current price, but we were looking at something that was $23 DITM. The price would have to drop a lot and volatility increase before we picked up much IV.
Apologies, I forgot to respond and then lost track of this thread. I took the opportunity to TLH a bit yesterday which reminded me about your reply in this thread.

I am starting to increase leverage for SHY to both take advantage of IV as you mentioned (DITM will have no extrinsic value to benefit from IV) and also to increase my allocation of UPRO.

I wanted to get your POV because it seems to be opposite of my expectations and I haven't been able to put my finger on why until I went through this exercise yesterday.

Let's use these values for SHY:

SHY Current price: $85.79
SHY 12/16/2022 $87 Call (let's just assume the below is correct for the sake of math)
  • Current price: $0.20
  • Delta: 0.21
That gives us a leverage ratio of 0.21 * 87 / 0.20 = 88.47x

Now with your implied financing formula:
  • Foregone dividends: 0.41 (0.46% yield * 85.79 * 381 / 365)
  • Total cost: 1.84 (0.41 + 0.20 + 87 - 85.79 - $0.01 commission)
  • Borrowed: 85.29 (85.79 - 0.20)
Gives us a whopping 2.05% implied financing. But that 2% financing isn't for each unit of SHY we're borrowing, its for the whole amount of 88x leverage

We can check this. Borrowing 88.47x of SHY @ 85.79 would cost us $7,589.84. If we were to actually be borrowing this at a 2.05% financing rate, our cost should be $155.59 for the equivalent exposure, but that's not our cost here. Our cost is only $1.84 for 88x of exposure. So our _per unit_ financing rate should be closer to 0.023% (2.05% / 88.47).

Now that seems more accurate to me. What am I missing? I am asking in earnest because next quarter, I'm going to rebalance from where I am right now, primarily DITM $82/83C to OTM $87Cs and load up on UPRO instead.

Right now I'm currently about 45% SHY DITM leaps / 55% UPRO, but with this new allocation I can get closer to 25% SHY OTM leaps / 75% UPRO all while maintaining a 9:1 short term treasury : equity exposure

ETA: I wanted to also point out at 88x leverage, a 1.1-1.2% drop would wipe out the options so its not for the faint of heart. But I'd also argue that OTM leaps somewhat limit your downside risk as well since the bottom caps out at 0 and can't go negative and if it recovers in the next 3 quarters, your $0 options are able to be resurrected.
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 »

adamhg wrote: Wed Dec 01, 2021 11:20 am
skierincolorado wrote: Wed Nov 10, 2021 2:44 pm If we assume yields aren't going to rise at all, then something that yields .45% with financing of .55% is a net -.1%. Leveraging it 10x would be -1%. That's a big oversimplification though. In reality we have two other factors to consider 1) market based expectations of interest rate increases 2) rolll yield. The former isn't market timing since these expectations are already baked into the yield curve. 2 year bonds yield .45% (higher today) *because* interest rates are expected to rise. The rational investor in 2 year bonds should expect some interest rate increases, which the .55% yield should help compensate them for. We can get a sense of market expected interest rate increases from interest rate forwards contracts. Interest rates are expected to increase nearly 0.5% in the next year, which would knock nearly 1% off the price of a 2 year bond. On the other hand, you have roll yield which is adding around .5% to your return. So on net SHY is expected to return around 0.1% in the next year. Minus the .55% financing and you have a -.45% expected return. Leveraged 10x and you get -4.5%.

The breakeven is pretty close to 0.2% rate increase. If rates increase less than 0.2% you'll make money, if they increase more than 0.2% you'll lose money. Right now the market expects around 0.5%. If rates somehow don't increase at all, you'd make close to 1% on the underlying after roll yield. After financing this would be .45%. Leveraged 10x this would be a 4.5% return. But the odds of rates not increasing at all are very very low according to the market.


I don't think your implied financing changes day to day. You're just making or losing money. The implied financing is an abstraction on the day of purchase based on how much you are overpaying if the underlying returned nothing. You've locked in those costs unless you are able to sell to somebody else willing to incur similar costs. We could repeat the calculation based on today's trading price for the option and underlying. Are you saying that if I were to buy one today I'd have higher implied financing than you did buying a few days ago?

You are probably right that options could have an added benefit as a hedge due to the IV. It would be interesting to backtest. I still very much doubt it's worth it though because the only reason you're getting even semi-reasonable financing costs on SHY is because the expected return is so low. On anything with more expected return like IEF (or SHY in the future when expected return is higher), the implied financing cost is going to be much higher. Also I'm not sure how much IV we would capture being so DITM. The fact that there is essentially zero IV at this strike price is how we could justify call all of the costs "implied financing" rather than a premium we paid for IV. From the IEF I looked at there wasn't much IV until we got within ~$8 of the current price, but we were looking at something that was $23 DITM. The price would have to drop a lot and volatility increase before we picked up much IV.
Apologies, I forgot to respond and then lost track of this thread. I took the opportunity to TLH a bit yesterday which reminded me about your reply in this thread.

I am starting to increase leverage for SHY to both take advantage of IV as you mentioned (DITM will have no extrinsic value to benefit from IV) and also to increase my allocation of UPRO.

I wanted to get your POV because it seems to be opposite of my expectations and I haven't been able to put my finger on why until I went through this exercise yesterday.

Let's use these values for SHY:

SHY Current price: $85.79
SHY 12/16/2022 $87 Call (let's just assume the below is correct for the sake of math)
  • Current price: $0.20
  • Delta: 0.21
That gives us a leverage ratio of 0.21 * 87 / 0.20 = 88.47x

Now with your implied financing formula:
  • Foregone dividends: 0.41 (0.46% yield * 85.79 * 381 / 365)
  • Total cost: 1.84 (0.41 + 0.20 + 87 - 85.79 - $0.01 commission)
  • Borrowed: 85.29 (85.79 - 0.20)
Gives us a whopping 2.05% implied financing. But that 2% financing isn't for each unit of SHY we're borrowing, its for the whole amount of 88x leverage

We can check this. Borrowing 88.47x of SHY @ 85.79 would cost us $7,589.84. If we were to actually be borrowing this at a 2.05% financing rate, our cost should be $155.59 for the equivalent exposure, but that's not our cost here. Our cost is only $1.84 for 88x of exposure. So our _per unit_ financing rate should be closer to 0.023% (2.05% / 88.47).

Now that seems more accurate to me. What am I missing? I am asking in earnest because next quarter, I'm going to rebalance from where I am right now, primarily DITM $82/83C to OTM $87Cs and load up on UPRO instead.

Right now I'm currently about 45% SHY DITM leaps / 55% UPRO, but with this new allocation I can get closer to 25% SHY OTM leaps / 75% UPRO all while maintaining a 9:1 short term treasury : equity exposure

ETA: I wanted to also point out at 88x leverage, a 1.1-1.2% drop would wipe out the options so its not for the faint of heart. But I'd also argue that OTM leaps somewhat limit your downside risk as well since the bottom caps out at 0 and can't go negative and if it recovers in the next 3 quarters, your $0 options are able to be resurrected.
The financing cost that we calculated of 2.05% is relative to the borrowed amount of 85.29 not the equity of the position. Thus it already factors in the fact the equity of the position is highly leveraged due to the *implied* borrowing of 85.29. We already divided the cost ($1.84) by the leveraged exposure amount ($85.29). We could also simply calculate that the cost is $1.84 which is 9.2x our equity. We could then divide by the leverage of 88x and it would be 10% financing cost. This is because the delta is not ~1. My calculation assumes that the delta is ~1. If the delta is not ~1, then we can do it this way and we get ~10% financing cost, although the majority of this cost is that you are paying for IV and not actual financing cost. The financing cost is either 2.05% if you assume delta of 1, or ~10% if you use the actual delta of .21. In neither case is the finanincing cost .023%.

Either way, the way you've done it essentially leverages the return twice and only leverages the cost once. The 2.05% financing cost was already the cost relative to the leveraged exposure, not your equity.

Think of it this way, we are paying $1.84 for exposure to 85.79 of SHY with .2 in equity. If the option price goes up by $1.84 (which would be a HUGE move for SHY and would require very negative interest rates), you've still lost your entire position. It's unlikely to make money even in the best scenario, and the expected value is very negative. You're paying a ton for IV that doesn't exist.

The cost is $1.84 per share. The expected return per share is ~$0.20. I'd strongly urge not doing this.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by EfficientInvestor »

adamhg wrote: Wed Dec 01, 2021 11:20 am Let's use these values for SHY:

SHY Current price: $85.79
SHY 12/16/2022 $87 Call (let's just assume the below is correct for the sake of math)
  • Current price: $0.20
  • Delta: 0.21
I haven't quite dug into this whole SHY topic, but I will say that SHY options are very illiquid. The contract you mention only has 125 contracts of open interest currently. The mid price might be 0.20 based on the bid/ask of 0.05/0.35. However, the actual fill price might be 0.25 or higher. Might be worth placing an order for a single contract to see what kind of fill price you can get. And if you try to close the contract before expiration, you might only get it to fill at 0.05 or more on the bid side of the mid price. So round-trip bid-ask slippage could be quite severe.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

EfficientInvestor wrote: Wed Dec 01, 2021 2:54 pm
adamhg wrote: Wed Dec 01, 2021 11:20 am Let's use these values for SHY:

SHY Current price: $85.79
SHY 12/16/2022 $87 Call (let's just assume the below is correct for the sake of math)
  • Current price: $0.20
  • Delta: 0.21
I haven't quite dug into this whole SHY topic, but I will say that SHY options are very illiquid. The contract you mention only has 125 contracts of open interest currently. The mid price might be 0.20 based on the bid/ask of 0.05/0.35. However, the actual fill price might be 0.25 or higher. Might be worth placing an order for a single contract to see what kind of fill price you can get. And if you try to close the contract before expiration, you might only get it to fill at 0.05 or more on the bid side of the mid price. So round-trip bid-ask slippage could be quite severe.
Also, I still struggle to see how leveraging a fee-bearing product can be efficient.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by adamhg »

skierincolorado wrote: Wed Dec 01, 2021 2:31 pm The financing cost that we calculated of 2.05% is relative to the borrowed amount of 85.29 not the equity of the position. Thus it already factors in the fact the equity of the position is highly leveraged due to the *implied* borrowing of 85.29. We already divided the cost ($1.84) by the leveraged exposure amount ($85.29). We could also simply calculate that the cost is $1.84 which is 9.2x our equity. We could then divide by the leverage of 88x and it would be 10% financing cost. This is because the delta is not ~1. My calculation assumes that the delta is ~1. If the delta is not ~1, then we can do it this way and we get ~10% financing cost, although the majority of this cost is that you are paying for IV and not actual financing cost. The financing cost is either 2.05% if you assume delta of 1, or ~10% if you use the actual delta of .21. In neither case is the finanincing cost .023%.

Either way, the way you've done it essentially leverages the return twice and only leverages the cost once. The 2.05% financing cost was already the cost relative to the leveraged exposure, not your equity.

Think of it this way, we are paying $1.84 for exposure to 85.79 of SHY with .2 in equity. If the option price goes up by $1.84 (which would be a HUGE move for SHY and would require very negative interest rates), you've still lost your entire position. It's unlikely to make money even in the best scenario, and the expected value is very negative. You're paying a ton for IV that doesn't exist.

The cost is $1.84 per share. The expected return per share is ~$0.20. I'd strongly urge not doing this.
As always, I appreciate your insight. You didn't need to spend that time responding, and yet you did. Thank you!
km91
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by km91 »

Can someone help me understand how margin requirements work for futures. Looking at ZN, IBKR says maintenance is ~$2200 and the total contract value of a single future is currently ~$130K. Does this mean I need to maintain an account NAV of $2200 or cash collateral of $2200?

Now let's say I have $150K in SPY, $3K cash, and a ZN contract and no other holdings in my account. If the contract falls by 1% / $1300, is the loss marked against the cash position and I have to sell some SPY to make up the deficit back to the initial margin, or is it marked against my account NAV in which case I don't have to do anything since my account equity is well above the margin requirement
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

km91 wrote: Thu Dec 02, 2021 12:41 pm Can someone help me understand how margin requirements work for futures. Looking at ZN, IBKR says maintenance is ~$2200 and the total contract value of a single future is currently ~$130K. Does this mean I need to maintain an account NAV of $2200 or cash collateral of $2200?

Now let's say I have $150K in SPY, $3K cash, and a ZN contract and no other holdings in my account. If the contract falls by 1% / $1300, is the loss marked against the cash position and I have to sell some SPY to make up the deficit back to the initial margin, or is it marked against my account NAV in which case I don't have to do anything since my account equity is well above the margin requirement
It depends if it’s a margin account. If it’s not margin you need to hold the cash, so sell spy. If it is a margin account it is similar to what you describe at the end, but not exactly correct. It’s not the NAV that matters, but the total margin requirement. 150k in SPY might have a 30k margin requirement on portfolio margin. The future adds 2.2k so yes you would be totally fine because ~152k > 32.2k. If the cash balance goes negative you would receive a margin loan. You could pay back the margin loan by selling spy or writing a box spread.

If it’s reg t margin, then you have to keep the sma positive. Which would basically require staying above the initial reg t requirement of 50% (75k). Normally with reg t that would only be an initial requirement and then the requirement would be more lax. But futures can cause the sma to go negative.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by perfectuncertainty »

adamhg wrote: Thu Dec 02, 2021 12:00 pm
skierincolorado wrote: Wed Dec 01, 2021 2:31 pm The financing cost that we calculated of 2.05% is relative to the borrowed amount of 85.29 not the equity of the position. Thus it already factors in the fact the equity of the position is highly leveraged due to the *implied* borrowing of 85.29. We already divided the cost ($1.84) by the leveraged exposure amount ($85.29). We could also simply calculate that the cost is $1.84 which is 9.2x our equity. We could then divide by the leverage of 88x and it would be 10% financing cost. This is because the delta is not ~1. My calculation assumes that the delta is ~1. If the delta is not ~1, then we can do it this way and we get ~10% financing cost, although the majority of this cost is that you are paying for IV and not actual financing cost. The financing cost is either 2.05% if you assume delta of 1, or ~10% if you use the actual delta of .21. In neither case is the finanincing cost .023%.

Either way, the way you've done it essentially leverages the return twice and only leverages the cost once. The 2.05% financing cost was already the cost relative to the leveraged exposure, not your equity.

Think of it this way, we are paying $1.84 for exposure to 85.79 of SHY with .2 in equity. If the option price goes up by $1.84 (which would be a HUGE move for SHY and would require very negative interest rates), you've still lost your entire position. It's unlikely to make money even in the best scenario, and the expected value is very negative. You're paying a ton for IV that doesn't exist.

The cost is $1.84 per share. The expected return per share is ~$0.20. I'd strongly urge not doing this.
As always, I appreciate your insight. You didn't need to spend that time responding, and yet you did. Thank you!
+1 - Skier you have been great. Thank you!!
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 »

adamhg wrote: Thu Dec 02, 2021 12:00 pm
As always, I appreciate your insight. You didn't need to spend that time responding, and yet you did. Thank you!
perfectuncertainty wrote: Thu Dec 02, 2021 8:12 pm

+1 - Skier you have been great. Thank you!!
No problem. This thread has been great.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by zkn »

comeinvest wrote: Fri Dec 03, 2021 6:05 pm Some "experts" now predict an inverted yield curve. Oops.
https://www.nb.com/en/global/insights/n ... es-flatter
https://blog.pimco.com/en//2021/11/yiel ... ary-policy
The Eurodollar curve for 2024-2025 inverted yesterday (see GEZ4-GEZ3).
Topic Author
skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Fri Dec 03, 2021 6:05 pm Some "experts" now predict an inverted yield curve. Oops.
https://www.nb.com/en/global/insights/n ... es-flatter
https://blog.pimco.com/en//2021/11/yiel ... ary-policy
While of course I consider all of this speculation and none of it be actionable, the PIMCO one actually has the opposite conclusion from the NB one. And while I'd still say this is all low confidence speculation, I tend to agree with the above PIMCO analysis quoted below more. The recent flattening seems excessive to me given we are about 3M below full employment. Personally I'd be a bit surprised if we have 6 rate hikes by the end of 2023.

PIMCO actually sounds extremely bullish on the front end of the curve. The market "continually overestimate the actual path because of recent yield curve moves and concerns about inflation expectations" and "excessive risk premium becomes embedded in the front end of yield curves" are basically the dream scenario!

Although we agree with the basic direction of the recent shift in sentiment, we think market expectations might be moving too quickly, for several reasons.

First, forward inflation expectations as embedded in inflation-linked securities see inflation beyond our cyclical horizon – roughly the next year – broadly consistent with central banks’ mandates.

Second, though central bankers will likely act to preserve inflation expectations, they are acutely aware that monetary policy is not the best tool to address upward price pressures emanating from a shock or disruption to the supply side of the economy.

Third, tail risks – or the possibility of unforeseen outcomes – from COVID-19 have diminished but haven’t gone away, and employment in most economies is still well below pre-pandemic levels. Though a well-calibrated withdrawal of monetary stimulus will be necessary, central banks are eager to continue supporting recovery in labor markets, and thus will not be keen to tighten too rapidly.

Change can create opportunities
The risk premium associated with the outlook for rate hikes may be more long-lasting at this point, meaning that the market’s anticipated path for monetary policy may continually overestimate the actual path because of recent yield curve moves and concerns about inflation expectations.

The rapid repricing of expectations has often resulted in good return-generating opportunities, as excessive risk premium becomes embedded in the front end of yield curves.
Last edited by skierincolorado on Sat Dec 04, 2021 9:39 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 Dec 04, 2021 6:20 pm
comeinvest wrote: Fri Dec 03, 2021 6:05 pm Some "experts" now predict an inverted yield curve. Oops.
https://www.nb.com/en/global/insights/n ... es-flatter
https://blog.pimco.com/en//2021/11/yiel ... ary-policy
While of course I consider all of this speculation and none of it be actionable, the PIMCO one actually has the opposite conclusion from the NB one. And while I'd still say this is all low confidence speculation, I tend to agree with the above PIMCO analysis quoted below more. The recent flattening seems excessive to me given we are about 3M below full employment. Personally I'd be very surprised if we have 6 rate hikes by the end of 2023.

PIMCO actually sounds extremely bullish on the front end of the curve. The market "continually overestimate the actual path because of recent yield curve moves and concerns about inflation expectations" and "excessive risk premium becomes embedded in the front end of yield curves" are basically the dream scenario!

Although we agree with the basic direction of the recent shift in sentiment, we think market expectations might be moving too quickly, for several reasons.

First, forward inflation expectations as embedded in inflation-linked securities see inflation beyond our cyclical horizon – roughly the next year – broadly consistent with central banks’ mandates.

Second, though central bankers will likely act to preserve inflation expectations, they are acutely aware that monetary policy is not the best tool to address upward price pressures emanating from a shock or disruption to the supply side of the economy.

Third, tail risks – or the possibility of unforeseen outcomes – from COVID-19 have diminished but haven’t gone away, and employment in most economies is still well below pre-pandemic levels. Though a well-calibrated withdrawal of monetary stimulus will be necessary, central banks are eager to continue supporting recovery in labor markets, and thus will not be keen to tighten too rapidly.

Change can create opportunities
The risk premium associated with the outlook for rate hikes may be more long-lasting at this point, meaning that the market’s anticipated path for monetary policy may continually overestimate the actual path because of recent yield curve moves and concerns about inflation expectations.

The rapid repricing of expectations has often resulted in good return-generating opportunities, as excessive risk premium becomes embedded in the front end of yield curves.
I don't infer much from ad-hoc "expert" commentaries. I implemented mHFEA with a several decade time horizon. I just read them for my general education. I'm not sure how much I will micro-manage or micro-monitor my strategy over the years. I hope less than at the beginning, otherwise any incremental profit (if and when it materializes) might not be a good use of my "research time" in terms of "compensation per hour" :) So the research is (hopefully) front-loaded. But then again times change, and strategies often evaporate once I implement them :) (lol. happened to me a few times.) I intend to somewhat monitor the situation over the years, as I intend to cut my losses if and when the situation becomes, for example, European-like. I know zkn argues for staying the course even at hugely negative rates and small and/or questionable term premia. (Not sure if he would actually stay the course no matter what, or if he just offered an argument for staying the course.) And I don't disagree with his rationale. But I would probably bail out in such a scenario.

I overlaid my mHFEA with a steepener overlay after the curve inverted at the long end, hoping for uncorrelated risk/returns to my portfolio in the long run once the carry differential "takes over" temporary flattening or steepening moves. I got hosed so far, but I hope the premise of this thread will work in the long run. A longer-term flat curve is the biggest threat to (m)HFEA.
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skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Sat Dec 04, 2021 8:09 pm
skierincolorado wrote: Sat Dec 04, 2021 6:20 pm
comeinvest wrote: Fri Dec 03, 2021 6:05 pm Some "experts" now predict an inverted yield curve. Oops.
https://www.nb.com/en/global/insights/n ... es-flatter
https://blog.pimco.com/en//2021/11/yiel ... ary-policy
While of course I consider all of this speculation and none of it be actionable, the PIMCO one actually has the opposite conclusion from the NB one. And while I'd still say this is all low confidence speculation, I tend to agree with the above PIMCO analysis quoted below more. The recent flattening seems excessive to me given we are about 3M below full employment. Personally I'd be very surprised if we have 6 rate hikes by the end of 2023.

PIMCO actually sounds extremely bullish on the front end of the curve. The market "continually overestimate the actual path because of recent yield curve moves and concerns about inflation expectations" and "excessive risk premium becomes embedded in the front end of yield curves" are basically the dream scenario!

Although we agree with the basic direction of the recent shift in sentiment, we think market expectations might be moving too quickly, for several reasons.

First, forward inflation expectations as embedded in inflation-linked securities see inflation beyond our cyclical horizon – roughly the next year – broadly consistent with central banks’ mandates.

Second, though central bankers will likely act to preserve inflation expectations, they are acutely aware that monetary policy is not the best tool to address upward price pressures emanating from a shock or disruption to the supply side of the economy.

Third, tail risks – or the possibility of unforeseen outcomes – from COVID-19 have diminished but haven’t gone away, and employment in most economies is still well below pre-pandemic levels. Though a well-calibrated withdrawal of monetary stimulus will be necessary, central banks are eager to continue supporting recovery in labor markets, and thus will not be keen to tighten too rapidly.

Change can create opportunities
The risk premium associated with the outlook for rate hikes may be more long-lasting at this point, meaning that the market’s anticipated path for monetary policy may continually overestimate the actual path because of recent yield curve moves and concerns about inflation expectations.

The rapid repricing of expectations has often resulted in good return-generating opportunities, as excessive risk premium becomes embedded in the front end of yield curves.
I don't infer much from ad-hoc "expert" commentaries. I implemented mHFEA with a several decade time horizon. I just read them for my general education. I'm not sure how much I will micro-manage or micro-monitor my strategy over the years. I hope less than at the beginning, otherwise any incremental profit (if and when it materializes) might not be a good use of my "research time" in terms of "compensation per hour" :) So the research is (hopefully) front-loaded. But then again times change, and strategies often evaporate once I implement them :) (lol. happened to me a few times.) I intend to somewhat monitor the situation over the years, as I intend to cut my losses if and when the situation becomes, for example, European-like. I know zkn argues for staying the course even at hugely negative rates and small and/or questionable term premia. (Not sure if he would actually stay the course no matter what, or if he just offered an argument for staying the course.) And I don't disagree with his rationale. But I would probably bail out in such a scenario.

I overlaid my mHFEA with a steepener overlay after the curve inverted at the long end, hoping for uncorrelated risk/returns to my portfolio in the long run once the carry differential "takes over" temporary flattening or steepening moves. I got hosed so far, but I hope the premise of this thread will work in the long run. A longer-term flat curve is the biggest threat to (m)HFEA.
Oh I know you get it - I just like to spell out the anti-market timing stuff for others reading. I also edited my post to say "a bit surprised" instead of "very surprised." If I was very confident in fewer than 6 rate hikes I'd probably own even more ITT.

But I really liked the sound of that "excessive risk premium embedded in the front end of the curve." :sharebeer
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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 »

I've been meaning to dig into something for a while. But perhaps I'll just ask it here instead to see what others have figured out already and get the conversation going:

If you were seeking leverage (but not necessarily perfect mHFEA AA) in an account that did not allow futures, would you use LETFs or LEAPs to gain leverage? I'm not particularly concerned with perfect mHFEA in an individual account so long as I achieve my desired mHFEA AA across all of my accounts. But I would like some leverage in my 401k even if it is equity only. I have been using SPY LEAPs.

I think it's a tossup and haven't concerned myself with it terribly. But I lean towards LEAPs based on the following reasoning.

The cons of LETFs are obvious.. high fees. Also would need to rebalance back into UPRO during a crash to prevent the 401k return from wildly diverging from accounts that aren't daily rebalanced (box spreads, futures). I'm not particularly concerned about volatility decay of LETFs overall. But holding UPRO in 401k and MES in futures could teleport you out of your 401k in a crash even if you maintain your overall AA across acounts.

The cons of LEAPs seems to be high implied financing cost (2-3%). But much of the financing cost is because the delta is not actually 1.0. If you buy a strike of 250 and SPY is 450, if SPY drops to 255, you won't actually lose $195 (unless it's very near expiration). A call option that is $5 ITM would be worth much more than $5 unless it was very near expiration. You could sell, harvest the implied volatility, and reinvest into a lower strike with a delta closer to 1 again. Or if held to expiration, and SPY drops below 250, losses are limited to $200. Basically a chunk of the 2-3% in implied financing cost, is actually paying for some downside protection. But I'm not entirely sure how often I would be able to make use of this downside protection in the long run. If I always hold to expiration, I might not ever make use of the downside protection (what are the odds SPY is down 40%+ on the day of expiration? certainly possible but not likely). If I sell anytime the delta goes below .8 or .9 to harvest the IV, will I harvest enough IV over time to make the higher implied financing worth it?

In the previous example where SPY falls to 255, let's say my option with $250 strike is worth $50. I sell for $50, and buy back in at a strike of $130 at a cost of $125. I sell a share of SPY @ 255 to pay for my new option. Since I sold a share of SPY, I must now buy two options. Cost is $125*2. I pay for it using the $50 from the old option, plus the $255 of the share of SPY I just sold. If SPY then rises to $300 I will make $45*2, whereas if I had stayed with the original I would only make $45 on my share of SPY, and maybe $20 on the old option contract with delta near .5.

Thus far I have chosen LEAPs based on EMH. According to EMH, the 2-3% "implied financing" must mostly be downside protection which maybe will come in handy or I can harvest IV. Whereas LETFs is just a middle man and money out of my pocket. So in theory LEAPs seem better, but in practice?
millennialmillions wrote: Fri Nov 26, 2021 9:55 am .
Quoting you MM because I know you're in a similar position re 401k moneys and have a similar philosophy on AA across accounts (ie not identical/perfect).
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by EfficientInvestor »

skierincolorado wrote: Sat Dec 04, 2021 10:20 pm If you were seeking leverage (but not necessarily perfect mHFEA AA) in an account that did not allow futures, would you use LETFs or LEAPs to gain leverage?
I use LEAPS and then sell just enough monthly covered calls (at the money) to offset the premium decay of the LEAPS. I find that I need to sell 1 monthly call for every 3-4 LEAPS purchased in order to stay around theta neutral. I set it up so that my net delta exposure is in line with the notional value I would have had if using futures. However, the delta exposure is definitely variable and something you need to keep an eye one when doing this. The LEAP delta doesn’t change too quickly because it’s so far out in time, but you have to have rules in place for yourself about how to manage the short position.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

EfficientInvestor wrote: Sat Dec 04, 2021 11:30 pm
skierincolorado wrote: Sat Dec 04, 2021 10:20 pm If you were seeking leverage (but not necessarily perfect mHFEA AA) in an account that did not allow futures, would you use LETFs or LEAPs to gain leverage?
I use LEAPS and then sell just enough monthly covered calls (at the money) to offset the premium decay of the LEAPS. I find that I need to sell 1 monthly call for every 3-4 LEAPS purchased in order to stay around theta neutral. I set it up so that my net delta exposure is in line with the notional value I would have had if using futures. However, the delta exposure is definitely variable and something you need to keep an eye one when doing this. The LEAP delta doesn’t change too quickly because it’s so far out in time, but you have to have rules in place for yourself about how to manage the short position.
I'm not sure if I can write covered calls, I will check.

I think I see how this would be theta neutral. But isn't the return profile still very different from futures? If SPY drops, you have more downside risk than upside potential. Over time, the covered call premium should offset. So is the idea that by staying theta neutral, it will all average out much faster? Over a long enough time period, the covered call position basically is just earning theta.

But it still seems problematic when SPY goes down substantially in a month or two. You'll lose money on the covered call which could force you to change your AA. It seems like it might be better to do what I suggested and harvest IV when SPY drops.

Also I don't understand why it's 1 monthly covered call for every 3-4 LEAPS. A covered call would have a ~3% monthly premium. Which is much more than the ~3% annual premium of the LEAP (12x more, not 3-4x more).
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by DMoogle »

Few thoughts, skier. Speaking as someone who has never traded an option in his life (except for box spreads) :
  • If your delta isn't pretty much 1 for this purpose, you're doing it wrong. The strike price should be so low that there should be no risk of the actual price reaching it. Like, strike price of 0 (or whatever the minimum step is).
  • I think it would be worth revisiting how volatility decay affects a return profile under different scenarios. I agree with you on previous points you've made that (1) it's not as bad as people say and (2) if it was truly long-run detrimental, then that could present an arbitrage opportunity. However, the affect shouldn't be ignored.
  • Be careful about putting too much weight into the EMH with illiquid securities. The EMH essentially just means that any alpha should be instantly arbitraged away, but you don't want to be the one that gets "arbitraged." Hope that makes sense. This is why it's so important for us to use limit pricing in Box Spreads. I'm going to assume you know this though. But I think it's a faulty to assume that the 2%-3% you're calculating is due to the downside protection; it's probably just due to the illiquidity of the security... It could be simply that nobody in the market wants to offer <2% for these securities.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

EfficientInvestor wrote: Sat Dec 04, 2021 11:30 pm
skierincolorado wrote: Sat Dec 04, 2021 10:20 pm If you were seeking leverage (but not necessarily perfect mHFEA AA) in an account that did not allow futures, would you use LETFs or LEAPs to gain leverage?
I use LEAPS and then sell just enough monthly covered calls (at the money) to offset the premium decay of the LEAPS. I find that I need to sell 1 monthly call for every 3-4 LEAPS purchased in order to stay around theta neutral. I set it up so that my net delta exposure is in line with the notional value I would have had if using futures. However, the delta exposure is definitely variable and something you need to keep an eye one when doing this. The LEAP delta doesn’t change too quickly because it’s so far out in time, but you have to have rules in place for yourself about how to manage the short position.
I'm late to this part of the game, trying to catch up with the LEAPs methodology - can you please explain with an example how a position of covered calls plus LEAPs would look like - covered calls means you also have the underlying in you portfolio, right?
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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 »

skierincolorado wrote: Sat Dec 04, 2021 10:20 pm Quoting you MM because I know you're in a similar position re 401k moneys and have a similar philosophy on AA across accounts (ie not identical/perfect).
EfficientInvestor and I have chatted before, and he understands the financial math much better than I do, so I'm glad he replied. As you know, my backtesting using 1955-present data only has 2 methods of leverage: LETFs (simulated before they were available) and a simple annual assumed cost of leverage. So I don't have any unique data on how to best leverage in accounts without futures. That said, here is a summary of my current portfolio and my subjective reasoning:

I think the ballpark asset allocation (including amount of leverage) and ballpark borrowing cost is what really matters. Trying to use historical data to select optimal rebalancing periods or precisely optimize leverage costs will surely overfit the data. LETFs really aren't that bad as a portion of your leveraged portfolio. I hold some UPRO my 401k to get to my desired overall portfolio AA. Yes, the borrowing cost is higher, but the daily rebalancing can be thought of as "rebalancing frequency diversification."

Here's some ending portfolio balance data that supports this. This is assuming borrowing at the treasury rate for everything except UPRO, which uses the combination of simulated and real data to incorporate all costs and daily rebalancing.

Image

I'm guessing the amount of UPRO you would have would be less than 25%? If so, I personally wouldn't worry about it. But if you're fine with the extra complexity of LEAPs, I don't doubt you could get the same leverage cheaper.
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Bentonkb
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Bentonkb »

You can get a theta neutral position using a long combo. You buy a call and sell a put with the same expiration. I have done it with both legs OTM so that the net premium is zero and I keep the collateral for the short put in a bond fund.

It might be a pain to maintain your AA if you do it that way, though. The position is very nonlinear, so it would go out of balance in a hurry.
Lock
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Lock »

Has anyone compared and contrasted the use of margin versus portfolio margin on IBKR? Any noticeable difference?
Investing Lawyer
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Investing Lawyer »

skierincolorado wrote: Sat Dec 04, 2021 10:20 pm I've been meaning to dig into something for a while. But perhaps I'll just ask it here instead to see what others have figured out already and get the conversation going:

If you were seeking leverage (but not necessarily perfect mHFEA AA) in an account that did not allow futures, would you use LETFs or LEAPs to gain leverage? I'm not particularly concerned with perfect mHFEA in an individual account so long as I achieve my desired mHFEA AA across all of my accounts. But I would like some leverage in my 401k even if it is equity only. I have been using SPY LEAPs.

I think it's a tossup and haven't concerned myself with it terribly. But I lean towards LEAPs based on the following reasoning.

The cons of LETFs are obvious.. high fees. Also would need to rebalance back into UPRO during a crash to prevent the 401k return from wildly diverging from accounts that aren't daily rebalanced (box spreads, futures). I'm not particularly concerned about volatility decay of LETFs overall. But holding UPRO in 401k and MES in futures could teleport you out of your 401k in a crash even if you maintain your overall AA across acounts.

The cons of LEAPs seems to be high implied financing cost (2-3%). But much of the financing cost is because the delta is not actually 1.0. If you buy a strike of 250 and SPY is 450, if SPY drops to 255, you won't actually lose $195 (unless it's very near expiration). A call option that is $5 ITM would be worth much more than $5 unless it was very near expiration. You could sell, harvest the implied volatility, and reinvest into a lower strike with a delta closer to 1 again. Or if held to expiration, and SPY drops below 250, losses are limited to $200. Basically a chunk of the 2-3% in implied financing cost, is actually paying for some downside protection. But I'm not entirely sure how often I would be able to make use of this downside protection in the long run. If I always hold to expiration, I might not ever make use of the downside protection (what are the odds SPY is down 40%+ on the day of expiration? certainly possible but not likely). If I sell anytime the delta goes below .8 or .9 to harvest the IV, will I harvest enough IV over time to make the higher implied financing worth it?

In the previous example where SPY falls to 255, let's say my option with $250 strike is worth $50. I sell for $50, and buy back in at a strike of $130 at a cost of $125. I sell a share of SPY @ 255 to pay for my new option. Since I sold a share of SPY, I must now buy two options. Cost is $125*2. I pay for it using the $50 from the old option, plus the $255 of the share of SPY I just sold. If SPY then rises to $300 I will make $45*2, whereas if I had stayed with the original I would only make $45 on my share of SPY, and maybe $20 on the old option contract with delta near .5.

Thus far I have chosen LEAPs based on EMH. According to EMH, the 2-3% "implied financing" must mostly be downside protection which maybe will come in handy or I can harvest IV. Whereas LETFs is just a middle man and money out of my pocket. So in theory LEAPs seem better, but in practice?
millennialmillions wrote: Fri Nov 26, 2021 9:55 am .
Quoting you MM because I know you're in a similar position re 401k moneys and have a similar philosophy on AA across accounts (ie not identical/perfect).
I personally just use LEFTS for ease of use in my 401k. But I have used synthetic forwards (buy call sell put) for various situations. I'd prefer the synthetic forward to just a LEAPS call. Primary reason you can do a synthetic forward ATM with high liquidity and therefore low bid/ask spread. Secondary reason, perfect 1.00 delta and no volatility or theta effects.
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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 »

Investing Lawyer wrote: Sun Dec 05, 2021 7:25 pm
skierincolorado wrote: Sat Dec 04, 2021 10:20 pm I've been meaning to dig into something for a while. But perhaps I'll just ask it here instead to see what others have figured out already and get the conversation going:

If you were seeking leverage (but not necessarily perfect mHFEA AA) in an account that did not allow futures, would you use LETFs or LEAPs to gain leverage? I'm not particularly concerned with perfect mHFEA in an individual account so long as I achieve my desired mHFEA AA across all of my accounts. But I would like some leverage in my 401k even if it is equity only. I have been using SPY LEAPs.

I think it's a tossup and haven't concerned myself with it terribly. But I lean towards LEAPs based on the following reasoning.

The cons of LETFs are obvious.. high fees. Also would need to rebalance back into UPRO during a crash to prevent the 401k return from wildly diverging from accounts that aren't daily rebalanced (box spreads, futures). I'm not particularly concerned about volatility decay of LETFs overall. But holding UPRO in 401k and MES in futures could teleport you out of your 401k in a crash even if you maintain your overall AA across acounts.

The cons of LEAPs seems to be high implied financing cost (2-3%). But much of the financing cost is because the delta is not actually 1.0. If you buy a strike of 250 and SPY is 450, if SPY drops to 255, you won't actually lose $195 (unless it's very near expiration). A call option that is $5 ITM would be worth much more than $5 unless it was very near expiration. You could sell, harvest the implied volatility, and reinvest into a lower strike with a delta closer to 1 again. Or if held to expiration, and SPY drops below 250, losses are limited to $200. Basically a chunk of the 2-3% in implied financing cost, is actually paying for some downside protection. But I'm not entirely sure how often I would be able to make use of this downside protection in the long run. If I always hold to expiration, I might not ever make use of the downside protection (what are the odds SPY is down 40%+ on the day of expiration? certainly possible but not likely). If I sell anytime the delta goes below .8 or .9 to harvest the IV, will I harvest enough IV over time to make the higher implied financing worth it?

In the previous example where SPY falls to 255, let's say my option with $250 strike is worth $50. I sell for $50, and buy back in at a strike of $130 at a cost of $125. I sell a share of SPY @ 255 to pay for my new option. Since I sold a share of SPY, I must now buy two options. Cost is $125*2. I pay for it using the $50 from the old option, plus the $255 of the share of SPY I just sold. If SPY then rises to $300 I will make $45*2, whereas if I had stayed with the original I would only make $45 on my share of SPY, and maybe $20 on the old option contract with delta near .5.

Thus far I have chosen LEAPs based on EMH. According to EMH, the 2-3% "implied financing" must mostly be downside protection which maybe will come in handy or I can harvest IV. Whereas LETFs is just a middle man and money out of my pocket. So in theory LEAPs seem better, but in practice?
millennialmillions wrote: Fri Nov 26, 2021 9:55 am .
Quoting you MM because I know you're in a similar position re 401k moneys and have a similar philosophy on AA across accounts (ie not identical/perfect).
I personally just use LEFTS for ease of use in my 401k. But I have used synthetic forwards (buy call sell put) for various situations. I'd prefer the synthetic forward to just a LEAPS call. Primary reason you can do a synthetic forward ATM with high liquidity and therefore low bid/ask spread. Secondary reason, perfect 1.00 delta and no volatility or theta effects.
Yeah would definitely prefer synthetic long, but no selling of puts in my 401k.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

Investing Lawyer wrote: Sun Dec 05, 2021 7:25 pm I personally just use LEFTS for ease of use in my 401k. But I have used synthetic forwards (buy call sell put) for various situations. I'd prefer the synthetic forward to just a LEAPS call. Primary reason you can do a synthetic forward ATM with high liquidity and therefore low bid/ask spread. Secondary reason, perfect 1.00 delta and no volatility or theta effects.
I think synthetic forwards are not allowed in IRA's and 401k's (except solo 401k's), which I think is skier's problem. Whoever has the chance to start some side business, I recommend setting up a solo 401k.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

millennialmillions wrote: Sun Dec 05, 2021 10:23 am
skierincolorado wrote: Sat Dec 04, 2021 10:20 pm Quoting you MM because I know you're in a similar position re 401k moneys and have a similar philosophy on AA across accounts (ie not identical/perfect).
EfficientInvestor and I have chatted before, and he understands the financial math much better than I do, so I'm glad he replied. As you know, my backtesting using 1955-present data only has 2 methods of leverage: LETFs (simulated before they were available) and a simple annual assumed cost of leverage. So I don't have any unique data on how to best leverage in accounts without futures. That said, here is a summary of my current portfolio and my subjective reasoning:

I think the ballpark asset allocation (including amount of leverage) and ballpark borrowing cost is what really matters. Trying to use historical data to select optimal rebalancing periods or precisely optimize leverage costs will surely overfit the data. LETFs really aren't that bad as a portion of your leveraged portfolio. I hold some UPRO my 401k to get to my desired overall portfolio AA. Yes, the borrowing cost is higher, but the daily rebalancing can be thought of as "rebalancing frequency diversification."

Here's some ending portfolio balance data that supports this. This is assuming borrowing at the treasury rate for everything except UPRO, which uses the combination of simulated and real data to incorporate all costs and daily rebalancing.

Image

I'm guessing the amount of UPRO you would have would be less than 25%? If so, I personally wouldn't worry about it. But if you're fine with the extra complexity of LEAPs, I don't doubt you could get the same leverage cheaper.
The ending balances of what time frame exactly does your table represent? The differences between left and right seem significant.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

I don't know about everybody else, but as this thread and this strategy are basically about profiting from the term premia embedded in the yield curve, I became addicted to watching the yield curve. The section of the curve that inverted is becoming more and more inverted almost every day (to my detriment, as I took a position to profit from eventual "normalization", independent from my mHFEA). I'm curious when the 7y-10y section will invert. All the while the 20y seems to stay stubbornly at a relatively high yield, creating an unnatural zig-zag.

Image
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