Refinements to Hedgefundie's excellent approach
Refinements to Hedgefundie's excellent approach
I've been backtesting aspects of Hedgefundie's approach with leveraged ETFs, and I thought it would be appropriate to start a new thread to keep the information more readily available. I'm expecting a few more posts as I go along, and the more the merrier!
This is inspired by the Hedgefundie (memberlist.php?mode=viewprofile&u=126222) thread on leveraged S&P 500 and longterm treasury ETFs (viewtopic.php?f=10&t=272007#p4364001), the EfficientInvestor (memberlist.php?mode=viewprofile&u=141318) and Siamond (memberlist.php?mode=viewprofile&u=37504) thread on leveraged ETFs (viewtopic.php?f=10&t=272640#p4376074), and the willthrill81 (memberlist.php?mode=viewprofile&u=116799) thread on trend following (viewtopic.php?f=10&t=270035&hilit=trend#p4326975). I’ve also been strongly inspired by the portfolio visualizer site (https://www.portfoliovisualizer.com/) and the portfolio charts site (https://portfoliocharts.com/).
A word of introduction. I am a hydrologist with a strong background in numerical modeling and probabilistic risk assessment. I am in no way an expert on finance, and I was actively disinterested in finance up to this year. But it was time to think about making sure that finances were in order ten years out from retirement. As it turns out, I’m getting interested now and some of my professional skills translate well to quantifying financial issues, at least at an amateur level.
After reading up on the Hedgefundie scheme, I invested 4 percent of my portfolio with M1 finance as a Roth IRA. The platform is attractive for the minimal costs and ability for frequent rebalancing. My intent with this is primarily as an inheritance for my children, so the time frame is hopefully at least 15 years. While I’ve bought into the general scheme, I’m a natural skeptic, and I have wanted to test out some aspects of the Hedgefundie scheme for myself to better understand. Also, I’m a bit concerned about the potential downside aspects of 3x leveraged funds, and I wanted to see if there were aspects of other schemes that could be adapted to reduce downside risks. So here we go.
I’ve first focused on the daily return sequence for UPRO and TMF (the UPROSIM and TMFSIM series in the Hedgefundie thread, extended with the most recent market data). UPRO is a 3x ETF tracking the S&P 500, and TMF is a 3x ETF tracking longterm US treasuries. With such noisy data, I wanted to make comparisons of investing strategies exactly apples to apples. I decided that a reasonable approach is to use fixed simulation durations (e.g., five years, ten years) with all available starting points considered. I calculate the portfolio return using daily steps, assuming that any rebalancing occurs between the market close and the next market open.
When assessing the viability of a scheme, I commonly plot the time history and the cumulative exceedance distribution of a parameter or outcome. The cumulative exceedance distribution simply describes the fraction of outcomes that are exceeded by a given value. For example, if half of the outcomes are less than a particular value, the exceedance fraction is 0.5.
When comparing the effects of two different options, I commonly compare the outcomes separately for each starting day. In essence, the idea is that a fair comparison regarding investing decisions requires that each decision has exactly the same market information available at the time of the decision, and the market returns exactly the same returns after the decision.
For the purposes of comparisons, I assume that a leveraged index is an exact multiple of the base index on a daily basis, and do all calculations with daily steps. I report all calculations using nominal market values, because the decisions are based on nominal market values. I do not impose costs; the UPRO and TMF ERs are roughly one percent higher than an equivalent unleveraged index.
The nominal scheme reported in the Hedgefundie thread is weighted 40 percent UPRO and 60 percent TMF, rebalanced quarterly. The approximate weights were developed from risk parity arguments and confirmed with backtesting. Hedgefundie selected the quarterly rebalancing frequency based on nominally better results during backtesting, but reported relatively little sensitivity to rebalancing frequency. Hedgefundie recognized that the 3x leveraging could create extreme drawdowns in the UPRO index, which is an admitted risk factor.
As I have been thinking about the scheme, the first questions that came to mind were related to the practical implementation aspects. How often should I rebalance? Are there better ways of calculating the UPRO and TMF weights? Are there ways of protecting against large drawdowns?
This is inspired by the Hedgefundie (memberlist.php?mode=viewprofile&u=126222) thread on leveraged S&P 500 and longterm treasury ETFs (viewtopic.php?f=10&t=272007#p4364001), the EfficientInvestor (memberlist.php?mode=viewprofile&u=141318) and Siamond (memberlist.php?mode=viewprofile&u=37504) thread on leveraged ETFs (viewtopic.php?f=10&t=272640#p4376074), and the willthrill81 (memberlist.php?mode=viewprofile&u=116799) thread on trend following (viewtopic.php?f=10&t=270035&hilit=trend#p4326975). I’ve also been strongly inspired by the portfolio visualizer site (https://www.portfoliovisualizer.com/) and the portfolio charts site (https://portfoliocharts.com/).
A word of introduction. I am a hydrologist with a strong background in numerical modeling and probabilistic risk assessment. I am in no way an expert on finance, and I was actively disinterested in finance up to this year. But it was time to think about making sure that finances were in order ten years out from retirement. As it turns out, I’m getting interested now and some of my professional skills translate well to quantifying financial issues, at least at an amateur level.
After reading up on the Hedgefundie scheme, I invested 4 percent of my portfolio with M1 finance as a Roth IRA. The platform is attractive for the minimal costs and ability for frequent rebalancing. My intent with this is primarily as an inheritance for my children, so the time frame is hopefully at least 15 years. While I’ve bought into the general scheme, I’m a natural skeptic, and I have wanted to test out some aspects of the Hedgefundie scheme for myself to better understand. Also, I’m a bit concerned about the potential downside aspects of 3x leveraged funds, and I wanted to see if there were aspects of other schemes that could be adapted to reduce downside risks. So here we go.
I’ve first focused on the daily return sequence for UPRO and TMF (the UPROSIM and TMFSIM series in the Hedgefundie thread, extended with the most recent market data). UPRO is a 3x ETF tracking the S&P 500, and TMF is a 3x ETF tracking longterm US treasuries. With such noisy data, I wanted to make comparisons of investing strategies exactly apples to apples. I decided that a reasonable approach is to use fixed simulation durations (e.g., five years, ten years) with all available starting points considered. I calculate the portfolio return using daily steps, assuming that any rebalancing occurs between the market close and the next market open.
When assessing the viability of a scheme, I commonly plot the time history and the cumulative exceedance distribution of a parameter or outcome. The cumulative exceedance distribution simply describes the fraction of outcomes that are exceeded by a given value. For example, if half of the outcomes are less than a particular value, the exceedance fraction is 0.5.
When comparing the effects of two different options, I commonly compare the outcomes separately for each starting day. In essence, the idea is that a fair comparison regarding investing decisions requires that each decision has exactly the same market information available at the time of the decision, and the market returns exactly the same returns after the decision.
For the purposes of comparisons, I assume that a leveraged index is an exact multiple of the base index on a daily basis, and do all calculations with daily steps. I report all calculations using nominal market values, because the decisions are based on nominal market values. I do not impose costs; the UPRO and TMF ERs are roughly one percent higher than an equivalent unleveraged index.
The nominal scheme reported in the Hedgefundie thread is weighted 40 percent UPRO and 60 percent TMF, rebalanced quarterly. The approximate weights were developed from risk parity arguments and confirmed with backtesting. Hedgefundie selected the quarterly rebalancing frequency based on nominally better results during backtesting, but reported relatively little sensitivity to rebalancing frequency. Hedgefundie recognized that the 3x leveraging could create extreme drawdowns in the UPRO index, which is an admitted risk factor.
As I have been thinking about the scheme, the first questions that came to mind were related to the practical implementation aspects. How often should I rebalance? Are there better ways of calculating the UPRO and TMF weights? Are there ways of protecting against large drawdowns?
Re: Refinements to Hedgefundie's excellent approach
Check out the content in the original thread on 20 trading day "Inverse Volatility" monthly rebalancing (you can backtest this on PV with UPROSIM/TMFSIM). There's some consensus that this might be a more systematic approach to rebalancing, though I wouldn't say it's universal consensus.
 lock.that.stock
 Posts: 136
 Joined: Sun Apr 28, 2019 2:01 pm
Re: Refinements to Hedgefundie's excellent approach
Subscribing and looking forward to your analysis and the evolution of thoughts to develop a refined strategy!
Re: Refinements to Hedgefundie's excellent approach
For now I assume that conditions over the relatively near future will mimic the period since 1982, as Hedgefundie assumes. The UPROSIM and TMFSIM series in the Hedgefundie thread is the best available series with daily returns that I am aware of; I added the most recent few months of UPRO and TMF to the series I’m working with. I’d be happy to look at daily data from 1955, if it were available. Later I will be looking at the monthly returns.
The two series I’m working with are shown in the first figure, which shows the adjusted daily close (accounting for dividends and splits) in the left panel and the cumulative exceedance function in the right panel. UPROSIM is in blue and TMFSIM is in red. I plotted the log of cumulative exceedance to show that a few events had very large daily drops (e.g., Black Monday in 1987). Unfortunately Black Monday is underrepresented in the sequence, because it is near the earliest day available. Perhaps later it would be interesting to roll the sequence of returns to extend the sequence.
As a check on Hedgefundie’s weights (40 percent UPRO, 60 percent TMF), I calculated the risk parity weights with different volatility windows. The volatility window is the period that volatility (standard deviation of returns) is calculated over. For example, a 10 day volatility window means that 10 days of returns are used to calculate volatility. Normally volatility is calculated symmetrically (both positive and negative returns are used), but some have suggested that downward volatility performs better. Downward volatility is calculated with all positive returns simply set to zero. One can perform such calculations at the portfolio visualizer site. In this following figure, risk parity UPRO weights are calculated with different volatility windows. The windows range from 10 (red) to 250 trading days (blue). In both cases, the average UPRO weight is approximately 40 percent and the weights with large volatility windows are approximately the same. Notice how the weights bounce around with short windows; it is generally the case that rebalancing frequencies longer than a few months should use larger volatility windows to avoid issues with spurious signals. The distribution of weights with a small volatility window is a bit wider with the downward volatility approach.
The two series I’m working with are shown in the first figure, which shows the adjusted daily close (accounting for dividends and splits) in the left panel and the cumulative exceedance function in the right panel. UPROSIM is in blue and TMFSIM is in red. I plotted the log of cumulative exceedance to show that a few events had very large daily drops (e.g., Black Monday in 1987). Unfortunately Black Monday is underrepresented in the sequence, because it is near the earliest day available. Perhaps later it would be interesting to roll the sequence of returns to extend the sequence.
As a check on Hedgefundie’s weights (40 percent UPRO, 60 percent TMF), I calculated the risk parity weights with different volatility windows. The volatility window is the period that volatility (standard deviation of returns) is calculated over. For example, a 10 day volatility window means that 10 days of returns are used to calculate volatility. Normally volatility is calculated symmetrically (both positive and negative returns are used), but some have suggested that downward volatility performs better. Downward volatility is calculated with all positive returns simply set to zero. One can perform such calculations at the portfolio visualizer site. In this following figure, risk parity UPRO weights are calculated with different volatility windows. The windows range from 10 (red) to 250 trading days (blue). In both cases, the average UPRO weight is approximately 40 percent and the weights with large volatility windows are approximately the same. Notice how the weights bounce around with short windows; it is generally the case that rebalancing frequencies longer than a few months should use larger volatility windows to avoid issues with spurious signals. The distribution of weights with a small volatility window is a bit wider with the downward volatility approach.
Re: Refinements to Hedgefundie's excellent approach
All of the following analyses were done in MATLAB. I wouldn't dream of trying this in Excel.
In the next set of figures, I consider (i) rebalancing frequency, (ii) sequence duration, and (iii) volatility window for a number of schemes. In each figure, different rebalancing frequencies (not volatility window!) are indicated with the line color. I considered rebalancing frequency cases of 1 (daily), 2, 5 (weekly), 10 (biweekly), 20 ("monthly"), 40 ("bimonthly"), 60 ("quarterly"), 120 ("semiannual"), and 250 ("annual") trading days. I assume 250 trading days per year. The color scale runs from red (daily) to blue (annual) rebalancing. Each figure considers one sequence duration and one volatility window.
To give context to the 3x schemes, I created simulated 1x S&P and 1x LTT sequences from UPROSIM and TMFSIM by dividing each daily return by three. The next figure shows the rolling nominal CAGR for a sequence of fiveyear periods using the 1x sequences. The three plots show (i) just the 1x LTT, (ii) just the 1x S&P, and (iii) a 60/40 mix of the two (mimicking a 60/40 portfolio). Rebalancing frequency is only meaningful for the mix. My code always tracks the volatility window, but the volatility window is not used for these cases.
Rebalancing frequency has a small effect on the 60/40 mix, indicated by a little blue (annual rebalance) peeking out from under the daily rebalance line and the blue line slightly to the left of the red line in the cumulative exceedance figure. In essence, this means that annual rebalancing may have done a little better or worse than frequent rebalancing for any particular start day, but frequent rebalancing would have been slightly favored most of the time (the small offset in the cumulative exceedance lines). This is consistent with annual rebalancing of standard index funds.
Several 3x schemes are shown in the following figures. In the first figure, the plots show the rolling 5yr CAGR for the (i) 3x LLT (TMFSIM), (ii) 3x S&P (UPROSIM), (iii) constant 40/60 UPRO/TMF (Hedgefundie’s scheme), and (iv) an adaptive scheme considering volatility and trend following based on the monthly unemployment rate. In the second figure, the plots show the rolling 5yr CAGR for the (i) constant 40/60 UPRO/TMF (Hedgefundie’s scheme), (ii) adaptive weights using symmetric volatility, (iii) adaptive weights using downward volatility, and (iv) the same adaptive scheme considering volatility and trend following based on the monthly unemployment rate. The second figure illustrates the effect of adaptively updating the weights.
The TMF returns were relatively consistent over the entire period, with 80 percent of the 5year nominal CAGR values between 7 and 22 percent and 50 percent greater than 13 percent. In contrast, the UPRO returns varied dramatically due to recessions. The nominal Hedgefundie scheme behaved in an intermediate way, with some negative periods but 80 percent of the 5year nominal CAGR values between around 3 and 32 percent. Notice that longer rebalance periods tend to yield scattered CAGR values with different start dates in the Hedgefundie scheme, suggesting that rebalancing periods longer than quarterly may give unexpectedly high or low return rates. This is even more the case with adaptive weights, especially with small volatility windows.
The example suggests that downward volatility calculations may provide substantially improved adaptive weights with very frequent rebalancing (daily to weekly). The advantage is essentially lost with biweekly or longer rebalancing.
Notice that the longer rebalancing periods show indications of annual cycles, with just a few months separation yielding very different returns. This type of offset is why it is important to compare different schemes over the same interval. Also note that extremely frequent rebalancing gives a wider spread in 5 year CAGR than the annual rebalancing.
The adaptive scheme in the bottom plot includes the adaptive risk parity weights, and selectively adjusts the weights to account for macroeconomic risk climate.
The macroeconomic risk is estimated using the trend for unemployment rate, which historically has been found to be a leading indicator for recessions. In essence, the risk parity weights are (i) readjusted to track TMF if a recession is indicated, (ii) readjusted to emphasize UPRO if a recession is unlikely, and (iii) left unchanged if the macroeconomic climate is uncertain. This is a slightly more nuanced version of the approach using the same unemployment rate indicator that is discussed in the willthrill81 (memberlist.php?mode=viewprofile&u=116799) thread. Recessions are signaled by rising unemployment, and are unlikely with falling unemployment. Over the example period, the scheme ends up basically tracking whichever index is more favorable, UPRO or TMF, but the decision is not made using market signals.
The macroeconomic indicator is intended to mitigate the risk of big drops. I know that market timing is a big issue with many Bogleheads, but given the excellent performance of the method Hedgefundie has provided, I’m quite comfortable sitting out and even missing the initial bounceback. Trend followers have long recognized that a rise in the monthly unemployment rate is a useful macroeconomic indicator that has tended to lead each recession by zero to six months since 1919. The FRED site (https://fred.stlouisfed.org/series/UNRATE) provides this data. One indicator that has been suggested is comparing the latest monthly unemployment rate with a moving average over N months. If the latest rate is higher, that is an indicator sensitive to recession. If the latest rate is lower, that is an indicator of economic health.
This information is particularly useful in two ways. It can indicate when to get out of the market (e.g., go completely to TMF), and it can indicate when the market is unlikely to badly misbehave in the short term. Folks tend to use averaging durations of 7 to 12 months as a crossover criterion between states. Short averaging durations give spurious signals, which can lead to whiplash. Long averaging durations may lag the actual start of a recession. I’ve done some playing with the index, and it seems like each of the recession events since 1986 would have been captured with an averaging period of 12 to 16 months.
I think that it is reasonable to use the index to systematically bias the overall strategy. If there is a clear signal of a recession, I would go completely to TMF. If there is a clear signal that there is no recession, I would bias the UPRO weights higher than calculated using the inversevolatility method. In transitions, or if it is ambiguous whether there is a transition, I would stick with the weights calculated using the inversevolatility method.
As a first approximation, I calculated a biased UPRO weight by increasing it a fraction of the way to 1 (full UPRO). For example, if the UPRO weight from the inversevolatility calculation is w = 0.5, the biased weight is 1 * f + w * (1 – f), where f is the bias fraction. If f = 0, there is no bias. If f = 1, the UPRO weight is 1 and the TMF weight is 0.
I played with the strategies to some extent. I settled on a 15month moving average period to detect crossovers, but the exact duration doesn’t seem too important. The best results, in terms of expected CAGR, seem to be dependent on the criterion for ambiguity. Overall, it appears that as soon as the sign changes on unemployment index criterion, the state should be considered ambiguous and no bias applied to the weights. Each succeeding month afterwards can be treated as unambiguous.
The bias fraction f is a matter of taste. Pushing f towards 1 improves the expected overall return by a couple of percentage points, but adds exposure to large dips. Black Monday (1987) is the largest crash in the sample period that does not show up with the unemployment index. When f is close to 1, the portfolio takes a large dive. When f is close to 0, the portfolio is largely buffered. I would likely tend to split the difference by setting f < 0.5, which buffers the Black Monday drop substantially. One may argue about whether a Black Monday will occur again within the next 20 or 30 years, of course. Note that the volatility weights become unimportant as f goes to 1 (the UPRO weight = 1 regardless of volatility).
The example provides an especially positive outcome; assuming monthly rebalancing, 90 percent of the periods return at least 14 percent nominal CAGR and 50 percent of the periods return at least 26 percent nominal CAGR. For comparison, the nominal scheme returns 3 and 18 percent nominal CAGR for 90 and 50 percent of the periods with monthly rebalancing.
The scheme does not handle sudden shocks, like Black Monday, that are not signaled by the unemployment rate. The scheme is more resilient when the risk parity weights are used. Accordingly, I would be judicious in how much to push the weights towards full UPRO weighting.
The next figures calculate the difference in nominal CAGR between two 3x schemes and the three nominal 1x schemes over the same integration intervals. The first 3x scheme is the Hedgefundie scheme and the second is the adaptive weight macroeconomic scheme. The third figure compares the adaptive scheme to the Hedgefundie scheme. Comparing apples to apples with respect to integration period, the Hedgefundie scheme essentially always would have done better than the 1x S&P, and almost always would have done better than the 60/40 portfolio. The 1x LTT index would have done better for 10 to 20 percent of the intervals. The adaptive weight macroeconomic scheme would have done even better compared to the 1x schemes.
So what have I learned so far?
• I can easily reproduce the risk parity weights selected by Hedgefundie.
• The Hedgefundie scheme would have beaten any scheme based on the unleveraged (1x) versions of UPRO and TMF for approximately 90 percent of the possible 5year intervals starting at the end of 1986. The exception is for periods with the S&P tanking but not treasuries. The scheme would have easily overcome the 1 percent ER for almost all of the outperformance sequences.
• Adaptively adjusting the risk parity weights would have provided some additional performance. The largest performance boost would have been with short volatility windows, downward volatility calculations, and very frequent rebalancing. Of course, this approach begs for automated calculations and trading, and will not be practical for most, and the effect of trading drag will likely degrade the boost.
• The performance boost from downward volatility is largely lost with biweekly or longer rebalancing.
• The volatility window should be tuned to the rebalance frequency. Performance degrades if the volatility window is much shorter than the rebalance frequency.
• The macroeconomic indicator provided by the unemployment rate had value as a predictor over the example period, and typically has provided a leading signal for every recession, of up to several months, since 1919.
I hope that this is interesting for folks. I guarantee that folks will be lost, so don't hesitate to ask questions.
I have a couple of ideas for followup analyses.
One question is the behavior if treasuries are longterm declining. I think this could be examined by simply adding a small negative return to every daily return.
Concurrent slumps in the S&P with declining LTT is a harder problem. I suspect that the trend indicator may help out in this scenario, so I hope to look at the trend indicator with prior recessions. This will likely be using monthly data, so conclusions will necessarily be murkier. It may take a while to get this done.
In the next set of figures, I consider (i) rebalancing frequency, (ii) sequence duration, and (iii) volatility window for a number of schemes. In each figure, different rebalancing frequencies (not volatility window!) are indicated with the line color. I considered rebalancing frequency cases of 1 (daily), 2, 5 (weekly), 10 (biweekly), 20 ("monthly"), 40 ("bimonthly"), 60 ("quarterly"), 120 ("semiannual"), and 250 ("annual") trading days. I assume 250 trading days per year. The color scale runs from red (daily) to blue (annual) rebalancing. Each figure considers one sequence duration and one volatility window.
To give context to the 3x schemes, I created simulated 1x S&P and 1x LTT sequences from UPROSIM and TMFSIM by dividing each daily return by three. The next figure shows the rolling nominal CAGR for a sequence of fiveyear periods using the 1x sequences. The three plots show (i) just the 1x LTT, (ii) just the 1x S&P, and (iii) a 60/40 mix of the two (mimicking a 60/40 portfolio). Rebalancing frequency is only meaningful for the mix. My code always tracks the volatility window, but the volatility window is not used for these cases.
Rebalancing frequency has a small effect on the 60/40 mix, indicated by a little blue (annual rebalance) peeking out from under the daily rebalance line and the blue line slightly to the left of the red line in the cumulative exceedance figure. In essence, this means that annual rebalancing may have done a little better or worse than frequent rebalancing for any particular start day, but frequent rebalancing would have been slightly favored most of the time (the small offset in the cumulative exceedance lines). This is consistent with annual rebalancing of standard index funds.
Several 3x schemes are shown in the following figures. In the first figure, the plots show the rolling 5yr CAGR for the (i) 3x LLT (TMFSIM), (ii) 3x S&P (UPROSIM), (iii) constant 40/60 UPRO/TMF (Hedgefundie’s scheme), and (iv) an adaptive scheme considering volatility and trend following based on the monthly unemployment rate. In the second figure, the plots show the rolling 5yr CAGR for the (i) constant 40/60 UPRO/TMF (Hedgefundie’s scheme), (ii) adaptive weights using symmetric volatility, (iii) adaptive weights using downward volatility, and (iv) the same adaptive scheme considering volatility and trend following based on the monthly unemployment rate. The second figure illustrates the effect of adaptively updating the weights.
The TMF returns were relatively consistent over the entire period, with 80 percent of the 5year nominal CAGR values between 7 and 22 percent and 50 percent greater than 13 percent. In contrast, the UPRO returns varied dramatically due to recessions. The nominal Hedgefundie scheme behaved in an intermediate way, with some negative periods but 80 percent of the 5year nominal CAGR values between around 3 and 32 percent. Notice that longer rebalance periods tend to yield scattered CAGR values with different start dates in the Hedgefundie scheme, suggesting that rebalancing periods longer than quarterly may give unexpectedly high or low return rates. This is even more the case with adaptive weights, especially with small volatility windows.
The example suggests that downward volatility calculations may provide substantially improved adaptive weights with very frequent rebalancing (daily to weekly). The advantage is essentially lost with biweekly or longer rebalancing.
Notice that the longer rebalancing periods show indications of annual cycles, with just a few months separation yielding very different returns. This type of offset is why it is important to compare different schemes over the same interval. Also note that extremely frequent rebalancing gives a wider spread in 5 year CAGR than the annual rebalancing.
The adaptive scheme in the bottom plot includes the adaptive risk parity weights, and selectively adjusts the weights to account for macroeconomic risk climate.
The macroeconomic risk is estimated using the trend for unemployment rate, which historically has been found to be a leading indicator for recessions. In essence, the risk parity weights are (i) readjusted to track TMF if a recession is indicated, (ii) readjusted to emphasize UPRO if a recession is unlikely, and (iii) left unchanged if the macroeconomic climate is uncertain. This is a slightly more nuanced version of the approach using the same unemployment rate indicator that is discussed in the willthrill81 (memberlist.php?mode=viewprofile&u=116799) thread. Recessions are signaled by rising unemployment, and are unlikely with falling unemployment. Over the example period, the scheme ends up basically tracking whichever index is more favorable, UPRO or TMF, but the decision is not made using market signals.
The macroeconomic indicator is intended to mitigate the risk of big drops. I know that market timing is a big issue with many Bogleheads, but given the excellent performance of the method Hedgefundie has provided, I’m quite comfortable sitting out and even missing the initial bounceback. Trend followers have long recognized that a rise in the monthly unemployment rate is a useful macroeconomic indicator that has tended to lead each recession by zero to six months since 1919. The FRED site (https://fred.stlouisfed.org/series/UNRATE) provides this data. One indicator that has been suggested is comparing the latest monthly unemployment rate with a moving average over N months. If the latest rate is higher, that is an indicator sensitive to recession. If the latest rate is lower, that is an indicator of economic health.
This information is particularly useful in two ways. It can indicate when to get out of the market (e.g., go completely to TMF), and it can indicate when the market is unlikely to badly misbehave in the short term. Folks tend to use averaging durations of 7 to 12 months as a crossover criterion between states. Short averaging durations give spurious signals, which can lead to whiplash. Long averaging durations may lag the actual start of a recession. I’ve done some playing with the index, and it seems like each of the recession events since 1986 would have been captured with an averaging period of 12 to 16 months.
I think that it is reasonable to use the index to systematically bias the overall strategy. If there is a clear signal of a recession, I would go completely to TMF. If there is a clear signal that there is no recession, I would bias the UPRO weights higher than calculated using the inversevolatility method. In transitions, or if it is ambiguous whether there is a transition, I would stick with the weights calculated using the inversevolatility method.
As a first approximation, I calculated a biased UPRO weight by increasing it a fraction of the way to 1 (full UPRO). For example, if the UPRO weight from the inversevolatility calculation is w = 0.5, the biased weight is 1 * f + w * (1 – f), where f is the bias fraction. If f = 0, there is no bias. If f = 1, the UPRO weight is 1 and the TMF weight is 0.
I played with the strategies to some extent. I settled on a 15month moving average period to detect crossovers, but the exact duration doesn’t seem too important. The best results, in terms of expected CAGR, seem to be dependent on the criterion for ambiguity. Overall, it appears that as soon as the sign changes on unemployment index criterion, the state should be considered ambiguous and no bias applied to the weights. Each succeeding month afterwards can be treated as unambiguous.
The bias fraction f is a matter of taste. Pushing f towards 1 improves the expected overall return by a couple of percentage points, but adds exposure to large dips. Black Monday (1987) is the largest crash in the sample period that does not show up with the unemployment index. When f is close to 1, the portfolio takes a large dive. When f is close to 0, the portfolio is largely buffered. I would likely tend to split the difference by setting f < 0.5, which buffers the Black Monday drop substantially. One may argue about whether a Black Monday will occur again within the next 20 or 30 years, of course. Note that the volatility weights become unimportant as f goes to 1 (the UPRO weight = 1 regardless of volatility).
The example provides an especially positive outcome; assuming monthly rebalancing, 90 percent of the periods return at least 14 percent nominal CAGR and 50 percent of the periods return at least 26 percent nominal CAGR. For comparison, the nominal scheme returns 3 and 18 percent nominal CAGR for 90 and 50 percent of the periods with monthly rebalancing.
The scheme does not handle sudden shocks, like Black Monday, that are not signaled by the unemployment rate. The scheme is more resilient when the risk parity weights are used. Accordingly, I would be judicious in how much to push the weights towards full UPRO weighting.
The next figures calculate the difference in nominal CAGR between two 3x schemes and the three nominal 1x schemes over the same integration intervals. The first 3x scheme is the Hedgefundie scheme and the second is the adaptive weight macroeconomic scheme. The third figure compares the adaptive scheme to the Hedgefundie scheme. Comparing apples to apples with respect to integration period, the Hedgefundie scheme essentially always would have done better than the 1x S&P, and almost always would have done better than the 60/40 portfolio. The 1x LTT index would have done better for 10 to 20 percent of the intervals. The adaptive weight macroeconomic scheme would have done even better compared to the 1x schemes.
So what have I learned so far?
• I can easily reproduce the risk parity weights selected by Hedgefundie.
• The Hedgefundie scheme would have beaten any scheme based on the unleveraged (1x) versions of UPRO and TMF for approximately 90 percent of the possible 5year intervals starting at the end of 1986. The exception is for periods with the S&P tanking but not treasuries. The scheme would have easily overcome the 1 percent ER for almost all of the outperformance sequences.
• Adaptively adjusting the risk parity weights would have provided some additional performance. The largest performance boost would have been with short volatility windows, downward volatility calculations, and very frequent rebalancing. Of course, this approach begs for automated calculations and trading, and will not be practical for most, and the effect of trading drag will likely degrade the boost.
• The performance boost from downward volatility is largely lost with biweekly or longer rebalancing.
• The volatility window should be tuned to the rebalance frequency. Performance degrades if the volatility window is much shorter than the rebalance frequency.
• The macroeconomic indicator provided by the unemployment rate had value as a predictor over the example period, and typically has provided a leading signal for every recession, of up to several months, since 1919.
I hope that this is interesting for folks. I guarantee that folks will be lost, so don't hesitate to ask questions.
I have a couple of ideas for followup analyses.
One question is the behavior if treasuries are longterm declining. I think this could be examined by simply adding a small negative return to every daily return.
Concurrent slumps in the S&P with declining LTT is a harder problem. I suspect that the trend indicator may help out in this scenario, so I hope to look at the trend indicator with prior recessions. This will likely be using monthly data, so conclusions will necessarily be murkier. It may take a while to get this done.

 Posts: 4801
 Joined: Sun Oct 22, 2017 2:06 pm
Re: Refinements to Hedgefundie's excellent approach
Would the adaptive strategy have kept you 100% in UPRO since the inception of the funds in 2009?

 Posts: 992
 Joined: Sun Sep 30, 2012 3:38 am
Re: Refinements to Hedgefundie's excellent approach
Suppose someone starts this right now, and over the next year, the Fed decides that employment looks good and raises rates to 3.5% from their current levels. Around the same time, stock market investors get nervous, then fullout panic after a war breaks out somewhere, and stocks dip 40% in a few months. These things happen in the same year.
What happens when both duration risk and equity risk get pummeled at the same time? How bad is the outcome?
What happens when both duration risk and equity risk get pummeled at the same time? How bad is the outcome?
Re: Refinements to Hedgefundie's excellent approach
MoneyMarathon wrote: ↑Sat Jul 06, 2019 2:52 amSuppose someone starts this right now, and over the next year, the Fed decides that employment looks good and raises rates to 3.5% from their current levels. Around the same time, stock market investors get nervous, then fullout panic after a war breaks out somewhere, and stocks dip 40% in a few months. These things happen in the same year.
What happens when both duration risk and equity risk get pummeled at the same time? How bad is the outcome?
What happens if stagflation occurs? Maybe that’s addressed in the simulated back testing of the 70s?
If you leave your head in the sand for too long, you might get run over by a Jeep.

 Posts: 4801
 Joined: Sun Oct 22, 2017 2:06 pm
Re: Refinements to Hedgefundie's excellent approach
As soon as the Fed begins to get an inkling of “stock market investors getting nervous”, do you think they would continue their rate raising? Witness what happened in December when stocks dropped 20%.MoneyMarathon wrote: ↑Sat Jul 06, 2019 2:52 amSuppose someone starts this right now, and over the next year, the Fed decides that employment looks good and raises rates to 3.5% from their current levels. Around the same time, stock market investors get nervous, then fullout panic after a war breaks out somewhere, and stocks dip 40% in a few months. These things happen in the same year.
What happens when both duration risk and equity risk get pummeled at the same time? How bad is the outcome?

 Posts: 10022
 Joined: Wed Feb 01, 2017 8:39 pm
Re: Refinements to Hedgefundie's excellent approach
You think rates would hold steady? Flight to safety.MoneyMarathon wrote: ↑Sat Jul 06, 2019 2:52 amSuppose someone starts this right now, and over the next year, the Fed decides that employment looks good and raises rates to 3.5% from their current levels. Around the same time, stock market investors get nervous, then fullout panic after a war breaks out somewhere, and stocks dip 40% in a few months. These things happen in the same year.
What happens when both duration risk and equity risk get pummeled at the same time? How bad is the outcome?

 Posts: 10022
 Joined: Wed Feb 01, 2017 8:39 pm
Re: Refinements to Hedgefundie's excellent approach
+1. Hydro, I’d love to see a plot (maybe I missed it) just showing the inverse lookback data for different rebalance periods, no unemployment. Also 1955+ data using monthly volatility/returns would be fascinating.HEDGEFUNDIE wrote: ↑Sat Jul 06, 2019 1:19 amWould the adaptive strategy have kept you 100% in UPRO since the inception of the funds in 2009?
Re: Refinements to Hedgefundie's excellent approach
Hydromod, warm welcome to the forum! It is very cool to have a new contributor with the kind of modeling/analytical skills that you just displayed.
I didn't pay much attention to the leveraged stuff in a while, but now that I read those excellent posts from the OP, I am a little confused. This seems to be based on daily series that go back to 1982 for both stocks (tracking the S&P 500) and bonds (tracking a Long Term Treasuries index).
Well, neither the S&P 500 numbers nor the LT Treasuries numbers allow to do so, because daily dividends historical data isn't available until end of 1987 for the S&P 500 and mid97 for LTTs. Only daily price information is available in the early 80s. This is good enough to produce meaningful monthly leveraged return numbers as we discussed in the modeling thread, but daily modeling (e.g. rebalancing) might be quite skewed when using numbers combining daily price information with monthly dividends information.
As a side note, we clearly established that leveraged funds (e.g. UPRO and the likes) track a daily Total Return index, not a Price index. It wasn't clear to start with, but we got solid evidence of it. And checking recent numbers, we can see that dividends are distributed by the individual securities part of the index on an almost daily basis (due to differences in individual distribution schedules).
I didn't pay much attention to the leveraged stuff in a while, but now that I read those excellent posts from the OP, I am a little confused. This seems to be based on daily series that go back to 1982 for both stocks (tracking the S&P 500) and bonds (tracking a Long Term Treasuries index).
Well, neither the S&P 500 numbers nor the LT Treasuries numbers allow to do so, because daily dividends historical data isn't available until end of 1987 for the S&P 500 and mid97 for LTTs. Only daily price information is available in the early 80s. This is good enough to produce meaningful monthly leveraged return numbers as we discussed in the modeling thread, but daily modeling (e.g. rebalancing) might be quite skewed when using numbers combining daily price information with monthly dividends information.
As a side note, we clearly established that leveraged funds (e.g. UPRO and the likes) track a daily Total Return index, not a Price index. It wasn't clear to start with, but we got solid evidence of it. And checking recent numbers, we can see that dividends are distributed by the individual securities part of the index on an almost daily basis (due to differences in individual distribution schedules).
Re: Refinements to Hedgefundie's excellent approach
The inversevolatility weights would not push you there (see the figure in my previous post). The unemployment strategy could have been interpreted as going whole hog to UPRO starting in early 2010, with a few ambiguous periods. I personally wouldn't have pushed to 100% UPRO, because the unemployment rate data gave no signal for Black Monday. This would have hit UPRO very hard with no forewarning. Some weight to TMF would have helped. With this leveraged strategy, IMO protecting against large downside volatility should be a significant consideration.HEDGEFUNDIE wrote: ↑Sat Jul 06, 2019 1:19 amWould the adaptive strategy have kept you 100% in UPRO since the inception of the funds in 2009?
Judge for yourself with the following.
The focus on unemployment rate is described by willthrill81.
The idea and links to good references are in his original post.
Link 1: https://www.philosophicaleconomics.com/2016/02/uetrend/willthrill81 wrote: ↑Thu Jan 17, 2019 7:16 pmFor the first part of this strategy, whether to be in stocks or fixed income (i.e. 100% in or out; this isn't necessary, but I prefer it), I use a nearly identical version of that advocated by the Philosophical Economist and detailed here. (He also provides an excellent overview to why trend following works here.) To put it simply, this system calls me to own stocks unless both (1) the U.S. unemployment rate (UER) is above its 12 month moving average and (2) all available stock indexes have had lower performance than that of bond indexes over the prior 7 months (the Philosophical Economist used the 10 month moving average, which is roughly analogous to the widely used 200 day moving average, but I prefer the 7 month moving average as it reacts more quickly to changes in the trend, although I don't expect a significant difference between the two over time as backtesting has shown results to be fairly stable over the longterm from a 3 month moving average out to beyond 1 year). As such, this is a very 'longbiased' system (i.e. it keeps you in stocks more so than most other trend following systems); from 1948 through 2016, it would have remained in stocks about 85% of the time. The UER is used as a recession indicator; for every recession that occurred since 1948, the UER first moved above its 12 month moving average. The average lead time was about 3.5 months, with a range of 0 to 8 months. However, there have been a few times when the UER crossed above the 12 month moving average but no recession occurred. This is where the second part of the strategy, the moving average of the stock indexes, comes in. It serves as what the Philosophical Economist calls a "double confirmation of danger that forces the strategy to take a safe position." The backtested results of this strategy were very good (i.e. better absolute returns, lower drawdowns) but should obviously be viewed with many grains of salt as it is not difficult to craft a strategy that would have performed well with the advantage of hindsight.
Link 2: https://www.philosophicaleconomics.com/ ... ngaverage/
The next figure is the online image for unemployment rate reported by FRED today. This image does not yet include an estimate for June. Note that the first estimate for month x is first included a little more than a week into month x + 1. Note that the first estimate is generally revised twice.
The unemployment rate is compared with the UPROSIM and TMFSIM sequences in the next figure. In the top plot, the black line is the monthly data, the red line is the 15month moving average, and the cyan line is the 4 month moving average. The middle plot shows the unemployment rate minus the 15 month moving average. Since 2009, for example, the black line crossed the red line briefly 3 or 4 times.
It looks like the unemployment rate gives a good signal most of the time, although the most reliable data is generally months old in the moment of making decisions. My first inclination would be to use different moving averages to determine when to exit the market and when to get back in, because of the uncertainty regarding recent data.
For an exit strategy, one reasonable approach might use a shortterm moving average compared to the longterm moving average.
The entrance strategy is harder, if one is trying to hit the bounceback surge. It might be reasonable to reenter once there is a downturn in unemployment or a downturn in a short moving average. For example, a simple crossing criterion would not have signaled reentry until early 2010, missing the 2009 bounce back, but would have been okay in the early 90's. This riskparity strategy does so well overall that missing the peak bounce back might cause me to shake my head, but it is not a tragedy.
Again, I would probably just use the riskparity weights whenever there is ambiguity about entering or exiting. This really should be the default.
Re: Refinements to Hedgefundie's excellent approach
Are you asking for something different than the moving average CAGR plots? The middle two plots in my fifth figure (one with four rows) show CAGR with just the two types of inverse volatility, leaving out the unemployment component. Color coding is by rebalancing periods.MotoTrojan wrote: ↑Sat Jul 06, 2019 9:16 am+1. Hydro, I’d love to see a plot (maybe I missed it) just showing the inverse lookback data for different rebalance periods, no unemployment. Also 1955+ data using monthly volatility/returns would be fascinating.
I can easily reproduce this figure with different volatility windows. Or redone by rebalance period, colored by volatility window. Given the impracticality of daily rebalancing, maybe just weekly/biweekly/monthly/bimonthly/quarterly.
The UPROSIM weights with just the inverse volatility calculations are shown in my second figure for the two schemes. Color coding is by volatility window.
I don't think that we have available the data to calculate daily volatility prior to the UPROSIM/TMFSIM data (end of 1986). I'm anxious to take a whack at the monthly data from 1955+, especially contrasting with the unemployment signals. It'll be a bit murky compared to using daily data, but still informative. In this case, probably the shortest volatility window we can use is based on windows of six months (pretty short!) to a year. Presumably this would generally give UPRO weights between 0.25 and 0.55 or so.

 Posts: 992
 Joined: Sun Sep 30, 2012 3:38 am
Re: Refinements to Hedgefundie's excellent approach
I'm asking about one of the worst case scenarios for this strategy.MotoTrojan wrote: ↑Sat Jul 06, 2019 9:14 amYou think rates would hold steady? Flight to safety.MoneyMarathon wrote: ↑Sat Jul 06, 2019 2:52 amSuppose someone starts this right now, and over the next year, the Fed decides that employment looks good and raises rates to 3.5% from their current levels. Around the same time, stock market investors get nervous, then fullout panic after a war breaks out somewhere, and stocks dip 40% in a few months. These things happen in the same year.
What happens when both duration risk and equity risk get pummeled at the same time? How bad is the outcome?
Yes, I think a worst case scenario is possible and that people have lost huge fortunes betting on correlations being as expected.
Re: Refinements to Hedgefundie's excellent approach
Can you try to formulate your synthesis in a paragraph?Hydromod wrote: ↑Sat Jul 06, 2019 12:03 amSo what have I learned so far?
• I can easily reproduce the risk parity weights selected by Hedgefundie.
• The Hedgefundie scheme would have beaten any scheme based on the unleveraged (1x) versions of UPRO and TMF for approximately 90 percent of the possible 5year intervals starting at the end of 1986. The exception is for periods with the S&P tanking but not treasuries. The scheme would have easily overcome the 1 percent ER for almost all of the outperformance sequences.
• Adaptively adjusting the risk parity weights would have provided some additional performance. The largest performance boost would have been with short volatility windows, downward volatility calculations, and very frequent rebalancing. Of course, this approach begs for automated calculations and trading, and will not be practical for most, and the effect of trading drag will likely degrade the boost.
• The performance boost from downward volatility is largely lost with biweekly or longer rebalancing.
• The volatility window should be tuned to the rebalance frequency. Performance degrades if the volatility window is much shorter than the rebalance frequency.
• The macroeconomic indicator provided by the unemployment rate had value as a predictor over the example period, and typically has provided a leading signal for every recession, of up to several months, since 1919.
Is it:
Adjust UPRO/TMF weights, every week, based on inverse (downwards) volatility. Further bias the weights based on unemployment trend.
so you are always 100% invested in these two funds.
35% US, 20 ExUS Dev, 10% EM, 10% EM Bonds, 10% Gold, 10% EDV, 5% I/EE Bonds. 50% value tilt in stocks.
Re: Refinements to Hedgefundie's excellent approach
siamond wrote: ↑Sat Jul 06, 2019 9:40 amHydromod, warm welcome to the forum! It is very cool to have a new contributor with the kind of modeling/analytical skills that you just displayed.
Aw shucks. Thanks for the praise.
I didn't pay much attention to the leveraged stuff in a while, but now that I read those excellent posts from the OP, I am a little confused. This seems to be based on daily series that go back to 1982 for both stocks (tracking the S&P 500) and bonds (tracking a Long Term Treasuries index).
Well, neither the S&P 500 numbers nor the LT Treasuries numbers allow to do so, because daily dividends historical data isn't available until end of 1987 for the S&P 500 and mid97 for LTTs. Only daily price information is available in the early 80s. This is good enough to produce meaningful monthly leveraged return numbers as we discussed in the modeling thread, but daily modeling (e.g. rebalancing) might be quite skewed when using numbers combining daily price information with monthly dividends information.
Sorry if it wasn't clear. This data only goes back to late 1986, it's the data Hedgefundie has been using.
By the way, I was wondering why it seemed like something changed in the data around 1997, the squiggles for long rebalancing frequencies change on the CAGR returns. A byproduct of some loss of daily volatility in the simulated LTT data, I would suppose.
As a side note, we clearly established that leveraged funds (e.g. UPRO and the likes) track a daily Total Return index, not a Price index. It wasn't clear to start with, but we got solid evidence of it. And checking recent numbers, we can see that dividends are distributed by the individual securities part of the index on an almost daily basis (due to differences in individual distribution schedules).
Good to know. I'm sure I would never have been able to track that down.
I suppose this turns out to be good news for MotoTrojan, because it remains simple to calculate volatilities going forward now that we know we don't have to worry about occasional dividends muddying returns. I wouldn't have even known to be concerned until you brought it up!

 Posts: 992
 Joined: Sun Sep 30, 2012 3:38 am
Re: Refinements to Hedgefundie's excellent approach
Maybe it is, maybe it isn't. What did the simulated back testing of the 70s show?columbia wrote: ↑Sat Jul 06, 2019 4:37 amWhat happens if stagflation occurs? Maybe that’s addressed in the simulated back testing of the 70s?MoneyMarathon wrote: ↑Sat Jul 06, 2019 2:52 amSuppose someone starts this right now, and over the next year, the Fed decides that employment looks good and raises rates to 3.5% from their current levels. Around the same time, stock market investors get nervous, then fullout panic after a war breaks out somewhere, and stocks dip 40% in a few months. These things happen in the same year.
What happens when both duration risk and equity risk get pummeled at the same time? How bad is the outcome?
In Hedgefundie's OP, there is this note: "Forum member pezblanco did just that. He simulated several thousand runs of 20year periods using 19852018 data. Here are the distribution of returns (20year CAGRs on the Xaxis, incidence of returns on the Yaxis), with the green bars being this 3x daily leveraged balanced portfolio, and the blue bars being the S&P 500. ... Here is the same simulation run from 19682018."
Based on the comments, this isn't a simulated backtest of the 70s. It's a simulation of multiple 20year periods from the sequence 19682018 (and the comments are less than completely clear about whether years are sequential or randomly picked out of order). Over a third of these 20year periods showed negative returns. Several showed negative CAGR below 10%, and that doesn't make it sound like there was a whole lot left after those particular runs of 20 years.
Apparently the 70s might not be good for this strategy. Also, apparently, graphs can be hard to read and can be used to mislead.
Is there a simple graph of the balance someone would have starting with this strategy in 1968?

 Posts: 4801
 Joined: Sun Oct 22, 2017 2:06 pm
Re: Refinements to Hedgefundie's excellent approach
And how much opportunity cost has been incurred by people preparing for the worst, only to see the world go on as usual?MoneyMarathon wrote: ↑Sat Jul 06, 2019 3:30 pmI'm asking about one of the worst case scenarios for this strategy.MotoTrojan wrote: ↑Sat Jul 06, 2019 9:14 amYou think rates would hold steady? Flight to safety.MoneyMarathon wrote: ↑Sat Jul 06, 2019 2:52 amSuppose someone starts this right now, and over the next year, the Fed decides that employment looks good and raises rates to 3.5% from their current levels. Around the same time, stock market investors get nervous, then fullout panic after a war breaks out somewhere, and stocks dip 40% in a few months. These things happen in the same year.
What happens when both duration risk and equity risk get pummeled at the same time? How bad is the outcome?
Yes, I think a worst case scenario is possible and that people have lost huge fortunes betting on correlations being as expected.
Re: Refinements to Hedgefundie's excellent approach
MoneyMarathon wrote: ↑Sat Jul 06, 2019 3:56 pmMaybe it is, maybe it isn't. What did the simulated back testing of the 70s show?columbia wrote: ↑Sat Jul 06, 2019 4:37 amWhat happens if stagflation occurs? Maybe that’s addressed in the simulated back testing of the 70s?MoneyMarathon wrote: ↑Sat Jul 06, 2019 2:52 amSuppose someone starts this right now, and over the next year, the Fed decides that employment looks good and raises rates to 3.5% from their current levels. Around the same time, stock market investors get nervous, then fullout panic after a war breaks out somewhere, and stocks dip 40% in a few months. These things happen in the same year.
What happens when both duration risk and equity risk get pummeled at the same time? How bad is the outcome?
In Hedgefundie's OP, there is this note: "Forum member pezblanco did just that. He simulated several thousand runs of 20year periods using 19852018 data. Here are the distribution of returns (20year CAGRs on the Xaxis, incidence of returns on the Yaxis), with the green bars being this 3x daily leveraged balanced portfolio, and the blue bars being the S&P 500. ... Here is the same simulation run from 19682018."
Based on the comments, this isn't a simulated backtest of the 70s. It's a simulation of multiple 20year periods from the sequence 19682018 (and the comments are less than completely clear about whether years are sequential or randomly picked out of order). Over a third of these 20year periods showed negative returns. Several showed negative CAGR below 10%, and that doesn't make it sound like there was a whole lot left after those particular runs of 20 years.
Apparently the 70s might not be good for this strategy. Also, apparently, graphs can be hard to read and can be used to mislead.
Is there a simple graph of the balance someone would have starting with this strategy in 1968?

 Posts: 992
 Joined: Sun Sep 30, 2012 3:38 am
Re: Refinements to Hedgefundie's excellent approach
A plan calling for a multidecade time horizon has to take into account entire decades of extremely poor historical results. The end result might be that you still decide to put your money in and take your chances. But it's irresponsible to downplay the risks.HEDGEFUNDIE wrote: ↑Sat Jul 06, 2019 4:17 pmAnd how much opportunity cost has been incurred by people preparing for the worst, only to see the world go on as usual?
Re: Refinements to Hedgefundie's excellent approach
You've just about hit it. I'm always 100% in at least one of the funds, but not always both at once. I haven't tried to see if there are cases that favor complete retreat to cash.klaus14 wrote: ↑Sat Jul 06, 2019 3:44 pmCan you try to formulate your synthesis in a paragraph?Hydromod wrote: ↑Sat Jul 06, 2019 12:03 amSo what have I learned so far?
• I can easily reproduce the risk parity weights selected by Hedgefundie.
• The Hedgefundie scheme would have beaten any scheme based on the unleveraged (1x) versions of UPRO and TMF for approximately 90 percent of the possible 5year intervals starting at the end of 1986. The exception is for periods with the S&P tanking but not treasuries. The scheme would have easily overcome the 1 percent ER for almost all of the outperformance sequences.
• Adaptively adjusting the risk parity weights would have provided some additional performance. The largest performance boost would have been with short volatility windows, downward volatility calculations, and very frequent rebalancing. Of course, this approach begs for automated calculations and trading, and will not be practical for most, and the effect of trading drag will likely degrade the boost.
• The performance boost from downward volatility is largely lost with biweekly or longer rebalancing.
• The volatility window should be tuned to the rebalance frequency. Performance degrades if the volatility window is much shorter than the rebalance frequency.
• The macroeconomic indicator provided by the unemployment rate had value as a predictor over the example period, and typically has provided a leading signal for every recession, of up to several months, since 1919.
Is it:
Adjust UPRO/TMF weights, every week, based on inverse (downwards) volatility. Further bias the weights based on unemployment trend.
so you are always 100% invested in these two funds.
The unemployment trend puts me into three conditions: (i) clear recession, (ii) clear expansion, or (iii) ambiguous. This condition is updated monthly.
My general strategy would be:
While it is a clear recession, retreat to 100% TMF.
If it isn't a clear recession, I would adjust the UPRO/TMF weights based on the inverse volatility. I would use these weights unless the unemployment trend indicates clear expansion. If so, I would move the weights about halfway to full UPRO.
If trading costs were a factor, I would probably use quarterly rebalancing by default and calculate the inverse volatility weights based on a twomonth volatility window or so. It shouldn't make a difference if you use symmetric or downward volatility. However, I would at least check on the unemployment rate monthly when it comes out, and adjust the scheme weights if the signal changes to a more adverse condition: to clear recession or from clear expansion. I don't want to take chances when the risk signal increases. One might also change early if the signal goes to clear expansion.
If trading costs were not a factor, I would probably drop to weekly as you said. I'd use a 10day volatility window with downward volatility for the weights. However, there would be no need to rebalance while the recession signal is on, because I'd be 100% TMF.
If I were an even less cautious sort, I would go full UPRO during clear expansion in addition to full TMF during clear recession. This would have the benefit of not requiring frequent trading and only monthly checking most of the time. This is essentially the willthrill81 strategy. This would be a strong bet that there's not a black swan event like Black Monday, though, and probably better for younger folks.
Now that I've stated this strategy, I will say that it is predicated on the assumption that the economic conditions over the last 30 years will generally continue (Hedgefundie's hypothesis).
Last edited by Hydromod on Sat Jul 06, 2019 4:51 pm, edited 1 time in total.
Re: Refinements to Hedgefundie's excellent approach
I’ve yet to see HEDGEFUNDIE downplay the risks or otherwise be irresponsible when communicating this strategy, imho. I have seen many, many posters, however, not read the original thread all the way through, where the risks, including the one you’re describing, are discussed till the horse has been beaten into dust.MoneyMarathon wrote: ↑Sat Jul 06, 2019 4:30 pmA plan calling for a multidecade time horizon has to take into account entire decades of extremely poor historical results. The end result might be that you still decide to put your money in and take your chances. But it's irresponsible to downplay the risks.HEDGEFUNDIE wrote: ↑Sat Jul 06, 2019 4:17 pmAnd how much opportunity cost has been incurred by people preparing for the worst, only to see the world go on as usual?
Can I ask you a question? Is there some reason the red graph below isn’t considered “decades of extremely poor historical results” when compared to this strategy? Why is the red graph considered sacrosanct?

 Posts: 992
 Joined: Sun Sep 30, 2012 3:38 am
Re: Refinements to Hedgefundie's excellent approach
One of the strategies is lower risk  lower volatility, less drawdown, less chance of ending in the red. Most people need to have most of their money in lowerrisk investments (relative to the excellent approach); they can't afford to lose very much of it for very long. I understand that Hedgefundie has been very clear about putting only a small portion of his portfolio in this strategy. I also do think that the risk of that part of the portfolio not giving outsized returns has been understated. The criticism of my own comments with statements of that risk is evidence of that.
Re: Refinements to Hedgefundie's excellent approach
Thanks. I am considering moving my roth ira (around 10% of my net worth) to a similar strategy. Would you qualify roth ira @ M1, as trading costs not a factor?Hydromod wrote: ↑Sat Jul 06, 2019 4:45 pm
You've just about hit it. I'm always 100% in at least one of the funds, but not always both at once. I haven't tried to see if there are cases that favor complete retreat to cash.
The unemployment trend puts me into three conditions: (i) clear recession, (ii) clear expansion, or (iii) ambiguous. This condition is updated monthly.
My general strategy would be:
While it is a clear recession, retreat to 100% TMF.
If it isn't a clear recession, I would adjust the UPRO/TMF weights based on the inverse volatility. I would use these weights unless the unemployment trend indicates clear expansion. If so, I would move the weights about halfway to full UPRO.
If trading costs were a factor, I would probably use quarterly rebalancing by default and calculate the inverse volatility weights based on a twomonth volatility window or so. It shouldn't make a difference if you use symmetric or downward volatility. However, I would at least check on the unemployment rate monthly when it comes out, and adjust the scheme weights if the signal changes to a more adverse condition: to clear recession or from clear expansion. I don't want to take chances when the risk signal increases. One might also change early if the signal goes to clear expansion.
If trading costs were not a factor, I would probably drop to weekly as you said. I'd use a 10day volatility window with downward volatility for the weights. However, there would be no need to rebalance while the recession signal is on, because I'd be 100% TMF.
If I were an even less cautious sort, I would go full UPRO during clear expansion in addition to full TMF during clear recession. This would have the benefit of not requiring frequent trading and only monthly checking most of the time. This is essentially the willthrill81 strategy. This would be a strong bet that there's not a black swan event like Black Monday, though, and probably better for younger folks.
Now that I've stated this strategy, I will say that it is predicated on the assumption that the economic conditions over the last 30 years will generally continue (Hedgefundie's hypothesis).
How do you define ambiguous? We are very close to full employment and labor participaction rate is increasing. I think this caused a false positive in willthrill81's strategy in January.
I think *monthly* schedule has some practical merits. unemployment is announced monthly. Portfolio Visualizer also works monthtomonth. So how about monthly rebalancing based on monthly volatility?
How about biasing based on the strength of the unemployment signal. If signal is very strong, then you completely get out of stock market. If signal is weak, then it's a small bias. How would you define the strength of this signal? One way could be counting. For example, in the first crossing, you move 40/60 to 30/70. If it is still above MA again in the next month, you move to 20/80 (assuming volatilities are same)
I am also curious about how to utilize volatility targeting in this framework. For example, if volatility of both of these assets double, maybe we want to move 50% to unleveraged (VTI/EDV)
Last edited by klaus14 on Sat Jul 06, 2019 5:51 pm, edited 2 times in total.
35% US, 20 ExUS Dev, 10% EM, 10% EM Bonds, 10% Gold, 10% EDV, 5% I/EE Bonds. 50% value tilt in stocks.

 Posts: 4801
 Joined: Sun Oct 22, 2017 2:06 pm
Re: Refinements to Hedgefundie's excellent approach
For a risk to be understated or overstated, there needs to be some notion of ordinary likelihood or probability that the risk would come to pass.MoneyMarathon wrote: ↑Sat Jul 06, 2019 5:10 pmOne of the strategies is lower risk  lower volatility, less drawdown, less chance of ending in the red. Most people need to have most of their money in lowerrisk investments (relative to the excellent approach); they can't afford to lose very much of it for very long. I understand that Hedgefundie has been very clear about putting only a small portion of his portfolio in this strategy. I also do think that the risk of that part of the portfolio not giving outsized returns has been understated. The criticism of my own comments with statements of that risk is evidence of that.
I am still waiting for someone to explain to me how we could return to a world where stocks are dropping year over year while long term Treasury rates are rising year over year.

 Posts: 10022
 Joined: Wed Feb 01, 2017 8:39 pm
Re: Refinements to Hedgefundie's excellent approach
Gotcha. Yes, the worst case scenario is the stock exchange removing its circuit breaker protection rules and then both assets dropping more than 33% on the same day.MoneyMarathon wrote: ↑Sat Jul 06, 2019 3:30 pmI'm asking about one of the worst case scenarios for this strategy.MotoTrojan wrote: ↑Sat Jul 06, 2019 9:14 amYou think rates would hold steady? Flight to safety.MoneyMarathon wrote: ↑Sat Jul 06, 2019 2:52 amSuppose someone starts this right now, and over the next year, the Fed decides that employment looks good and raises rates to 3.5% from their current levels. Around the same time, stock market investors get nervous, then fullout panic after a war breaks out somewhere, and stocks dip 40% in a few months. These things happen in the same year.
What happens when both duration risk and equity risk get pummeled at the same time? How bad is the outcome?
Yes, I think a worst case scenario is possible and that people have lost huge fortunes betting on correlations being as expected.
Some would say they expect people to lose fortunes in the future by investing in solely US equities but people blindly follow past results (correlations).
Last edited by MotoTrojan on Sat Jul 06, 2019 6:45 pm, edited 1 time in total.

 Posts: 10022
 Joined: Wed Feb 01, 2017 8:39 pm
Re: Refinements to Hedgefundie's excellent approach
M1 will still have trading costs due to market orders (M1 forces that) and bidask spread (you’ll get that anywhere).klaus14 wrote: ↑Sat Jul 06, 2019 5:47 pmThanks. I am considering moving my roth ira (around 10% of my net worth) to a similar strategy. Would you qualify roth ira @ M1, as trading costs not a factor?Hydromod wrote: ↑Sat Jul 06, 2019 4:45 pm
You've just about hit it. I'm always 100% in at least one of the funds, but not always both at once. I haven't tried to see if there are cases that favor complete retreat to cash.
The unemployment trend puts me into three conditions: (i) clear recession, (ii) clear expansion, or (iii) ambiguous. This condition is updated monthly.
My general strategy would be:
While it is a clear recession, retreat to 100% TMF.
If it isn't a clear recession, I would adjust the UPRO/TMF weights based on the inverse volatility. I would use these weights unless the unemployment trend indicates clear expansion. If so, I would move the weights about halfway to full UPRO.
If trading costs were a factor, I would probably use quarterly rebalancing by default and calculate the inverse volatility weights based on a twomonth volatility window or so. It shouldn't make a difference if you use symmetric or downward volatility. However, I would at least check on the unemployment rate monthly when it comes out, and adjust the scheme weights if the signal changes to a more adverse condition: to clear recession or from clear expansion. I don't want to take chances when the risk signal increases. One might also change early if the signal goes to clear expansion.
If trading costs were not a factor, I would probably drop to weekly as you said. I'd use a 10day volatility window with downward volatility for the weights. However, there would be no need to rebalance while the recession signal is on, because I'd be 100% TMF.
If I were an even less cautious sort, I would go full UPRO during clear expansion in addition to full TMF during clear recession. This would have the benefit of not requiring frequent trading and only monthly checking most of the time. This is essentially the willthrill81 strategy. This would be a strong bet that there's not a black swan event like Black Monday, though, and probably better for younger folks.
Now that I've stated this strategy, I will say that it is predicated on the assumption that the economic conditions over the last 30 years will generally continue (Hedgefundie's hypothesis).
How do you define ambiguous? We are very close to full employment and labor participaction rate is increasing. I think this caused a false positive in willthrill81's strategy in January.
I think *monthly* schedule has some practical merits. unemployment is announced monthly. Portfolio Visualizer also works monthtomonth. So how about monthly rebalancing based on monthly volatility?
How about biasing based on the strength of the unemployment signal. If signal is very strong, then you completely get out of stock market. If signal is weak, then it's a small bias. How would you define the strength of this signal? One way could be counting. For example, in the first crossing, you move 40/60 to 30/70. If it is still above MA again in the next month, you move to 20/80 (assuming volatilities are same)
I am also curious about how to utilize volatility targeting in this framework. For example, if volatility of both of these assets double, maybe we want to move 50% to unleveraged (VTI/EDV)
For me personally the economic indicators is too big a leap but I like the resetting risk parity amounts as it has intuitive reasoning in my eyes. If both double then I’ll just maintain the allocation.

 Posts: 10022
 Joined: Wed Feb 01, 2017 8:39 pm
Re: Refinements to Hedgefundie's excellent approach
Thank you. I think what I’m really looking for then is a comparison of static 40/60 (quarterly or whatever) to the inverse volatility cases; so an overlay of your two plots.Hydromod wrote: ↑Sat Jul 06, 2019 3:26 pmAre you asking for something different than the moving average CAGR plots? The middle two plots in my fifth figure (one with four rows) show CAGR with just the two types of inverse volatility, leaving out the unemployment component. Color coding is by rebalancing periods.MotoTrojan wrote: ↑Sat Jul 06, 2019 9:16 am+1. Hydro, I’d love to see a plot (maybe I missed it) just showing the inverse lookback data for different rebalance periods, no unemployment. Also 1955+ data using monthly volatility/returns would be fascinating.
I can easily reproduce this figure with different volatility windows. Or redone by rebalance period, colored by volatility window. Given the impracticality of daily rebalancing, maybe just weekly/biweekly/monthly/bimonthly/quarterly.
The UPROSIM weights with just the inverse volatility calculations are shown in my second figure for the two schemes. Color coding is by volatility window.
I don't think that we have available the data to calculate daily volatility prior to the UPROSIM/TMFSIM data (end of 1986). I'm anxious to take a whack at the monthly data from 1955+, especially contrasting with the unemployment signals. It'll be a bit murky compared to using daily data, but still informative. In this case, probably the shortest volatility window we can use is based on windows of six months (pretty short!) to a year. Presumably this would generally give UPRO weights between 0.25 and 0.55 or so.
12 pack on me if you can give actual simulated CAGR of inverse volatility (using monthly data) from 1955 to present for various rebalance options.
Re: Refinements to Hedgefundie's excellent approach
Then monthly schedule is indeed a good compromise.MotoTrojan wrote: ↑Sat Jul 06, 2019 6:40 pmM1 will still have trading costs due to market orders (M1 forces that) and bidask spread (you’ll get that anywhere).
For me personally the economic indicators is too big a leap but I like the resetting risk parity amounts as it has intuitive reasoning in my eyes. If both double then I’ll just maintain the allocation.
The issue with always being 100% invested in leveraged funds is that you may get wiped out if both assets exhibit strong downwards volatility. Volatility targeting and/or unemployment signal can prevent that.
35% US, 20 ExUS Dev, 10% EM, 10% EM Bonds, 10% Gold, 10% EDV, 5% I/EE Bonds. 50% value tilt in stocks.

 Posts: 10022
 Joined: Wed Feb 01, 2017 8:39 pm
Re: Refinements to Hedgefundie's excellent approach
Fair enough. I’m sticking to the 3x funds but personally using 1 month as noted, with a 20 day look back.klaus14 wrote: ↑Sat Jul 06, 2019 6:50 pmThen monthly schedule is indeed a good compromise.MotoTrojan wrote: ↑Sat Jul 06, 2019 6:40 pmM1 will still have trading costs due to market orders (M1 forces that) and bidask spread (you’ll get that anywhere).
For me personally the economic indicators is too big a leap but I like the resetting risk parity amounts as it has intuitive reasoning in my eyes. If both double then I’ll just maintain the allocation.
The issue with always being 100% invested in leveraged funds is that you may get wiped out if both assets exhibit strong downwards volatility. Volatility targeting and/or unemployment signal can prevent that.
Re: Refinements to Hedgefundie's excellent approach
I don't think there should be overall too much difference between monthly and quarterly rebalancing. Monthly does make a good amount of sense, given the monthly employment rate update. There might be a small incremental improvement with biweekly, but it would be hard to see in an actual time history, given all of the bouncing around. Maybe 10 percent better return over a decade or less?klaus14 wrote: ↑Sat Jul 06, 2019 5:47 pmHow do you define ambiguous? We are very close to full employment and labor participaction rate is increasing. I think this caused a false positive in willthrill81's strategy in January.
I think *monthly* schedule has some practical merits. unemployment is announced monthly. Portfolio Visualizer also works monthtomonth. So how about monthly rebalancing based on monthly volatility?
How about biasing based on the strength of the unemployment signal. If signal is very strong, then you completely get out of stock market. If signal is weak, then it's a small bias. How would you define the strength of this signal? One way could be counting. For example, in the first crossing, you move 40/60 to 30/70. If it is still above MA again in the next month, you move to 20/80 (assuming volatilities are same)
I am also curious about how to utilize volatility targeting in this framework. For example, if volatility of both of these assets double, maybe we want to move 50% to unleveraged (VTI/EDV)
I only have had a chance to test the exit/reentry strategy a little, and I'm not at all satisfied that it is nailed. That's on the horizon. I did want people to be aware that something like this has the potential to help with downside risk, and if there are ideas for strategies I will be glad to test them. You might compare the employment signal with the figure below. Volatility weighting is something I do want to look at.
I did test a few moving average lengths and criteria for ambiguity, but this was by no means exhaustive. A main advantage of the ambiguous state is to cut down on whipsawing.
I basically defined a sequence that tracked the number of months since the last upward trigger (counting positive from 1 month) and the number of months since the last downward (counting negative from 1). An upward trigger was defined as an increase in unemployment relative to the moving average and a downward trigger was defined as decrease in unemployment relative to the moving average.
The best strategy I found out of the limited testing defined an ambiguous month as having +1 or 1, clearly recessive month having > +1, and clearly expansive month as having < 1. I haven't yet tried (i) grading the weights, (ii) being very careful about when unemployment information becomes available for decisions, and (iii) accounting for uncertainty in the unemployment data.
The improved performance tended to perform by keeping high in UPRO weighting during the run up to the peak before the fall, then holding relatively steady using TMF until well after the rebound started. The improved performance during the run up and relatively small fall during the recession tended to outweigh the missed rebound. Likely a criterion for earlier reentry would have helped overall, in order to catch the rebound, but I don't see an obvious candidate with the moving averages that would have worked for every case. Perhaps a criterion considering a zero crossing or drop in the unemployment rate criterion by 1.5 percent, whichever arrives first?
Re: Refinements to Hedgefundie's excellent approach
Does the strategy rely on declining long term interest rates? What happens if rates don't change?
Also, how does the bond fund triple dividends? What is the mechanism?
Also, how does the bond fund triple dividends? What is the mechanism?

 Posts: 10022
 Joined: Wed Feb 01, 2017 8:39 pm
Re: Refinements to Hedgefundie's excellent approach
I read through the first six pages and decided I'm okay not reading the rest.
Also, most of the stuff dealing with that question was more or less resolved by probably not, but this is my strategy and I'm sticking to it. Or the whole point of the bond fund is to hedge against stock declines.
So no, this question was not answered in the first half of the thread.

 Posts: 4801
 Joined: Sun Oct 22, 2017 2:06 pm
Re: Refinements to Hedgefundie's excellent approach
Both of your questions are addressed in the very first post.Lee_WSP wrote: ↑Sat Jul 06, 2019 8:45 pmI read through the first six pages and decided I'm okay not reading the rest.
Also, most of the stuff dealing with that question was more or less resolved by probably not, but this is my strategy and I'm sticking to it. Or the whole point of the bond fund is to hedge against stock declines.
So no, this question was not answered in the first half of the thread.
Re: Refinements to Hedgefundie's excellent approach
The first is addressed by a chart I don't exactly understand and the second is not answered.HEDGEFUNDIE wrote: ↑Sat Jul 06, 2019 9:18 pmBoth of your questions are addressed in the very first post.Lee_WSP wrote: ↑Sat Jul 06, 2019 8:45 pmI read through the first six pages and decided I'm okay not reading the rest.
Also, most of the stuff dealing with that question was more or less resolved by probably not, but this is my strategy and I'm sticking to it. Or the whole point of the bond fund is to hedge against stock declines.
So no, this question was not answered in the first half of the thread.
Re: Refinements to Hedgefundie's excellent approach
Late 1986 is definitely better than 1982, but I would definitely suggest to ignore any daily number before 1988 for stocks, as daily dividends were definitely NOT available by then. As to treasuries, we only have monthly total returns until June 1997, so any daily number before that would be entirely meaningless. Between Jun97 and Dec97, the LTT index displayed some weird vagaries, I think you should skip that too (as we did for the monthly modeling). Overall, for experiments where daily values are important, I'm afraid you should restrict yourself to 1998+. Sorry, historical records are really lacking when it comes to daily data.Hydromod wrote: ↑Sat Jul 06, 2019 3:50 pmSorry if it wasn't clear. This data only goes back to late 1986, it's the data Hedgefundie has been using.siamond wrote: ↑Sat Jul 06, 2019 9:40 amI didn't pay much attention to the leveraged stuff in a while, but now that I read those excellent posts from the OP, I am a little confused. This seems to be based on daily series that go back to 1982 for both stocks (tracking the S&P 500) and bonds (tracking a Long Term Treasuries index).
Well, neither the S&P 500 numbers nor the LT Treasuries numbers allow to do so, because daily dividends historical data isn't available until end of 1987 for the S&P 500 and mid97 for LTTs. Only daily price information is available in the early 80s. This is good enough to produce meaningful monthly leveraged return numbers as we discussed in the modeling thread, but daily modeling (e.g. rebalancing) might be quite skewed when using numbers combining daily price information with monthly dividends information.
By the way, I was wondering why it seemed like something changed in the data around 1997, the squiggles for long rebalancing frequencies change on the CAGR returns. A byproduct of some loss of daily volatility in the simulated LTT data, I would suppose.
Re: Refinements to Hedgefundie's excellent approach
I am very skeptical about anything involving daily or weekly actions. The amount of work to sustain such discipline, plus the transaction costs (direct and indirect, e.g. bid/ask spreads) would probably make it unrealistic.Hydromod wrote: ↑Sat Jul 06, 2019 12:03 amIn the next set of figures, I consider (i) rebalancing frequency, (ii) sequence duration, and (iii) volatility window for a number of schemes. In each figure, different rebalancing frequencies (not volatility window!) are indicated with the line color. I considered rebalancing frequency cases of 1 (daily), 2, 5 (weekly), 10 (biweekly), 20 ("monthly"), 40 ("bimonthly"), 60 ("quarterly"), 120 ("semiannual"), and 250 ("annual") trading days. I assume 250 trading days per year.
Now those of us fiddling around with rebalancing logic tend to use triggerbased rebalancing. For example, when the current % of stocks (or bonds) is off by more than 20% RELATIVE to the target AA, then rebalance. For unleveraged funds, such events are actually quite rare (e.g. once a year on average, but possibly more in troubled times). This requires frequent (e.g. daily or weekly) monitoring, but this is easy to automate with a Google Script and a corresponding spreadsheet. Heck, I do something like that myself! Now for a leveraged portfolio, I suspect the rebalancing events would be more frequent, but still stay reasonable in terms of number of transactions per year. And I would be quite curious about the outcome. Maybe something to add to your TODO list.
PS. you may want to take a look at the rebalancing wiki page for more details. I would only focus on the relative technique, skip the absolute % thing. The adaptive method is better imho, but not necessary in a simple case like 60/40.
Hm, no, that is quite incorrect. The relation between 1x numbers and 3x numbers is more complex, due to borrowing costs, expense ratios, etc. Plus we do have the daily 1x numbers (that is, for 1998+), no need to go back & forth. Let me sync up with you by PM to help you with that.
This is the first time I've seen this type of chart. This is pretty cool. Maybe something we should use more often when running other types of analysis. I even wonder if it wouldn't be worth it to create a wiki page about this concept (e.g. similar to the Telltale chart wiki page we have). Or at least mention the concept with proper references in some existing wiki page?Hydromod wrote: ↑Fri Jul 05, 2019 10:59 pmWhen assessing the viability of a scheme, I commonly plot the time history and the cumulative exceedance distribution of a parameter or outcome. The cumulative exceedance distribution simply describes the fraction of outcomes that are exceeded by a given value. For example, if half of the outcomes are less than a particular value, the exceedance fraction is 0.5.
Re: Refinements to Hedgefundie's excellent approach
siamond wrote: ↑Sat Jul 06, 2019 10:12 pmI am very skeptical about anything involving daily or weekly actions. The amount of work to sustain such discipline, plus the transaction costs (direct and indirect, e.g. bid/ask spreads) would probably make it unrealistic.Hydromod wrote: ↑Sat Jul 06, 2019 12:03 amIn the next set of figures, I consider (i) rebalancing frequency, (ii) sequence duration, and (iii) volatility window for a number of schemes. In each figure, different rebalancing frequencies (not volatility window!) are indicated with the line color. I considered rebalancing frequency cases of 1 (daily), 2, 5 (weekly), 10 (biweekly), 20 ("monthly"), 40 ("bimonthly"), 60 ("quarterly"), 120 ("semiannual"), and 250 ("annual") trading days. I assume 250 trading days per year.
Sure. This was more for gaining understanding of the overall behavior in theory. When I first mentioned in in the other thread, I mentioned that the very short rebalancing frames might be something that some fund might be encouraged to undertake.
Wouldn't it be cool if there was an ETF for 0.4*UPRO and 0.6*TMF rebalanced daily (actually the volatilityweighted version)?
Now those of us fiddling around with rebalancing logic tend to use triggerbased rebalancing. For example, when the current % of stocks (or bonds) is off by more than 20% RELATIVE to the target AA, then rebalance. For unleveraged funds, such events are actually quite rare (e.g. once a year on average, but possibly more in troubled times). This requires frequent (e.g. daily or weekly) monitoring, but this is easy to automate with a Google Script and a corresponding spreadsheet. Heck, I do something like that myself! Now for a leveraged portfolio, I suspect the rebalancing events would be more frequent, but still stay reasonable in terms of number of transactions per year. And I would be quite curious about the outcome. Maybe something to add to your TODO list.
This has been on my list already. Gonna play with the monthly data first.
PS. you may want to take a look at the rebalancing wiki page for more details. I would only focus on the relative technique, skip the absolute % thing. The adaptive method is better imho, but not necessary in a simple case like 60/40.
Hm, no, that is quite incorrect. The relation between 1x numbers and 3x numbers is more complex, due to borrowing costs, expense ratios, etc. Plus we do have the daily 1x numbers (that is, for 1998+), no need to go back & forth. Let me sync up with you by PM to help you with that.
Oh certainly, I agree. The comparison with the 1x was simply to confirm the point that these leveraged schemes would have almost always far outperformed the unleveraged alternative for any reasonable interval. I mentally just take off 1 percentage point from the CAGR to approximately account for the ER.
This first bit was to get my feet wet. I'm more been trying to get the broad picture first, to see where things are likely to make a big difference. In operation, adaptive volatility weights will need to be determined from the daily returns, so I'm a little cautious about how the algorithm receives returns.
This is the first time I've seen this type of chart. This is pretty cool. Maybe something we should use more often when running other types of analysis. I even wonder if it wouldn't be worth it to create a wiki page about this concept (e.g. similar to the Telltale chart wiki page we have). Or at least mention the concept with proper references in some existing wiki page?Hydromod wrote: ↑Fri Jul 05, 2019 10:59 pmWhen assessing the viability of a scheme, I commonly plot the time history and the cumulative exceedance distribution of a parameter or outcome. The cumulative exceedance distribution simply describes the fraction of outcomes that are exceeded by a given value. For example, if half of the outcomes are less than a particular value, the exceedance fraction is 0.5.
This is actually a basic concept in probability. I think I called it the wrong thing in these threads, I always forget the terminology and I rushed the plots. It's really the cumulative density function, often called the CDF, which is the probability that a particular value is less than a reference value. The cumulative exceedance function is 1  CDF.
I was waiting for someone to rush in and point accusing fingers at the terminology!
Re: Refinements to Hedgefundie's excellent approach
Here is a thought hot off the computer!
Siamond was kind enough to provide his database of monthly returns from 1955 through 2018. I started looking at this tonight to do some thought experiments on the controlling factors for the riskparity approach, including the data prior to 1987. This is a very broad brush, first look thing.
Hedgefundie is basing the approach on inverse correlation, and recognizes that the approach performed poorly prior to 1982. The effect of longterm treasury returns has been brought up as an alternative explanation.
So with this though experiment I just want to try and separate out the effects of correlation from the effects of longterm treasury returns and check if there is some hope for using the unemployment rate index under additional economic conditions.
Assumptions:
• Monthly rebalancing
• ER not included
• All calculations in nominal terms
• I consider two x3 indexes for LTT: (i) TMF for the entire time, and (ii) TMV before 1982, replaced by x3 TMF after 1982. I simply multiplied the TMF returns by 1 to simulate TMV. I recognize that this is questionable for accurate calculations, but this is just a first simpleminded cut.
• I consider a case with a simple unemployment index: 3month moving average minus 15month moving average. If the index is negative, I fully went to the x3 S&P, otherwise I fully went to the x3 LTT index.
The following figure has four plots.
The top plot shows the correlation coefficient between monthly returns for UPRO (Siamond’s x3 S&P 500) and TMF (Siamond’s x3 LTT20+). The correlation coefficient is calculated with the returns from the prior 12 months. Notice that the correlation coefficient is generally negative 1955 to 1975, generally positive from 1975 to 2002, and generally negative since 2002.
The second plot shows my simple index. Positive values are the signal for “recession” and negative values are the signal for “expansion”. Notice that there is a fair amount of bouncing around, and it’s not at all clear that the signals perfectly line up at early years. This may be a data issue or something to do with my quick interpretation.
The third plot shows the cumulative returns for UPRO alone (red), TMF alone (blue), and the mixed TMV/TMF index (cyan). Notice that TMV would have had a small positive nominal return through 1980, while TMF dropped by an order of magnitude from 1955 to 1982.
The fourth plot shows four cases. The solid lines use the UPRO/TMF combinations. The dotted lines use the UPRO/TMV/TMF combinations. The olive cases use the nominal 40/60 weights, rebalanced monthly. The purple cases use the trend following scheme, switching between UPRO and TMF/TMV index.
I have several observations from the figure:
• The falling LTT returns prior to 1982 systematically degrade the performance, evidenced by the dashed lines consistently above the solid lines.
• Adding the unemployment trend signal has a clear potential benefit. Both purple lines are consistently above the corresponding olive lines. This appears to be mainly due to riding out some of the recessions better and pushing the UPRO returns harder than the 40/60 assumption.
• While the devil is in the details, and all sorts of caveats apply, in this example the combination of the unemployment trend signal and matching the x3 LTT ETF to the longterm bull or bear trend increased the portfolio by an order of magnitude each decade since 1955 (before accounting for inflation, trading costs, and ER, of course).
• The correlation between S&P 500 and LTT appears to have a secondary effect on performance compared to the other factors.
Again, this is a very simpleminded example and the numbers are merely a first cut. And certainly I may be making some simple mistakes somewhere. But I would argue that the performance since 1982 has been largely due to falling interest rates, not inverse correlations as Hedgefundie is supposing.
So what to do with an environment with longterm rising interest rates? Switch from TMF to TMV, maybe.
Some strong incentive to follow up some more...
Siamond was kind enough to provide his database of monthly returns from 1955 through 2018. I started looking at this tonight to do some thought experiments on the controlling factors for the riskparity approach, including the data prior to 1987. This is a very broad brush, first look thing.
Hedgefundie is basing the approach on inverse correlation, and recognizes that the approach performed poorly prior to 1982. The effect of longterm treasury returns has been brought up as an alternative explanation.
So with this though experiment I just want to try and separate out the effects of correlation from the effects of longterm treasury returns and check if there is some hope for using the unemployment rate index under additional economic conditions.
Assumptions:
• Monthly rebalancing
• ER not included
• All calculations in nominal terms
• I consider two x3 indexes for LTT: (i) TMF for the entire time, and (ii) TMV before 1982, replaced by x3 TMF after 1982. I simply multiplied the TMF returns by 1 to simulate TMV. I recognize that this is questionable for accurate calculations, but this is just a first simpleminded cut.
• I consider a case with a simple unemployment index: 3month moving average minus 15month moving average. If the index is negative, I fully went to the x3 S&P, otherwise I fully went to the x3 LTT index.
The following figure has four plots.
The top plot shows the correlation coefficient between monthly returns for UPRO (Siamond’s x3 S&P 500) and TMF (Siamond’s x3 LTT20+). The correlation coefficient is calculated with the returns from the prior 12 months. Notice that the correlation coefficient is generally negative 1955 to 1975, generally positive from 1975 to 2002, and generally negative since 2002.
The second plot shows my simple index. Positive values are the signal for “recession” and negative values are the signal for “expansion”. Notice that there is a fair amount of bouncing around, and it’s not at all clear that the signals perfectly line up at early years. This may be a data issue or something to do with my quick interpretation.
The third plot shows the cumulative returns for UPRO alone (red), TMF alone (blue), and the mixed TMV/TMF index (cyan). Notice that TMV would have had a small positive nominal return through 1980, while TMF dropped by an order of magnitude from 1955 to 1982.
The fourth plot shows four cases. The solid lines use the UPRO/TMF combinations. The dotted lines use the UPRO/TMV/TMF combinations. The olive cases use the nominal 40/60 weights, rebalanced monthly. The purple cases use the trend following scheme, switching between UPRO and TMF/TMV index.
I have several observations from the figure:
• The falling LTT returns prior to 1982 systematically degrade the performance, evidenced by the dashed lines consistently above the solid lines.
• Adding the unemployment trend signal has a clear potential benefit. Both purple lines are consistently above the corresponding olive lines. This appears to be mainly due to riding out some of the recessions better and pushing the UPRO returns harder than the 40/60 assumption.
• While the devil is in the details, and all sorts of caveats apply, in this example the combination of the unemployment trend signal and matching the x3 LTT ETF to the longterm bull or bear trend increased the portfolio by an order of magnitude each decade since 1955 (before accounting for inflation, trading costs, and ER, of course).
• The correlation between S&P 500 and LTT appears to have a secondary effect on performance compared to the other factors.
Again, this is a very simpleminded example and the numbers are merely a first cut. And certainly I may be making some simple mistakes somewhere. But I would argue that the performance since 1982 has been largely due to falling interest rates, not inverse correlations as Hedgefundie is supposing.
So what to do with an environment with longterm rising interest rates? Switch from TMF to TMV, maybe.
Some strong incentive to follow up some more...
Re: Refinements to Hedgefundie's excellent approach
In the name of simplicity and since there seems to be no simple criteria, how would some thumb rule like, "always reenter within one year of exit" have performed?Hydromod wrote: ↑Sat Jul 06, 2019 2:52 pm
The entrance strategy is harder, if one is trying to hit the bounceback surge. It might be reasonable to reenter once there is a downturn in unemployment or a downturn in a short moving average. For example, a simple crossing criterion would not have signaled reentry until early 2010, missing the 2009 bounce back, but would have been okay in the early 90's. This riskparity strategy does so well overall that missing the peak bounce back might cause me to shake my head, but it is not a tragedy.
Again, I would probably just use the riskparity weights whenever there is ambiguity about entering or exiting. This really should be the default.
Re: Refinements to Hedgefundie's excellent approach
One more refinement. I think you mean the Cumulative distribution function. The rest is fine (I'm an engineer and use exceedance in a very different environment.)Hydromod wrote: ↑Sun Jul 07, 2019 1:12 amThis is the first time I've seen this type of chart. This is pretty cool. Maybe something we should use more often when running other types of analysis. I even wonder if it wouldn't be worth it to create a wiki page about this concept (e.g. similar to the Telltale chart wiki page we have). Or at least mention the concept with proper references in some existing wiki page?Hydromod wrote: ↑Fri Jul 05, 2019 10:59 pmWhen assessing the viability of a scheme, I commonly plot the time history and the cumulative exceedance distribution of a parameter or outcome. The cumulative exceedance distribution simply describes the fraction of outcomes that are exceeded by a given value. For example, if half of the outcomes are less than a particular value, the exceedance fraction is 0.5.
This is actually a basic concept in probability. I think I called it the wrong thing in these threads, I always forget the terminology and I rushed the plots. It's really the cumulative density function, often called the CDF, which is the probability that a particular value is less than a reference value. The cumulative exceedance function is 1  CDF.
I was waiting for someone to rush in and point accusing fingers at the terminology!
Finance has been using statistics since forever. For example, there have been many attempts to model the S&P 500 historical performance as a statistical process. The closest one gets is to assume a lognormal distribution. Those assumptions don't hold when you start selecting different periods over time, but that's the closest you can get.
1. Statistical functions have a fundamental requirement, which is to be a Stochastic process.
2. The one big stumbling block is that humans tend to see patterns where none exist.
(1) and (2) are mutually exclusive, with the result that humans tend to assign statistical functions to financial performance which usually results in a poor fit. The best that can be done is to assign a normal distribution to everything and accept that it won't work as well as one hoped.
Likewise if I got anything wrong, please correct me.
====================
Here's a fun tutorial on distributions: Stock Return Distributions, then Distributions3, from Gummystuff  finiki, the Canadian financial wiki (our sister Canadian site)
Re: Refinements to Hedgefundie's excellent approach
Ah, thank you, thinking in terms of cumulative distribution is indeed much clearer. Ok, then I confess my level of interest of such charts is dropping a bit. Making them cumulative seems to hide a lot of useful information that a regular distribution chart would show more clearly (see the first gummy_stuff pointer Ladygeek provided for a quick illustration). I mean, sure, the cumulative display shows another perspective which has its own value, but it seems a tad limited.LadyGeek wrote: ↑Sun Jul 07, 2019 7:45 amOne more refinement. I think you mean the Cumulative distribution function.
I was vaguely entertaining the idea of adding such an exceedance/CDF chart in the Simba backtesting spreadsheet, but on second thought, I think it's good enough to have the rolling distribution chart that is already in there. Still, thanks for educating me, we learn something every day on this forum!
Re: Refinements to Hedgefundie's excellent approach
The CDF is really useful for checking systematic effects of different assumptions, especially when the effects are fairly subtle in something with a lot of noise. For example, the effects of rebalancing frequency on rolling cagr show up as a systematic shift and/or systematic change in spread. But yeah, it isn't always the best tool for everything.siamond wrote: ↑Sun Jul 07, 2019 9:28 amAh, thank you, thinking in terms of cumulative distribution is indeed much clearer. Ok, then I confess my level of interest of such charts is dropping a bit. Making them cumulative seems to hide a lot of useful information that a regular distribution chart would show more clearly (see the first gummy_stuff pointer Ladygeek provided for a quick illustration). I mean, sure, the cumulative display shows another perspective which has its own value, but it seems a tad limited.LadyGeek wrote: ↑Sun Jul 07, 2019 7:45 amOne more refinement. I think you mean the Cumulative distribution function.
There, I told you I screw terminology up at the drop of a hat! (Especially after midnight...)
I was vaguely entertaining the idea of adding such an exceedance/CDF chart in the Simba backtesting spreadsheet, but on second thought, I think it's good enough to have the rolling distribution chart that is already in there. Still, thanks for educating me, we learn something every day on this forum!
Re: Refinements to Hedgefundie's excellent approach
Yes, I think this part is quite clear. And I would definitely NOT rely on correlation patterns over the past few decades as something indicative of the future... Those things just go by big ebbs & flows...
Yeah, well, predicting the future trajectory of interest rates is an interesting challenge where very bright economists miserably failed year after year, including in the recent years where it seemed 'pretty obvious' where interest rates were going... I am not very keen on the 'nobody knows nothing' mantra of some posters on this forum, but future interest rates do seem to fall in this category (from what we can tell of past trajectories).
Re: Refinements to Hedgefundie's excellent approach
The previous example got me thinking some more, to see if I could avoid the use of the unemployment index.
I started fussing with some of the models in portfolio visualizer a bit more and found that I could largely avoid the 20002010 doldrums using the dual momentum model, given just UPROSIM and TMFSIM. The key with this model seems to be using two performance periods, one annual and one monthly, to trigger changes. The blue line is the timing portfolio and the red line is the 40/60 constant weighting. Both use monthly rebalancing.
I set this to only consider UPRO and TMF, require 2 assets, and swap out to TMF. The resulting weights are either 50/50 UPRO/TMF or 100 percent TMF.
A moving average model that only considers 100 percent UPRO or 100 percent TMF does even better.
So I decided to play a bit more. Using Siamond’s monthly database, I created the monthly equivalent of TMV (x3 inverse LTT) as well as UPRO and TMF (x3 LTT) back to 1955. Then I created the equivalent monthly returns with monthly rebalancing for various combinations of UPRO and TMF, and UPRO and TMV. After fussing a bit, I ended up presenting the dual momentum model with options of UPRO, TMF, TMV, 30/70 UPRO/TMF, 45/55 UPRO/TMF, 60/40 UPRO/TMF, 30/70 UPRO/TMV, 45/55 UPRO/TMV, and 60/40 UPRO/TMV.
The model is required to hold 3 of these assets, which can be postprocessed into weights for the three components (I haven’t done that yet). The model selects 3 assets, each weighted 1/3. The model can select the same asset 1, 2, or 3 times, in which case it gets weighted 1/3, 2/3 or 1. The model swaps to 100 percent TMF if it isn’t satisfied with any of the options. I found that performance seemed to drop if it is required to hold more than 3 allowable assets or less than 3 allowable assets. I also found that performance seemed to drop if I gave it more options to select from.
I weighted the momentum timings as 70 percent annual and 30 percent monthly.
The model does quite well from 1956 to present, as shown in the figure. Allowing both TMF and TMV to be selected allows relatively steady growth throughout the entire period, with a CAGR of 19 percent (blue line). The model does a bit better than the constant 40/60 model even from 1982 to present.
The link is posted below. I don't know if it will break for others, given the private set of assets.
https://www.portfoliovisualizer.com/te ... &total1=0
I tried the relative strength model with the same set of assets and generally the same settings. It seemed to do best when selecting 4 assets. The overall performance was poorer from 1955 to 1982, but considerably better since 1982 (albeit with larger drawdowns). I think this pushes UPRO harder. Again the blue line is the timing model and the red line is the constant 40/60 model.
More food for thought. This example shows why some people are happy with certain types of market timing models. In these data, there was enough persistence from month to month to make informed estimates about future conditions for the next month. This persistence was actionable enough that very good results were obtained in this example without consulting macroeconomic models.
These results suggests that it may be useful to consider three leveraged funds to hedge against different interest rate environments, although I don’t know exactly how to interpret cases that suggest weights for both TMF and TMV. There would have been no way to try this strategy before inverse leveraged funds became available.
That's enough for tonight.
I started fussing with some of the models in portfolio visualizer a bit more and found that I could largely avoid the 20002010 doldrums using the dual momentum model, given just UPROSIM and TMFSIM. The key with this model seems to be using two performance periods, one annual and one monthly, to trigger changes. The blue line is the timing portfolio and the red line is the 40/60 constant weighting. Both use monthly rebalancing.
I set this to only consider UPRO and TMF, require 2 assets, and swap out to TMF. The resulting weights are either 50/50 UPRO/TMF or 100 percent TMF.
A moving average model that only considers 100 percent UPRO or 100 percent TMF does even better.
So I decided to play a bit more. Using Siamond’s monthly database, I created the monthly equivalent of TMV (x3 inverse LTT) as well as UPRO and TMF (x3 LTT) back to 1955. Then I created the equivalent monthly returns with monthly rebalancing for various combinations of UPRO and TMF, and UPRO and TMV. After fussing a bit, I ended up presenting the dual momentum model with options of UPRO, TMF, TMV, 30/70 UPRO/TMF, 45/55 UPRO/TMF, 60/40 UPRO/TMF, 30/70 UPRO/TMV, 45/55 UPRO/TMV, and 60/40 UPRO/TMV.
The model is required to hold 3 of these assets, which can be postprocessed into weights for the three components (I haven’t done that yet). The model selects 3 assets, each weighted 1/3. The model can select the same asset 1, 2, or 3 times, in which case it gets weighted 1/3, 2/3 or 1. The model swaps to 100 percent TMF if it isn’t satisfied with any of the options. I found that performance seemed to drop if it is required to hold more than 3 allowable assets or less than 3 allowable assets. I also found that performance seemed to drop if I gave it more options to select from.
I weighted the momentum timings as 70 percent annual and 30 percent monthly.
The model does quite well from 1956 to present, as shown in the figure. Allowing both TMF and TMV to be selected allows relatively steady growth throughout the entire period, with a CAGR of 19 percent (blue line). The model does a bit better than the constant 40/60 model even from 1982 to present.
The link is posted below. I don't know if it will break for others, given the private set of assets.
https://www.portfoliovisualizer.com/te ... &total1=0
I tried the relative strength model with the same set of assets and generally the same settings. It seemed to do best when selecting 4 assets. The overall performance was poorer from 1955 to 1982, but considerably better since 1982 (albeit with larger drawdowns). I think this pushes UPRO harder. Again the blue line is the timing model and the red line is the constant 40/60 model.
More food for thought. This example shows why some people are happy with certain types of market timing models. In these data, there was enough persistence from month to month to make informed estimates about future conditions for the next month. This persistence was actionable enough that very good results were obtained in this example without consulting macroeconomic models.
These results suggests that it may be useful to consider three leveraged funds to hedge against different interest rate environments, although I don’t know exactly how to interpret cases that suggest weights for both TMF and TMV. There would have been no way to try this strategy before inverse leveraged funds became available.
That's enough for tonight.

 Posts: 10022
 Joined: Wed Feb 01, 2017 8:39 pm
Re: Refinements to Hedgefundie's excellent approach
Would you mind going a bit deeper into how these were constructed? Simply 3x the monthly return is not an accurate representation; you also need to factor in borrowing costs. A quick test would be to compare them with the actual funds since inception.
Re: Refinements to Hedgefundie's excellent approach
You need to ask Siamond for the details of the approach. The math is described in the thread on creating simulated leveraged ETFs. But Siamond implemented it in a slick way, all you need to change is the leverage level in one place and this gets propagated throughout, including accounting for borrowing costs. He used this clever approach for each ETF, and checked against a 2x inverse ETF with good results. I just changed the number and copied the results.MotoTrojan wrote: ↑Mon Jul 08, 2019 11:24 pmWould you mind going a bit deeper into how these were constructed? Simply 3x the monthly return is not an accurate representation; you also need to factor in borrowing costs. A quick test would be to compare them with the actual funds since inception.
I'm taking this development of leveraged ETFs on faith a bit. I'm mostly concerned that comparisons between models use the exact same assumptions for the input data so we are comparing macintosh apples to macintosh apples, even if the past was golden delicious.
Re: Refinements to Hedgefundie's excellent approach
Yes, this is just using the very exact same formulas we've been using for 'bull' leveraged funds. See here for a reminder. I ran a test against the S&P 2x inverse index and against an actual 'bear' fund of the same nature, and this worked well (I hinted at it here, but I didn't provide a lot of details at the time  I could easily reconstruct such test if needs be).Hydromod wrote: ↑Mon Jul 08, 2019 11:41 pmYou need to ask Siamond for the details of the approach. The math is described in the thread on creating simulated leveraged ETFs. But Siamond implemented it in a slick way, all you need to change is the leverage level in one place and this gets propagated throughout, including accounting for borrowing costs. He used this clever approach for each ETF, and checked against a 2x inverse ETF with good results. I just changed the number and copied the results.MotoTrojan wrote: ↑Mon Jul 08, 2019 11:24 pmWould you mind going a bit deeper into how these were constructed? Simply 3x the monthly return is not an accurate representation; you also need to factor in borrowing costs. A quick test would be to compare them with the actual funds since inception.
For full disclosure, the numbers used by Hydromod in his 'dual momentum' test were fully based on the 'magic formula' (the one derived from intramonth volatility). I could run the daily actuals for the past couple of decades, but we know that the 'magic formula' works extremely well, so no point making our life complicated. I provided an easy way to do so by simply tweaking a couple of cells in the monthly simulation model. Send me a PM for more details if interested.