Flirting with Models

The Research Library of Newfound Research

Month: April 2019

Style Surfing the Business Cycle

By

On April 29, 2019

In Risk & Style Premia, Weekly Commentary

This post is available as a PDF download here.

Summary­

  • In this commentary, we ask whether we should consider rotating factor exposure based upon the business cycle.
  • To eliminate a source of model risk, we assume perfect knowledge of future recessions, allowing us to focus only on whether prevailing wisdom about which factors work during certain economic phases actually adds value.
  • Using two models of factor rotation and two definitions of business cycles, we construct four timing portfolios and ultimately find that rotating factor exposures does not add meaningful value above a diversified benchmark.
  • We find that the cycle-driven factor rotation recommendations are extremely close to data-mined optimal results. The similarity of the recommendations coupled with the lackluster performance of conventional style timing recommendations may highlight how fragile the rotation process inherently is.

Just as soon as the market began to meaningfully adopt factor investing, someone had to go and ask, “yeah, but can they be timed?”  After all, while the potential opportunity to harvest excess returns is great, who wants to live through a decade of relative drawdowns like we’re seeing with the value factor?

And thus the great valuation-spread factor timing debates of 2017 were born and from the ensuing chaos emerged new, dynamic factor rotation products.

There is no shortage of ways to test factor rotation: valuation-spreads, momentum, and mean-reversion to name a few.  We have even found mild success using momentum and mean reversion, though we ultimately question whether the post-cost headache is worth the potential benefit above a well-diversified portfolio.

Another potential idea is to time factor exposure based upon the state of the economic or business cycle.

It is easy to construct a narrative for this approach.  For example, it sounds logical that you might want to hold higher quality, defensive stocks during a recession to take advantage of the market’s flight-to-safety.  On the other hand, it may make sense to overweight value during a recovery to exploit larger mispricings that might have occurred during the contraction period.

An easy counter-example, however, is the performance of value during the last two recessions.  During the dot-com fall-out, cheap out-performed expensive by a wide margin. This fit a wonderful narrative of value as a defensive style of investing, as we are buying assets at a discount to intrinsic value and therefore establishing a margin of safety.

Of course, we need only look towards 2008 to see a very different scenario.  From peak to trough, AQR’s HML Devil factor had a drawdown of nearly 40% during that crisis.

Two recessions with two very different outcomes for a single factor.  But perhaps there is still hope for this approach if we diversify across enough factors and apply it over the long run.

The problem we face with business cycle style timing is really two-fold.  First, we have to be able to identify the factors that will do well in a given market environment.  Equally important, however, is our ability to predict the future economic environment.

Philosophically, there are limitations in our ability to accurately identify both simultaneously.  After all, if we could predict both perfectly, we could construct an arbitrage.

If we believe the markets are at all efficient, then being able to identify the factors that will out-perform in a given state of the business cycle should lead us to conclude that we cannot predict the future state of the business cycle. Similarly, if we believe we can predict the future state of the business cycle, we should not be able to predict which factors will necessarily do well.

Philosophical arguments aside, we wanted to test the efficacy of this approach. 

Which Factors and When?

Rather than simply perform a data-mining exercise to determine which factors have done well in each economic environment, we wanted to test prevalent beliefs about factor performance and economic cycles.  To do this, we identified marketing and research materials from two investment institutions that tie factor allocation recommendations to the business cycle.

Both models expressed a view using four stages of the economic environment: a slowdown, a contraction, a recovery, and an economic expansion.

Model #1

  • Slowdown: Momentum, Quality, Low Volatility
  • Contraction: Value, Quality, Low Volatility
  • Recovery: Value, Size
  • Expansion: Value, Size, Momentum

Model #2

  • Slowdown: Quality, Low Volatility
  • Contraction: Momentum, Quality, Low Volatility
  • Recovery: Value, Size
  • Expansion: Value, Size, Momentum

Defining the Business Cycle

Given these models, our next step was to build a model to identify the current economic environment.  Rather than build a model, however, we decided to dust off our crystal ball. After all, if business-cycle-based factor rotation does not work with perfect foresight of the economic environment, what hope do we have for when we have to predict the environment?

We elected to use the National Bureau of Economic Research’s (“NBER”) listed history of US business cycle expansions and contractions.  With the benefit of hindsight, they label recessions as the peak of the business cycle prior to the subsequent trough.

Unfortunately, NBER only provides a simple indicator as to whether a given month is in a recession or not.  We were left to fill in the blanks around what constitutes a slowdown, a contraction, a recovery, and an expansionary period.  Here we settled on two definitions:

Definition #1

  • Slowdown: The first half of an identified recession
  • Contraction: The second half of an identified recession
  • Recovery: The first third of a non-recessionary period
  • Expansion: The remaining part of a non-recessionary period

Definition #2

  • Slowdown: The 12-months leading up to a recession
  • Contraction: The identified recessionary periods
  • Recovery: The 12-months after an identified recession
  • Expansion: The remaining non-recessionary period

For definition #2, in the case where two recessions were 12 or fewer months apart (as was the case in the 1980s), the intermediate period was split equivalently into recovery and slowdown.  

Implementing Factor Rotation

After establishing the rotation rules and using our crystal ball to identify the different periods of the business cycle, our next step was to build the factor rotation portfolios.

We first sourced monthly long/short equity factor returns for size, value, momentum, and quality from AQR’s data library.  To construct a low-volatility factor, we used portfolios sorted on variance from the Kenneth French library and subtracted bottom-quintile returns from top-quintile returns.

As the goal of our study is to identify the benefit of factor timing, we de-meaned the monthly returns by the average of all factor returns in that month to identify relative performance.

We constructed four portfolios using the two factor rotation definitions and the two economic cycle definitions.  Generically, at the end of each month, we would use the next month’s economic cycle label to identify which factors to hold in our portfolio.  Identified factors were held in equal weight.

Below we plot the four equity curves.  Remember that these series are generated using de-meaned return data, so reflect the out-performance against an equal-weight factor benchmark.

 Source: NBER, AQR, and Kenneth French Data Library. Calculations by Newfound Research. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions.  Returns are gross of all fees.  None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary.  You cannot invest in an index.

It would appear that even with a crystal ball, conventional wisdom about style rotation and business cycles may not hold.  And even where it might, we can see multi-decade periods where it adds little-to-no value.

Data-Mining Our Way to Success

If we are going to use a crystal ball, we might as well just blatantly data-mine our way to success and see what we learn along the way.

To achieve this goal, we can simply look at the annualized de-meaned returns of each factor during each period of the business cycle.

Source: NBER, AQR, and Kenneth French Data Library.  Calculations by Newfound Research.  Returns are backtested and hypothetical.  Returns assume the reinvestment of all distributions.  Returns are gross of all fees.  None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary.  You cannot invest in an index.

Despite two different definitions of the business cycle, we can see a strong alignment in which factors work when.  Slow-downs / pre-recessionary periods are tilted towards momentum and defensive factors like quality and low-volatility.  Momentum may seem like a curious factor, but its high turnover may give it a chameleon-like nature that can tilt it defensively in certain scenarios.

In a recession, momentum is replaced with value while quality and low-volatility remain. In the initial recovery, small-caps, value, and momentum are favored.  In this case, while value may actually be benefiting from multiple expansion, small-caps may simply be a way to play higher beta.  Finally, momentum is strongly favored during an expansion.

Yet even a data-mined solution is not without its flaws.  Below we plot rolling 3-year returns for our data-mined timing strategies.  Again, remember that these series are generated using de-meaned return data, so reflect the out-performance against an equal-weight factor benchmark.

Source: NBER, AQR, and Kenneth French Data Library.  Calculations by Newfound Research.  Returns are backtested and hypothetical.  Returns assume the reinvestment of all distributions.  Returns are gross of all fees.  None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary.  You cannot invest in an index.

Despite a crystal ball telling us what part of the business cycle we are in and completely data-mined results, there are still a number of 3-year periods with low-to-negative results.  And we have not even considered manager costs, transaction costs, or taxes yet.

A few more important things to note.

Several of these factors exhibit strong negative performance during certain parts of the market cycle, indicating a potential for out-performance by taking the opposite side of the factor.  For example, value appears to do poorly during pre-recession and expansion periods.  One hypothesis is that during expansionary periods, markets tend to over-extrapolate earnings growth potential, favoring growth companies that appear more expensive.

We should also remember that our test is on long/short portfolios and may not necessarily be relevant for long-only investors.  While we can think of a long-only portfolio as a market-cap portfolio plus a long/short portfolio, the implicit long/short is not necessarily identical to academic factor definitions.

Finally, it is worth considering that these results are data-mined over a 50+ year period, which may allow outlier events to dramatically skew the results.  Momentum, for example, famously exhibited dramatic crashes during the Great Depression and in the 2008-crisis, but may have actually relatively out-performed in other recessions.

Conclusion

In this commentary we sought to answer the question, “can we use the business cycle to time factor exposures?”  Assuming access to a crystal ball that could tell us where we stood precisely in the business cycle, we found that conventional wisdom about factor timing did not add meaningful value over time.  We do not hold out much hope, based on this conventional wisdom, that someone without a crystal ball would fare much better.

Despite explicitly trying to select models that reflected conventional wisdom, we found a significant degree of similarity in these recommendations with those that came from blindly data-mining optimal results.  Nevertheless, even slight recommendation differences lead to lackluster results.

The similarities between data-mined results and conventional wisdom, however, should give us pause.  While the argument for conventional wisdom is often a well-articulated economic rationale, we have to wonder whether we have simply fooled ourselves with a narrative that has been inherently constructed with the benefit of hindsight.

The Path-Dependent Nature of Perfect Withdrawal Rates

By

On April 22, 2019

In Risk Management, Sequence Risk, Weekly Commentary

This post is available as a PDF download here.

Summary

  • The Perfect Withdrawal Rate (PWR) is the rate of regular portfolio withdrawals that leads to a zero balance over a given time frame.
  • 4% is the commonly accepted lower bound for safe withdrawal rates, but this is only based on one realization of history and the actual risk investors take on by using this number may be uncertain.
  • Using simulation techniques, we aim to explore how different assumptions match the historical experience of retirement portfolios.
  • We find that simple assumptions commonly used in financial planning Monte Carlo simulations do not seem to reflect as much variation as we have seen in the historical PWR.
  • Including more stress testing and utilizing richer simulation methods may be necessary to successfully gauge that risk in a proposed PWR, especially as it pertains to the risk of failure in the financial plan.

Financial planning for retirement is a combination of art and science. The problem is highly multidimensional, requiring estimates of cash flows, investment returns and risk, taxation, life events, and behavioral effects. Reduction along the dimensions can simplify the analysis, but introduces consequences in the applicability and interpretation of the results. This is especially true for investors who are close to the line between success and failure.

One of the primary simplifying assumptions is the 4% rule. This heuristic was derived using worst-case historical data for portfolio withdrawals under a set of assumptions, such as constant inflation adjusted withdrawals, a fixed mix of stock and bonds, and a set time horizon.

Below we construct a monthly-rebalanced, fixed-mix 60/40 portfolio using the S&P 500 index for U.S. equities and the Dow Jones Corporate Bond index for U.S. bonds. Using historical data from 12/31/1940 through 12/31/2018, we can evaluate the margin for error the 4% rule has historically provided and how much opportunity for higher withdrawal rates was sacrificed in “better” market environments.

Source: Global Financial Data and Shiller Data Library. Calculations by Newfound Research. Returns are backtested and hypothetical. Past performance is not a guarantee of future results. Returns are gross of all fees. Returns assume the reinvestment of all distributions. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

But the history is only a single realization of the world. Risk is hard to gauge.

Perfect Withdrawal Rates

The formula (in plain English) for the perfect withdrawal rate (“PWR”) in a portfolio, assuming an ending value of zero, is relatively simple since it is just a function of portfolio returns:

The portfolio value in the numerator is the final value of the portfolio over the entire period, assuming no withdrawals. The sequence risk in the denominator is a term that accounts for both the order and magnitude of the returns.

Larger negative returns earlier on in the period increase the sequence risk term and therefore reduce the PWR.

From a calculation perspective, the final portfolio value in the equation is typically described (e.g. when using Monte Carlo techniques) as a log-normal random variable, i.e. the log-returns of the portfolio are assumed to be normally distributed. This type of random variable lends itself well to analytic solutions that do not require numerical simulations.

The sequence risk term, however, is not so friendly to closed-form methods. The path-dependent, additive structure of returns within the sequence risk term means that we must rely on numerical simulations.

To get a feel for some features of this equation, we can look at the PWR in the context of the historical portfolio return and volatility.

Source: Global Financial Data and Shiller Data Library. Calculations by Newfound Research. Returns are backtested and hypothetical. Past performance is not a guarantee of future results. Returns are gross of all fees. Returns assume the reinvestment of all distributions. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

The relationship is difficult to pin down.

As we saw in the equation shown before, the –annualized return of the portfolio– does appear to impact the ­–PWR– (correlation of 0.51), but there are periods (e.g. those starting in the 1940s) that had higher PWRs with lower returns than in the 1960s. Therefore, investors beginning withdrawals in the 1960s must have had higher sequence risk.

Correlation between –annualized volatility– and –PWR– was slightly negative (-0.35).

The Risk in Withdrawal Rates

Since our goal is to assess the risk in the historical PWR with a focus on the sequence risk, we will use the technique of Brownian Bridges to match the return of all simulation paths to the historical return of the 60/40 portfolio over rolling 30-year periods. We will use the historical full-period volatility of the portfolio over the period for the simulation.

This is essentially a conditional PWR risk based on assuming we know the full-period return of the path beforehand.

To more explicitly describe the process, consider a given 30-year period. We begin by computing the full-period annualized return and volatility of the 60/40 portfolio over that period.  We will then generate 10,000 simulations over this 30-year period but using the Brownian Bridge technique to ensure that all of the simulations have the exact same full-period annualized return and intrinsic volatility.  In essence, this approach allows us to vary the path of portfolio returns without altering the final return.  As PWR is a path-dependent metric, we should gain insight into the distribution of PWRs.

The percentile bands for the simulations using this method are shown below with the actual PWR in each period overlaid.

Source: Global Financial Data and Shiller Data Library. Calculations by Newfound Research. Returns are backtested and hypothetical. Past performance is not a guarantee of future results. Returns are gross of all fees. Returns assume the reinvestment of all distributions. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

From this chart, we see two items of note: The percentile bands in the distribution roughly track the historical return over each of the periods, and the actual PWR fluctuates into the left and right tails of the distribution rather frequently.  Below we plot where the actual PWR actually falls within the simulated PWR distribution.

Source: Global Financial Data and Shiller Data Library. Calculations by Newfound Research. Returns are backtested and hypothetical. Past performance is not a guarantee of future results. Returns are gross of all fees. Returns assume the reinvestment of all distributions. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

The actual PWR is below the 5th percentile 12% of the time, below the 1st percentile 4% of the time, above the 95th percentile 11% of the time, and above the 99th percentile 7% of the time.  Had our model been more well calibrated, we would expect the percentiles to align; e.g. the PWR should be below the 5th percentile 5% of the time and above the 99th percentile 1% of the time.

This seems odd until we realize that our model for the portfolio returns was likely too simplistic. We are assuming Geometric Brownian Motion for the returns. And while we are fixing the return over the entire simulation path to match that of the actual portfolio, the path to get there is assumed to have constant volatility and independent returns from one month to the next.

In reality, returns do not always follow these rules. For example, the skew of the monthly returns over the entire history is -0.36 and the excess kurtosis is 1.30. This tendency toward larger magnitude returns and returns that are skewed to the left can obscure some of the risk that is inherent in the PWRs.

Additionally, returns are not totally independent. While this is good for trend following strategies, it can lead to an understatement of risk as we explored in our previous commentary on Accounting for Autocorrelation in Assessing Drawdown Risk.

Over the full period, monthly returns of lags 1, 4, and 5 exhibit autocorrelation that is significant at the 95% confidence level.

Source: Global Financial Data and Shiller Data Library. Calculations by Newfound Research. Returns are backtested and hypothetical. Past performance is not a guarantee of future results. Returns are gross of all fees. Returns assume the reinvestment of all distributions. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

To incorporate some of these effects in our simulations, we must move beyond the simplistic assumption of normally distributed returns.

First, we will fit a skewed normal distribution to the rolling historical data and use that to draw our random variables for each period. This is essentially what was done in the previous section for the normally distributed returns.

Then, to account for some autocorrelation, we will use the same adjustment to volatility as we used in the previously reference commentary on autocorrelation risk. For positive autocorrelations (which we saw in the previous graphs), this results in a higher volatility for the simulations (typically around 10% – 25% higher).

The two graphs below show the same analysis as before under this modified framework.

Source: Global Financial Data and Shiller Data Library. Calculations by Newfound Research. Returns are backtested and hypothetical. Past performance is not a guarantee of future results. Returns are gross of all fees. Returns assume the reinvestment of all distributions. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

The historical PWR now fall more within the bounds of our simulated results.

Additionally, the 5th percentile band now shows that there were periods where a 4% withdrawal rule may not have made the cut.

Source: Global Financial Data and Shiller Data Library. Calculations by Newfound Research. Returns are backtested and hypothetical. Past performance is not a guarantee of future results. Returns are gross of all fees. Returns assume the reinvestment of all distributions. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

Conclusion

Heuristics can be a great way to distill complex data into actionable insights, and the perfect withdrawal rate in retirement portfolios is no exception.

The 4% rule is a classic example where we may not be aware of the risk in using it. It is the commonly accepted lower bound for safe withdrawal rates, but this is only based on one realization of history.

The actual risk investors take on by using this number may be uncertain.

Using simulation techniques, we explored how different assumptions match the historical experience of retirement portfolios.

The simple assumptions (expected return and volatility) commonly used in financial planning Monte Carlo simulations do not seem to reflect as much variation as we have seen in the historical PWR. Therefore, relying on these assumptions can be risky for investors who are close to the “go-no-go” point; they do not have much room for failure and will be more likely to have to make cash flow adjustments in retirement.

Utilizing richer simulation methods (e.g. accounting for negative skew and autocorrelation like we did here or using a downside shocking method like we explored in A Shock to the Covariance System) may be necessary to successfully gauge that risk in a proposed PWR, especially as it pertains to the risk of failure in the financial plan.

Having a number to base planning calculations on makes life easier in the moment, but knowing the risk in using that number makes life easier going forward.

The Speed Limit of Trend

By

On April 15, 2019

In Trend, Weekly Commentary

This post is available as a PDF download here.

Summary­

  • Trend following is “mechanically convex,” meaning that the convexity profile it generates is driven by the rules that govern the strategy.
  • While the convexity can be measured analytically, the unknown nature of future price dynamics makes it difficult to say anything specific about expected behavior.
  • Using simulation techniques, we aim to explore how different trend speed models behave for different drawdown sizes, durations, and volatility levels.
  • We find that shallow drawdowns are difficult for almost all models to exploit, that faster drawdowns generally require faster models, and that lower levels of price volatility tend to make all models more effective.
  • Finally, we perform historical scenario analysis on U.S. equities to determine if our derived expectations align with historical performance.

We like to use the phrase “mechanically convex” when it comes to trend following.  It implies a transparent and deterministic “if-this-then-that” relationship between the price dynamics of an asset, the rules of a trend following, and the performance achieved by a strategy.

Of course, nobody knows how an asset’s future price dynamics will play out.  Nevertheless, the deterministic nature of the rules with trend following should, at least, allow us to set semi-reasonable expectations about the outcomes we are trying to achieve.

A January 2018 paper from OneRiver Asset Management titled The Interplay Between Trend Following and Volatility in an Evolving “Crisis Alpha” Industry touches precisely upon this mechanical nature.  Rather than trying to draw conclusions analytically, the paper employs numerical simulation to explore how certain trend speeds react to different drawdown profiles.

Specifically, the authors simulate 5-years of daily equity returns by assuming a geometric Brownian motion with 13% drift and 13% volatility.  They then simulate drawdowns of different magnitudes occurring over different time horizons by assuming a Brownian bridge process with 35% volatility.

The authors then construct trend following strategies of varying speeds to be run on these simulations and calculate the median performance.

Below we re-create this test.  Specifically,

  • We generate 10,000 5-year simulations assuming a geometric Brownian motion with 13% drift and 13% volatility.
  • To the end of each simulation, we attach a 20% drawdown simulation, occurring over T days, assuming a geometric Brownian bridge with 35% volatility.
  • We then calculate the performance of different NxM moving-average-cross-over strategies, assuming all trades are executed at the next day’s closing price. When the short moving average (N periods) is above the long moving average (M periods), the strategy is long, and when the short moving average is below the long moving average, the strategy is short.
  • For a given T-day drawdown period and NxM trend strategy, we report the median performance across the 10,000 simulations over the drawdown period.

By varying T and the NxM models, we can attempt to get a sense as to how different trend speeds should behave in different drawdown profiles.

Note that the generated tables report on the median performance of the trend following strategy over only the drawdown period.  The initial five years of positive expected returns are essentially treated as a burn-in period for the trend signal.  Thus, if we are looking at a drawdown of 20% and an entry in the table reads -20%, it implies that the trend model was exposed to the full drawdown without regard to what happened in the years prior to the drawdown.  The return of the trend following strategies over the drawdown period can be larger than the drawdown because of whipsaw and the fact that the underlying equity can be down more than 20% at points during the period.

Furthermore, these results are for long/short implementations.  Recall that a long/flat strategy can be thought of as 50% explore to equity plus 50% exposure to a long/short strategy.  Thus, the results of long/flat implementations can be approximated by halving the reported result and adding half the drawdown profile.  For example, in the table below, the 20×60 trend system on the 6-month drawdown horizon is reported to have a drawdown of -4.3%.  This would imply that a long/flat implementation of this strategy would have a drawdown of approximately -12.2%.

Calculations by Newfound Research.  Results are hypothetical.  Returns are gross of all fees, including manager fees, transaction costs, and taxes.

There are several potential conclusions we can draw from this table:

  1. None of the trend models are able to avoid an immediate 1-day loss.
  2. Very-fast (10×30 to 10×50) and fast (20×60 and 20×100) trend models are able to limit losses for week-long drawdowns, and several are even able to profit during month-long drawdowns but begin to degrade for drawdowns that take over a year.
  3. Intermediate (50×150 to 50×250) and slow (75×225 to 75×375) trend models appear to do best for drawdowns in the 3-month to 1-year range.
  4. Very slow (100×300 to 200×400) trend models do very little at all for drawdowns over any timeframe.

Note that these results align with results found in earlier research commentaries about the relationship between measured convexity and trend speed.  Namely, faster trends appear to exhibit convexity when measured over shorter horizons, whereas slower trend speeds require longer measurement horizons.

But what happens if we change the drawdown profile from 20%?

Varying Drawdown Size

Calculations by Newfound Research.  Results are hypothetical.  Returns are gross of all fees, including manager fees, transaction costs, and taxes.

We can see some interesting patterns emerge.

First, for more shallow drawdowns, slower trend models struggle over almost all drawdown horizons.  On the one hand, a 10% drawdown occurring over a month will be too fast to capture.  On the other hand, a 10% drawdown occurring over several years will be swamped by the 35% volatility profile we simulated; there is too much noise and too little signal.

We can see that as the drawdowns become larger and the duration of the drawdown is extended, slower models begin to perform much better and faster models begin to degrade in relative performance.

Thus, if our goal is to protect against large losses over sustained periods (e.g. 20%+ over 6+ months), intermediate-to-slow trend models may be better suited our needs.

However, if we want to try to avoid more rapid, but shallow drawdowns (e.g. Q4 2018), faster trend models will likely have to be employed.

Varying Volatility

In our test, we specified that the drawdown periods would be simulated with an intrinsic volatility of 35%.  As we have explored briefly in the past, we expect that the optimal trend speed would be a function of both the dynamics of the trend process and the dynamics of the price process.  In simplified models (i.e. constant trend), we might assume the model speed is proportional to the trend speed relative to the price volatility.  For a more complex model, others have proposed that model speed should be proportional to the volatility of the trend process relative to the volatility of the price process.

Therefore, we also want to ask the question, “what happens if the volatility profile changes?”  Below, we re-create tables for a 20% and 40% drawdown, but now assume a 20% volatility level, about half of what was previously used.

Calculations by Newfound Research.  Results are hypothetical.  Returns are gross of all fees, including manager fees, transaction costs, and taxes.

We can see that results are improved almost without exception.1

Not only do faster models now perform better over longer drawdown horizons, but intermediate and slow models are now much more effective at horizons where they had previously not been.  For example, the classic 50×200 model saw an increase in its median return from -23.1% to -5.3% for 20% drawdowns occurring over 1.5 years.

It is worth acknowledging, however, that even with a reduced volatility profile, a shallower drawdown over a long horizon is still difficult for trend models to exploit.  We can see this in the last three rows of the 20% drawdown / 20% volatility table where none of the trend models exhibit a positive median return, despite having the ability to profit from shorting during a negative trend.

Conclusion

The transparent, “if-this-then-that” nature of trend following makes it well suited for scenario analysis.  However, the uncertainty of how price dynamics may evolve can make it difficult to say anything about the future with a high degree of precision.

In this commentary, we sought to evaluate the relationship between trend speed, drawdown size, drawdown speed, and asset volatility and a trend following systems ability to perform in drawdown scenarios.  We generally find that:

  • The effectiveness of trend speed appears to be positively correlated with drawdown speed. Intuitively, faster drawdowns require faster trend models.
  • Trend models struggle to capture shallow drawdowns (e.g. 10%). Faster trend models appear to be effective in capturing relatively shallow drawdowns (~20%), so long as they happen with sufficient speed (<6 months).  Slower models appear relatively ineffective against this class of drawdowns over all horizons, unless they occur with very little volatility.
  • Intermediate-to-slow trend models are most effective for larger, more prolonged drawdowns (e.g. 30%+ over 6+ months).
  • Lower intrinsic asset volatility appears to make trend models effective over longer drawdown horizons.

From peak-to-trough, the dot-com bubble imploded over about 2.5 years, with a drawdown of about -50% and a volatility of 24%.  The market meltdown in 2008, on the other hand, unraveled in 1.4 years, but had a -55% drawdown with 37% volatility.  Knowing this, we might expect a slower model to have performed better in early 2000, while an intermediate model might have performed best in 2008.

If only reality were that simple!

While our tests may have told us something about the expected performance, we only live through one realization.  The precise and idiosyncratic nature of how each drawdown unfolds will ultimately determine which trend models are successful and which are not.  Nevertheless, evaluating the historical periods of large U.S. equity drawdowns, we do see some common patterns emerge.

Calculations by Newfound Research.  Results are hypothetical.  Returns are gross of all fees, including manager fees, transaction costs, and taxes.

The sudden drawdown of 1987, for example, remains elusive for most of the models.  The dot-com and Great Recession were periods where intermediate-to-slow models did best.  But we can also see that trend is not a panacea: the 1946-1949 drawdown was very difficult for most trend models to navigate successfully.

Our conclusion is two-fold.  First, we should ensure that the trend model we select is in-line with the sorts of drawdown profiles we are looking to create convexity against.  Second, given the unknown nature of how drawdowns might evolve, it may be prudent to employ a variety of trend following models.

 

Taxes and Trend Equity

By

On April 1, 2019

In Popular, Weekly Commentary

This post is available as a PDF download here.

Summary

  • Due to their highly active nature, trend following strategies are generally assumed to be tax inefficient.
  • Through the lens of a simple trend equity strategy, we explore this assertion to see what the actual profile of capital gains has looked like historically.
  • While a strategic allocation may only realize small capital gains at each rebalance, a trend equity strategy has a combination of large long-term capital gains interspersed with years that have either no gains or short-term capital losses.
  • Adding a little craftsmanship to the trend equity strategy can potentially improve the tax profile to make it less lumpy, thereby balancing the risk of having large unrealized gains with the risk of getting a large unwanted tax bill.
  • We believe that investors who expect to have higher tax rates in the future may benefit from strategies like trend equity that systematically lock in their gains more evenly through time.

Tax season for the year is quickly coming to a close, and while taxes are not a topic we cover frequently in these commentaries, it has a large impact on investor portfolios.

Source: xkcd

One of the primary reasons we do not cover it more is that it is investor-specific. Actionable insights are difficult to translate across investors without making broad assumptions about state and federal tax rates, security location (tax-exempt, tax deferred, or taxable), purchase time and holding period, losses or gains in other assets, health and family situation, etc.

Some sweeping generalizations can be made, such as that it is better to realize long-term capital gains than short-term ones, that having qualified dividends is better than having non-qualified ones, and that it is better to hold bonds in tax-deferred or tax-exempt accounts. But even these assertions are nuanced and depend on a variety of factors specific to an individual investor.

Trend equity strategies – and tactical strategies, in general – get a bad rap for being tax-inefficient. As assets are sold, capital gains are realized, often with no regard as to whether they are short-term or long-term. Wash sales are often ignored and holding periods may exclude dividends from qualifying status.

However, taxes represent yet another risk in a portfolio, and as you can likely guess if you are a frequent reader of these commentaries, reducing one risk is often done at the expense of increasing another.

The Risk in Taxes

Tax rates have been constant for long periods of time historically, especially in recent years, but they can change very rapidly depending on the overall economic environment.

Source: IRS, U.S. Census Bureau, and Tax Foundation. Calculations by Newfound Research. Series are limited by historical data availability.

The history shows a wide array of scenarios.

Prior to the 1980s, marginal tax rates spanned an extremely wide band, with the lowest tier near 0% and the top rate approaching 95%. However, this range has been much narrower for the past 30 years.

In the late 1980s when tax policy became much less progressive, investors could fall into only two tax brackets.

While the income quantile data history is limited, even prior to the narrowing of the marginal tax range, the bulk of individuals had marginal tax rates under 30%.

Turning to long-term capital gains rates, which apply to asset held for more than a year, we see similar changes over time.

Source: U.S. Department of the Treasury, Office of Tax Analysis and Tax Foundation.

For all earners, these rates are less than their marginal rates, which is currently the tax rate applied to short-term capital gains. While there were times in the 1970s when these long-term rates topped out at 40%, the maximum rate has dipped down as low as 15%. And since the Financial Crisis in 2008, taxpayers in the lower tax brackets pay 0% on long-term capital gains.

It is these large potential shifts in tax rates that introduce risk into the tax-aware investment planning process.

To see this more concretely, consider a hypothetical investment that earns 7% every year. Somehow – how is not relevant for this example – you have the choice of having the gains distributed annually as long-term capital gains or deferred until the sale of the asset.

Which option should you choose?

The natural choice is to have the taxes deferred until the sale of the asset. For a 10-year holding period where long-term capital gains are taxed at 20%, the pre-tax and after-tax values of a $1,000 investment are shown below.

The price return only version had a substantially higher pre-tax value as the full 7% was allowed to compound from year to year without the hinderance of an annual tax hit.

At the end of the 10-year period, the tax basis of the approach that distributed gains annually had increased up to the pre-tax amount, so it owed no additional taxes once the asset was sold. However, the approach that deferred taxes still ended up better after factoring in the tax on the embedded long-term capital gains that were realized upon the sale.

Now let’s consider the same assets but this time invested from 2004 to 2014 when the maximum long-term capital gains rate jumped to 25% in 2013 after being around 15% for the first 8 years.

The pre-tax picture is still the same: the deferred approach easily beat the asset that distributed capital gains annually.

But the after-tax values have changed order. Locking in more of the return when long-term capital gains tax rates were lower was advantageous.

The difference in this case may not be that significant. But consider a more extreme – yet still realistic – example where your tax rate on the gains jumps by more than ten percentage points (e.g. due to a change in employment or family situation or tax law changes), and the decision over which type of asset you prefer is not as clear cut.

Moving beyond this simple thought experiment, we now turn to the tax impacts on trend equity strategies.

Tax Impacts in Trend Equity

We will begin with a simple trend equity strategy that buys the U.S. stock market (the ETF VTI) when it has a positive 9-month return and buys short-term U.S. Treasuries (the ETF SHV) otherwise. Prior to ETF inception, we will rely on data from the Kenneth French Data Library to extend the analysis back to the 1920s. We will evaluate the strategy monthly and, for simplicity, will treat dividends as price returns.

With taxes now in the mix, we must track the individual tax lots as the strategy trades over time based on the tactical model. For deciding which tax lots to sell, we will select the ones with the lowest tax cost, making the assumption that short-term capital gains are taxed 50% higher than long-term capital gains (approximately true for investors with tax rates of 22% and 15%, respectively, in the current tax code).

We must address the question of when an investor purchases the trend equity strategy as a long bull market with a consistent positive trend would have very different tax costs for an investor holding all the way through versus one who bought at end.

To keep the analysis as simple as possible given the already difficult specification, we will look at an investment that is made at the very beginning, assume that taxes are paid at the end of each year, and compare the average annualized pre-tax and after-tax returns. Fortunately, for this type of trend strategy that can move entirely in and out of assets, the tax memory will occasionally reset.

To set some context, first, we need a benchmark.

Obviously, if you purchased VTI and held it for the entire time, you would be sitting on some large embedded capital gains.1

Instead, we will use a more appropriate benchmark for trend equity: a 50%/50% blend of VTI and SHV. We will rebalance this blend annually, which will lead to some capital gains.

The following chart shows the capital gains aggregated by year as a percentage of the end of the year account value.

Source: CSI Data and Kenneth French Data Library. Calculations by Newfound.

As expected with the annual rebalancing, all of the capital gains are long-term. Any short-term gains are an artifact of the rigidity of the rebalancing system where the first business day of subsequent years might be fewer than 365 days apart. In reality, you would likely incorporate some flexibility in the rebalances to ensure all long-term capital gains.

While this strategy incurs some capital gains, they are modest, with none surpassing 10%. Paying taxes on these gains is a small price to pay for maintaining a target allocation, supposing that is the primary goal.

Assuming tax rates of 15% for long-term gains and 25% for short-term gains, the annualized returns of the strategic allocation pre-tax and after-tax are shown below. The difference is minor.

Source: CSI Data and Kenneth French Data Library. Calculations by Newfound.

Now on to the trend equity strategy.

The historical capital gains look very different than those of the strategic portfolio.

Source: CSI Data and Kenneth French Data Library. Calculations by Newfound.

In certain years, the strategy locks in long-term capital gains greater than 50%. The time between these years is interspersed with larger short-term capital losses from whipsaws or year with essentially no realized gains or losses, either short- or long-term.

In fact, 31 of the 91 years had absolute realized gains/losses of less than 1% for both short- and long-term.

Now the difference between pre-tax and after-tax returns is 100 bps per year using the assumed tax rates (15% and 25%). This is significantly higher than with the strategic allocation.

Source: CSI Data and Kenneth French Data Library. Calculations by Newfound.

It would appear that trend equity is far less tax efficient than the strategic benchmark. As with all things taxes, however, there are nuances. As we mentioned in the first section of this commentary, tax rates can change at any time, either from a federal mandate or a change in an individual’s situation. If you are stuck with a considerable unrealized capital gain, it may be too late to adjust the course.

Source: CSI Data and Kenneth French Data Library. Calculations by Newfound.

The median unrealized capital gain for the trend equity strategy is 10%. This, of course, means that you must realize the gains periodically and therefore pay taxes.

But if you are sitting with a 400% unrealized gain in a different strategy, behaviorally, it may be difficult to make a prudent investment decision knowing that a large tax bill will soon follow a sale. And a 10 percentage point increase in the capital gains tax rate can have a much larger impact in dollar terms on the large unrealized gain than missing out on some compounding when rates were lower.

Even so, the thought of paying taxes intermediately and missing out on compound growth can still be irksome. Some small improvement to the trend equity strategy design can prove beneficial.

Improving the Tax Profile Within Trend Equity

This commentary would be incomplete without a further exploration down some of the axes of diversification.

We can take the simple 9-month trend following strategy and diversify it along the “how” axis using a multi-model approach with multiple lookback periods.

Specifically, we will use price versus moving average and moving average cross-overs in addition to the trailing return signal and look at windows of data ranging from 6 to 12 months.2

We can also diversify along the “when” axis by tranching the monthly strategy over 20 days. This has the effect of removing the luck – either good or bad – of rebalancing on a certain day of the month.

Below, we plot the characteristics of the long-term capital gains for the strategies in years in which a long-term gain was realized.

Source: CSI Data and Kenneth French Data Library. Calculations by Newfound.

The single monthly model had about a third of the years with long-term gains. Tranching it took that fraction to over a half. Moving to a multi-model approach brought the fraction to 60%, and tranching that upped it to 2 out of every 3 years.

Source: CSI Data and Kenneth French Data Library. Calculations by Newfound.

From an annualized return perspective, all of these trend equity strategies exhibited similar return differentials between pre-tax and after-tax.

In previous commentaries, we have illustrated how tranching to remove timing luck and utilizing multiple trend following models can remove the potential dispersion in realized terminal wealth. However, in the case of taxes, these embellishments did not yield a reduction in the tax gap.

While these improvements to trend equity strategies reduce specification-based whipsaw, they often result in similar allocations for large periods of time, especially since these strategies only utilize a single asset.

But to assume that simplicity trumps complexity just because the return differentials are not improved misses the point.3

With similar returns among within the trend-following strategies, using an approach that realizes more long-term capital gains could still be beneficial from a tax perspective.

In essence, this can be thought of as akin to dollar-cost averaging.

Dollar-cost averaging to invest a lump sum of capital is often not optimal if the sole goal is to generate the highest return.4 However, it is often beneficial in that it reduces the risk of bad outcomes (i.e. tail events).

Having a strategy – like trend equity – that has the potential to generate strong returns while taking some of those returns as long-term capital gains can be a good hedge against rising tax rates. And having a diversified trend equity strategy that can realize these capital gains in a smoother fashion is icing on the cake.

Conclusion

Taxes are a tricky subject, especially from the asset manager’s perspective. How do you design a strategy that suits all tax needs of its investors?

Rather than trying to develop a one-size-fits-all strategy, we believe that a better approach to the tax question is education. By more thoroughly understanding the tax profile of a strategy, investors can more comfortably deploy it appropriately in their portfolios.

As highly active strategies, trend equity mandates are generally assumed to be highly tax-inefficient. We believe it is more meaningful to represent the tax characteristics an exchange of risks: capital gains are locked in at the current tax rates (most often long-term) while unrealized capital gains are kept below a reasonable level. These strategies have also historically exhibited occasional periods with short-term capital losses.

These strategies can benefit investors who expect to have higher tax rates in the future without the option of having a way to mitigate this risk otherwise (e.g. a large tax-deferred account like a cash balance plan, donations to charity, a step-up in cost basis, etc.).

Of course, the question about the interplay between tax rates and asset returns, which was ignored in this analysis, remains. But in an uncertain future, the best course of investment action is often the one that diversifies away as much uncompensated risk as possible and includes a comprehensive plan for risk management.

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