Category: Weekly Commentary Page 2 of 21

Straddles and Trend Following

On May 11, 2020

In Momentum, Portfolio Construction, Risk Management, Trend, Weekly Commentary

This post is available as a PDF download here.

Summary

The convex payoff profile of trend following strategies naturally lends itself to comparative analysis with option strategies. Unlike options, however, the payout of trend following is not guaranteed.
To compare and contrast the two approaches, we replicate simple trend following strategies with corresponding option straddle strategies.
While trend-following has no explicit up-front cost, it also bears the full brunt of any price reversals. The straddle-based approach, on the other hand, pays an explicit cost to insure against sudden and large reversals.
This transformation of whipsaw risk into an up-front option premium can be costly during strongly trending market environments where the option buyer would have been rewarded more for setting a higher deductible for their implicit insurance policy and paying a lower premium.
From 2005-2020, avoiding this upfront premium was beneficial. The sudden loss of equity markets in March 2020, however, allowed straddle-based approaches to make up for 15-years of relative underperformance in a single month.
Whether an investor wishes to avoid these up-front costs or pay them is ultimately a function of the risks they are willing to bear. As we like to say, “risk cannot be destroyed, only transformed.”

We often repeat the mantra that, “risk cannot be destroyed, only transformed.” While not being able to destroy risk seems like a limitation, the assertion that risk can be transformed is nearly limitless.

With a wide variety of investment options, investors have the ability to mold, shape, skew, and shift their risks to fit their preferences and investing requirements (e.g. cash flows, liquidity, growth, etc.).

The payoff profile of a strategy is a key way in which this transformation of risk manifests, and the profile of trend following is one example that we have written much on historically. The convex payoff of many long/short trend following strategies is evident from the historical payoff diagram.

Source: Newfound Research. Payoff Diversification (February 10^th, 2020). Source: Kenneth French Data Library; Federal Reserve Bank of St. Louis. Calculations by Newfound Research. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. The 60/40 portfolio is comprised of a 60% allocation to broad U.S. equities and a 40% allocation to a constant maturity 10-Year U.S. Treasury index. The momentum portfolio is rebalanced monthly and selects the asset with the highest prior 12-month returns whereas the buy-and-hold variation is allowed to drift over the 1-year period. The 10-Year U.S. Treasuries index is a constant maturity index calculated by assuming a 10-year bond is purchased at the beginning of every month and sold at the end of that month to purchase a new bond at par at the beginning of the next month. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results.

This characteristic “V” shape in the diagram is reminiscent of an option straddle, where an investor buys a put and call option of the same maturity struck at the same price. This position allows the investor to profit if the price of the underlying security moves significantly in either direction, but they pay for this opportunity in the option premiums.

Source: theoptionsguide.com

The similarity of these payoff profiles is no coincidence. As we demonstrated in Trend – Convexity and Premium (February 11^th, 2019), simple total return trend following signals coarsely approximate the delta of the straddle. For those less familiar with the parlance of options, delta is the sensitivity in the value of the options to changes in the underlying stock. For example, if delta is +1, then the value of the option position will match price changes in the underlying dollar-for-dollar. If delta is -1, then the position will lose $1 for every dollar gained in the underlying and vice versa (i.e. the position is effectively short).

How does this connection arise? Consider a naïve S&P 500 trend strategy that rebalances monthly and uses 12-month total returns as a trend signal, buying when prior returns are positive and shorting when prior returns are negative. The key components of this strategy are today’s S&P 500 level and the level 12 months ago.

Now consider a strategy that buys a 1-month straddle with a strike equal to the level of the S&P 500 12 months ago. When the current level is above the strike, the strategy’s delta will be positive and when the level is below the strike, the delta will be negative. What we can see is that the sensitivity of our options trade to changes in the S&P 500 will match the sign of the trend strategy!

There are two key differences, however. First, our trend strategy was designed to always be 100% long or 100% short, whereas the straddle’s sensitivity can vary between -100% and 100%. Second, the trend strategy cannot change its exposure intramonth whereas the straddle will. In fact, if price starts above the strike price (a positive trend) but ultimately ends below – so far as it is sufficiently far that we can make up for the premium paid for our options – the straddle can still profit!

In this commentary, we will compare and contrast the trend and option-based approaches for a variety of lookback horizons.

Methodology and Data

For this analysis, we will use the S&P 500 index for equity returns, the iShares Short-term U.S. Treasury Bond ETF (ticker: SHV) as the risk-free rate, and monthly options data on the S&P 500 (SPX options).

The long/short trend equity strategy looks at total returns of equities over a given number of months. If this return is positive, the strategy invests in equities for the following month. If the return is negative, the strategy shorts equities for the following month and earns the short-term Treasury rate on the cash. The strategy is rebalanced monthly on the third Friday of each month to coincide with the options expiration dates.

For the (semi-equivalent) straddle replication, at the end of each month we purchase a call option and a put option struck at the level of the S&P 500 at the beginning of the lookback window of the trend following strategy. We can also back out the strike price using the current trend signal value and S&P 500. For example, if the trend signal is 25% and the S&P 500 is trading at $3000, we would set the strike of the options at $2400.

The options account is assumed to be fully cash collateralized. Any premium is paid on the options roll date, interest is earned on the remaining account balance, and the option payout is realized on the next roll date.

To value the options, we employ Black-Scholes pricing on an implied volatility surface derived from available out-of-the money options. Specifically, on a given day we fit a parabola to the implied variances versus log-moneyness (i.e. log(strike/price)) of the options for each time to maturity.

In prior research, we created straddle-derived trend-following models by purchasing S&P 500 exposure in proportion to the delta of the strategy. To calculate delta, we had previously priced the options using 21-day realized volatility as a proxy for implied volatility. This generally leads to over-pricing the options during crisis times and underpricing during more tame market environments, especially for deeper out of the money puts. In this commentary we are actually purchasing the straddles and holding them for one month.

Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.

Straddle vs. Trend Following

Below we plot the ratio of the equity curves for the straddle strategies versus their corresponding trend following strategies. When the line is increasing, the straddle strategy is out-performing, and when the line is decreasing the trend strategy is out-performing.

Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.

We can see, generally, that trend following out-performed the explicit purchase of options for almost all lookback periods for the majority of the 15-year test period.

It is only with the most recent expiration – March 20, 2020 – that many of the straddle strategies came to out-perform their respective trend strategies. With the straddle strategy, we pay an explicit premium to help insure our position against sudden and large intra-month price reversals. This did not occur very frequently during the 15 year history, but was very valuable protection in March when the trend strategies were largely still long coming off markets hitting all-time-highs in late February.

Shorter-term lookbacks fared particularly well during that month, as the trend following strategy was in a long position on the February 2020 options expiry date, and the straddles set by the short-term lookback window were relatively cheap from a historical perspective.

Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.

Note the curious case of the 14-month lookback. Entering March, the S&P 500 was +45% over a 14-month lookback (almost perfectly anchored to December 2018 lows). Therefore, the straddle was struck so deep in the money that it did not create any protection against the market’s sudden and large drawdown.

Prior to March 2020, only the 8- and 15-month lookback window strategies had outperformed their corresponding trend following strategies. In both cases, it was just barely and just recently.

Another interesting point to note is that longer-term straddle strategies (lookbacks greater than 9 months) shared similar movements during many periods while shorter-term lookbacks (3-6 months) showed more dispersion over time.

Overall, many of the straddles exhibit more “crisis alpha” than their trend following counterparts. This is an explicit risk we pay to hedge with the straddle approach and a fact we will discuss in more detail later on.

How Equity Movements Affect Straddles

Before we move into a discussion of how we can frame the straddle strategies, it will be helpful to revisit how straddles are affected by changing equity prices and how this effect changes with different lookback windows for the strategies.

Consider the delta of a straddle versus how far away price is from the strike (normalized by volatility).

Naively, we might consider that the longer our trend lookback window – and therefore the further back in time we set our strike price – the further away from the strike that price has had the opportunity to move. Consider two extremes: a strike set equal to the price of the S&P 500 10 years ago versus one set a day ago. We would expect that today’s price is much closer to that from a day ago than 10 years ago.

Therefore, for a longer lookback horizon we might expect that there is a greater chance that the straddle is currently deeper in the money, leading to a delta closer to +/- 1. In the case of straddles struck at index levels more recently realized, it is more likely that price is close to at the money, leading to deltas closer to 0.

This also means that while the trend following strategy is taking a binary bet, the straddle is able to modulate exposure to equity moves when the trend is less pronounced. For example, if a 12-month trend signal is +1%, the trend model will retain a +1 exposure while the delta of the straddle may be closer to 0.

Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.

Additionally, when the delta of a straddle is closer to zero, its gamma is higher. Gamma reflects how quickly the straddle’s sensitivity to changes in the underlying asset – i.e. the delta – will change. The trend strategy has no intra-month gamma, as once the position is set it remains static until the next rebalance.

As we generally expect the straddles struck longer ago to be deeper in the money than those struck more recently, we would also expect them to have lower gamma.

This also serves to nicely connect trend speed with the length of the lookback window. Shorter lookback windows are associated with trend models that change signals more rapidly while longer lookback windows are slower. Given that a total return trend signal can be thought of as the average of daily log returns, we would expect a longer lookback to react more slowly to recent changes than a shorter lookback because the longer lookback is averaging over more data.

But if we think of it through the lens of options – that the shorter lookback is coarsely replicating the delta of a straddle struck more recently – then the ideas of speed and gamma become linked.

Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.

The Straddle Strategy as an Insurance Policy

One of the key differences between the trend strategy and the straddle is that the straddle has features that act as insurance against price reversals. As an example, consider a case where the trend strategy has a positive signal. To first replicate the payoff, the straddle strategy buys an in-the-money call option. This is the first form of insurance, as the total amount this position can lose is the premium paid for the option, while the trend strategy can lose significantly more.

The straddle strategy goes one step further, though, and would also buy a put option. So not only does it have a fixed loss on the call if price reverses course, but it can also profit if it reverses sufficiently.

One way to model the straddle strategies, then, is as insurance policies with varying deductibles. There is an up-front premium that is paid, and the strategy does not pay out until the deductible – the distance that the option is struck in the money – is met.

When the deductible is high – that is, when the trend is very strong in either direction – the premium for the insurance policy tends to be low. On the other hand, a strategy that purchases at the money straddles would be equivalent to buying insurance with no deductible.

Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.

On average, the 3-month straddle strategy pays annual premiums of about 14% for the benefit of only having to wait for a price reversal of 6% before protection kicks in. Toward the other end of the spectrum, the 12-month strategy has an annual average premium of under 6% with a 16% deductible.

We can also visualize how often each straddle strategy pays higher premiums by looking at the deltas of the straddles over time. When these values deviate significantly from +1 or -1, then the straddle is lowering its insurance deductible in favor of paying more in premium. When the delta is nearly +1 or -1, then the straddle is buying higher deductible insurance that will take a larger whipsaw to payout.

The charts below show the delta over time in the straddle strategies vs. the trend allocation for 3-, 6-, and 12-month lookback windows.

There is significant overlap, especially as trends get longer. The differences in the deltas in the 3-month straddle model highlight its tradeoff between lower deductibles and higher insurance premiums. However, this leads it to be more adaptive at capitalizing on equity moves in the opposite direction that lead to losses in the binary trend-following model.

Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.

The chart below shows the annualized performance of the straddle strategies when they underperform trend following (premium) and the annualized performance of the straddle strategies when they outperform trend following (payout). As the lookback window increases, both of these figures generally decline in absolute value.

Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.

Even though we saw previously that the 3-month straddle strategy had the highest annual premium, its overall payout when it outperforms trend following is substantial. The longer lookbacks do not provide as much of a buffer due to their higher deductible levels, despite their lower premiums.

When the naïve trend strategy is right, it captures the full price change with no up-front premium. When it is wrong, however, it bears the full brunt of losses.

With the straddle strategy, the cost is paid up front for the benefit to not only protect against price reversals, but even potentially profit from them.

As a brief aside, a simpler options strategy with similar characteristics would be to buy only either a call option or put option depending on the trend signal. This strategy would not profit from a reversion of the trend, but it would cap losses. Comparing it to the straddle strategies highlights the cost and benefit of the added protection.

Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.

Buying only puts or calls generally helped both of the strategies shown in the chart. This came in reduced premiums over a time period when trimming premiums whenever possible paid off, especially for the 12-month lookback strategy. However, there are some notable instances where the extra protection of the straddle was very helpful, e.g. August 2011 and late 2014 for the 3-month lookback strategy and March 2020 for both.

Despite the similarities between the options and trend strategies, this difference in when the payment is made – either up-front in the straddle strategy or after-the fact in whipsaw in the trend following strategy – ends up being the key differentiator.

The relative performance of the strategies shows that investors mostly benefitted over the past 15 years by bearing this risk of whipsaw and large, sudden price-reversals. However, as the final moths of data indicates, option strategies can provide benefits that option-like strategies cannot.

Ultimately, the choice between risks is up to investor preferences, and a diversified approach that pairs strategies different convex strategies such as trend following and options is likely most appropriate.

Conclusion

The convex payoff profile of trend following strategies naturally lends itself to comparative analysis with option strategies, which also have a convex payoff profile. In fact, we would argue – as we have many times in the past – that trend following strategies coarsely replicate the delta profile of option straddles.

In this commentary, we sought to make that connection more explicit by building option straddle strategies that correspond to a naïve trend following strategies of varying lookback lengths.

While the trend following approach has no explicit up-front cost, it risks bearing the full brunt of sudden and large price reversals. With the straddle-based approach, an investor explicitly pays an up-front premium to insure against these risks.

When evaluated through the lens of an insurance policy, the straddle strategy dynamically adjusts its associated premium and deductible over time. When trends are strong, for example, premiums paid tend to be lower, but the cost is a higher deductible. Conversely, when trends are flat, the premium is much higher, but the deductible is much lower.

We found that over the 2005-2020 test period, the cost of the option premiums exceeded the cost of whipsaw in the trend strategies in almost all cases. That is, until March 2020, when a significant and sudden market reversal allowed the straddle strategies to make up for 15 years of relative losses in a single month.

As we like to say: risk cannot be destroyed, only transformed. In this case, the trend strategy was willing to bear the risk of large intra-month price reversals to avoid paying any up-front premium. This was a benefit to the trend investor for 15 years. And then it wasn’t.

By constructing straddle strategies, we believe that we can better measure the trade-offs of trend following versus the explicit cost of insurance. While trend following may approximate the profile of a straddle, it sacrifices some of the intra-month insurance qualities to avoid an up-front premium. Whether this risk trade-off is ultimately worth it depends upon the risks an investor is willing to bear.

Tranching, Trend, and Mean Reversion

By Corey Hoffstein

On April 27, 2020

In Craftsmanship, Momentum, Portfolio Construction, Weekly Commentary

This post is available as a PDF download here.

Summary

In past research we have explored the potential benefits of how-based diversification through the lens of pay-off functions.
Specifically, we explored how strategic rebalancing created a concave payoff while momentum / trend-following created a convex payoff. By combining these two approaches, total portfolio payoff became more neutral to the dispersion in return of underlying assets.
We have also spent considerable time exploring when-based diversification through our writing on rebalance timing luck.
To manage rebalance timing luck, we advocate for a tranching methodology that can be best distilled as rebalancing “a little but frequently.”
Herein, we demonstrate that the resulting payoff profile of a tranche-based rebalancing strategy closely resembles that of a portfolio that combines both strategic rebalancing and momentum/trend-following.
While we typically think of tranching as simply a way to de-emphasize the impact of a specific rebalancing date choice, this research suggests that for certain horizons, tranching may also be effective because it naturally introduces momentum/trend-following into the portfolio.

In Payoff Diversification (February 10^th, 2020), we explored the idea of combining concave and convex payoff profiles. Specifically, we demonstrated that rebalancing a strategic asset allocation was inherently concave (i.e. mean reversionary) whereas trend-following and momentum was inherently convex. By combining the two approaches together, we could neutralize the implicit payoff profile of our portfolio with respect to performance of the underlying assets.

Source: Newfound Research. Payoff Diversification (February 10^th, 2020). Source: Kenneth French Data Library; Federal Reserve Bank of St. Louis. Calculations by Newfound Research. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. The 60/40 portfolio is comprised of a 60% allocation to broad U.S. equities and a 40% allocation to a constant maturity 10-Year U.S. Treasury index. The rebalanced variation is rebalanced at the end of each month whereas the buy-and-hold variation is allowed to drift over the 1-year period. The momentum portfolio is rebalanced monthly and selects the asset with the highest prior 12-month returns whereas the buy-and-hold variation is allowed to drift over the 1-year period. The 10-Year U.S. Treasuries index is a constant maturity index calculated by assuming a 10-year bond is purchased at the beginning of every month and sold at the end of that month to purchase a new bond at par at the beginning of the next month. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results.

The intuition behind why rebalancing is inherently mean-reversionary is fairly simple. Consider a simple 50% stock / 50% bond portfolio. Between rebalances, this allocation will drift based upon the relative performance of stocks and bonds. When we rebalance, to right-size our relative allocations we must sell the asset that has out-performed and buy the one that has under-performed. “Sell your winners and buy your losers” certainly sounds mean-reversionary to us.

In fact, one way to think about a rebalance is as the application of a long/short overlay on your portfolio. For example, if the 50/50 portfolio drifted to a 45/55, we could think about rebalancing as holding the 45/55 and overlaying it with a +5/-5 long/short portfolio. This perspective explicitly expresses the “buy the loser, short the winner” strategy. In other words, we’re actively placing a trade that benefits when future returns between the two assets reverts.

While we may not be actively trying to express a view or forecast about future returns when we rebalance, we should consider the performance implications of our choice based upon whether the relative performance of these two assets continues to expand or contract:

	Relative Performance Expands	Relative Performance Contracts
Rebalance	–	+
Do Not Rebalance	+	–

Our argument in Payoff Diversification was that by combining strategic rebalancing and momentum / trend following, we could help neutralize this implicit bet.

What we can also see in the table above, though, is that the simple act of not rebalancing benefits from a continuation of relative returns just as trend/momentum does.

Let’s keep that in the back of our minds and switch gears, for a moment, to portfolio tranching. Frequent readers of our research notes will know we have spent considerable time researching the implications of rebalance timing luck. We won’t go into great detail here, but the research can be broadly summarized as, “when you rebalance your portfolio can have meaningful implications for performance.”

Given the discussion above, why that result holds true follows naturally. If two people hold 60/40 portfolios but rebalance them at different times in the year, their results will diverge based upon the relative performance of stocks and bonds between the rebalance periods.

As a trivial example, consider two 60/40 investors who each rebalance once a year. One chooses to rebalance every March and one chooses to rebalance every September. In 2008, the September investor would have re-upped his allocation to equities only to watch them sell-off for the next six months. The March investor, on the other hand, would have rebalanced earlier that year and her equity allocation would have drifted lower as the 2008 crisis wore on.

Even better, she would rebalance in March 2009, re-upping her equity allocation near the market bottom and almost perfectly timing the performance mean-reversion that would unfold. The September investor, on the other hand, would be underweight equities due to drift at this point.

Below we plot hypothetical drifted equity allocations for these investors over time.

Source: Tiingo. Calculations by Newfound Research.

The implications are that rebalancing can imbed large, albeit unintentional, market-timing bets.

In Rebalance Timing Luck: The Difference between Hired and Fired we derived that the optimal solution for avoiding the impact of these rebalance decisions is portfolio tranching. This is the same solution proposed by Blitz, van der Grient, and van Vliet (2010).

The whole concept of tranching can be summarized with the phrase: “a little but frequently.” In other words, rebalance your portfolio more frequently, but only make small changes. As an example, rather than rebalance once a year, we could rebalance 1/12^th of our portfolio every month. If our portfolio had drifted from a 60/40 to a 55/45, rather than rebalancing all the way back, we would just correct 1/12^th of the drift, trading to a 55.42/44.58.¹

Another way to think about this approach is as a collection of sub-portfolios. For example, if we elected to implement a 12-month tranche, we might think of it as 12 separate sub-portfolios, each of which rebalances every 12 months but does so at the end of a different month (e.g. one rebalances in January, one in February, et cetera).

But why does this approach work? It helps de-emphasize the mean-reversion bet for any given rebalance date. We can see this by constructing the same payoff plots as before for different tranching speeds. The 1-month tranche reflects a full monthly rebalance; a 3-month tranche reflects rebalancing 33.33% of the portfolio; a 6-month tranche reflects rebalancing 16.66% of the portfolio each month; et cetera.

Source: Newfound Research. Payoff Diversification (February 10^th, 2020). Source: Kenneth French Data Library; Federal Reserve Bank of St. Louis. Calculations by Newfound Research. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. The 60/40 portfolio is comprised of a 60% allocation to broad U.S. equities and a 40% allocation to a constant maturity 10-Year U.S. Treasury index. The rebalanced variation is rebalanced partially at the end of each month whereas the buy-and-hold variation is allowed to drift over the 1-year period. The 10-Year U.S. Treasuries index is a constant maturity index calculated by assuming a 10-year bond is purchased at the beginning of every month and sold at the end of that month to purchase a new bond at par at the beginning of the next month. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results.

Note how the concave payoff function appears to “unbend” and the 12-month tranche appears similar in shape to payoff of the 90% strategic rebalance / 10% momentum strategy portfolio we plotted in the introduction.

Why might this be the case? Recall that not rebalancing can be effective so long as there is continuation (i.e. momentum / trend) in the relative performance between stocks and bonds. By allowing our portfolio to drift, our portfolio will naturally tilt itself towards the out-performing asset. Furthermore, drift serves as an interesting amplifier to the momentum signal: the more persistent the relative out-performance, and the larger the relative out-performance in magnitude, the greater the resulting tilt.

While tranching naturally helps reduce rebalance timing luck by de-emphasizing each specific rebalance, we can also see that we may be able to naturally embed momentum into our process.

Conclusion

In portfolio management research, the answer we find is often a reflection of the angle by which a question is asked.

For example, in prior research notes, we have spent considerable time documenting the impact of rebalance timing luck in strategic asset allocation, tactical asset allocation, and factor investing. The simple choice of when, though often overlooked in analysis, can have a significant impact upon realized results. Therefore, in order to de-emphasize the choice of when, we introduce portfolio tranching.

We have also spent a good deal of time discussing the how axis of diversification (i.e. process). Not only have we research this topic through the lens of ensemble techniques, but we have also explored it through the payoff profiles generated by each process. We find that by combining diversifying concave and convex profiles – e.g. mean-reversion and momentum – we can potentially create a return profile that is more robust to different outcomes.

Herein, we found that tranching the rebalance of a strategic asset allocation may, in fact, allow us to naturally embed momentum without having to explicitly introduce a momentum strategy. What we find, then, is that the two topics may not actually be independent avenues of research about when and how. Rather, they may just different ways of exploring how to diversify the impacts of convexity and concavity in portfolio construction.

One Hedge to Rule Them All

By Nathan Faber

On March 30, 2020

In Craftsmanship, Portfolio Construction, Risk Management, Weekly Commentary

This post is available as a PDF download here.

Summary

About two years ago, we compared and contrasted different approaches to risk managing equity exposure; including fixed income, risk parity, managed futures, tactical equity, and options-based strategies.
Given the recent market events as the world navigates through the COVID-19 crisis, we revisit this analysis to see how these strategies would have fared over the past two years.
We find that all eight strategies studied have continued to successfully reduce risk, with two of the previously underperforming options-based strategies now jumping to the forefront of the pack.
Over time, performance of the risk management strategies still varies significantly both relative to the S&P 500 and compared to the other strategies. Generally, risk-managed strategies tend to behave like insurance, underperforming on the upside and outperforming on the downside.
Diversifying your diversifiers by blending a number of complementary risk-managed strategies together – even at random – can be a powerful method of improving long-term outcomes.

“The primary requirement of historical time is that inly one of the possible alternatives coming at you from the future can be actualized in the present where it will flow into the pat and remain forever after unalterable. You may sometimes have “another chance” and be able to make a different choice in some later present, but this can in no way change the choice you did in fact make in the first instance.”

– Dr. William G. Pollard, Prof. of Physics, Manhattan Project

23 trading days.

In a little over a month, the S&P 500 dropped nearly 35% from all-time highs in a sell-off that was one of the fastest in history. Many investors experienced the largest drawdowns their portfolios had seen since the Financial Crisis.

While the market currently sits in a drawdown closer to 25% (as of the time of this writing), the future remains could take any path. Following the relative calm in the market over the preceding year, we are now living through a historic time with the uncertainty and severity of the growing COVID-19 pandemic and its far-reaching ramifications.

However, as a firm that focuses on managing risk, we are used to not knowing the answers.

In the summer of 2018, we published a piece entitled The State of Risk Management where we examined the historical trade-offs in terms of returns during market downturns versus returns during calm market environments of a variety of risk management methods.

Since that time, especially with the benefit of hindsight, one might argue that risk management was unnecessary until this past month. While the S&P 500 experienced a 19% drawdown in Q4 of 2018, it quickly recovered and went on to post a gain of 32% in 2019, rewarding those who stayed the course (or, better yet, bought the dip).

Source: Tiingo. Returns are gross of all management fees, transaction fees, and taxes, but net of underlying fund fees. Total return series assumes the reinvestment of all distributions. Data through 3/27/2020.

With the future poised to follow a variety of uncertain paths, we think it is a prudent time to check in on some of the more popular ways to manage risk and see how they are handling the current events.

The Updated Historical Track Record

For risk management, we examine eight strategies that roughly fit into four categories:

Diversification Strategies: strategic 60/40 stock/bond mix¹and risk parity²
Options Strategies: equity collar³, protective put⁴, and put-write⁵,⁶
Equity Strategies: long-only defensive equity that blends a minimum volatility strategy⁷, a quality strategy⁸, and a dividend growth strategy⁹ in equal weights
Trend-Following Strategies: managed futures¹⁰ and tactical equity¹¹

Index data was used prior to fund inception when necessary, and the common inception data is December 1997.

The following charts show the return and risk characteristics of the strategies over the entire historical period. Previously, we had used maximum drawdown as a measure of risk but have now switched to using the ulcer index to quantify both the duration and severity of drawdowns.

Data Source: CBOE, Tiingo, S&P. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. Data is from December 1997 to 3/27/2020.

Relative to when we previously presented these statistics (as of July 2018), the most notable changes are that the 95-100 Collar index and Risk Parity have improved and that Managed Futures moved into the top-performing spot up from the middle of the pack. Trend Equity dropped slightly in the rankings, which is partially attributable to our switching over to using the Newfound Trend Equity Index, which includes exposure to small- and mid-cap companies and invests in cash rather than corporate bonds for the defensive position.

Six of the eight strategies still exhibit strong risk-adjusted performance relative to the S&P over the entire time period.

But as we also showed in 2018, the dispersion in strategy performance is significant.

This chart also highlights the current trailing one-year performance for each strategy as of 3/27/2020.

Both the 95-110 Collar and the 5% Put Protection indices are in the top 10% of their historical one-year returns, with the put protection index forging new maximum territory. Trend equity and defensive equity have exhibited returns closer to their median levels, while managed futures, strategic diversification with bonds, and risk parity have had returns above their medians.

When we examine the current market environment, this makes sense. Many options were relatively cheap (i.e. implied volatility was low) heading into and early in February, and the option rollover date was close to when the drawdown began (positive timing luck). Equity trends were also very strong coming out of 2019.

With the sharp reversal in equity prices, option strategies provided a strong static hedge that any investors had been paying premiums for through the previous years of bull market returns.

Trend equity strategies were slower to act as trends took time to reverse before cash was introduced into the portfolio, and managed futures were eventually able to capitalize on short positions and diversification once these trends were established.

Zooming in more granularly, we can see the trade-offs between the hedging performance of each strategy in down markets and the premiums paid through negative returns in up-markets. This chart shows the returns relative to the S&P 500 (SPY). When the lines are increasing (decreasing), the hedge is outperforming (underperforming). A flatter line during periods of calm markets indicates lower premiums if we think of these strategies as insurance policies.

All eight strategies have provided hedging in both Q4 2018 and the current downturn. The -95-100 Collar- provided some of the lowest premiums. -Trend Equity- also provided low premiums but had a slower time getting back in the market after the hedging period in 2018.

-Managed Futures- have provided some of the best hedging through both down periods but had the highest premium during the strong market of 2019.

With the continued dispersion in performance, especially with the “new” market crisis, this highlights the importance of diversification.

Diversifying Your Diversifiers

Not every risk management strategy will perfectly hedge every downturn while also having a low cost during up markets.

We see the power of diversifying your diversifiers when we test simple equal-weight blends of the risk management strategies. In our 2018 update, we had used an equal weight blend of all eight strategies and a blend of the six strategies that had historical Sharpe ratios above the S&P 500. This latter selection was admittedly biased with hindsight. The two excluded strategies – the 95-110 Collar and the 5% Put Protection indices – were some of the best performing over the period from August 2018 to March 2020!

Our own biases notwithstanding, we still include both blends for comparison.

Both blends have higher Sharpe ratios than 6 of the 8 individual strategies and higher excess return to ulcer index ratios than all of the eight individual strategies.

This is a very powerful result, indicating that naïve diversification is nearly as good as being able to pick the best individual strategies with perfect foresight.

But holding eight – or even six – strategies can be daunting, especially for more aggressive investors who may only want to allocate a small portion of their portfolio to a risk management sleeve.

How much diversification is enough?

The following charts show the distribution of risk-adjusted returns from randomly choosing any number of the 8 strategies and holding them in equal weight.

As is to be expected, the cost of choosing the “wrong” blend of strategies decreases as the number of strategies held increases. The potential benefits initially increase and then back off as the luck of choosing the “right” strategy blend is reduced through holding a greater number of strategies.

Both charts show the distributions converging for the single choice for an 8-strategy portfolio.

Even holding 3 or 4 of the eight risk management strategies, chosen at random, leads to robust results, in general, with narrowed bands in the distribution (e.g. 25^th to 75^th percentiles).

Blending strategies from each of the different categories – static diversification, options, equity, and trend-following – can further reduce concentration risk verses selection at random and ensure that a variety of risk factors within the hedging strategies (e.g. interest rates from bonds, volatility from options, beta from equity, and whipsaw from trend-following) are mitigated.

Conclusion

We’ve said it many times before: There is no holy grail when it comes to risk management. While finding the perfect hedge that beats all others in every environment is enticing, it is impossible via the simple fact that risk cannot be destroyed, only transformed.

In an uncertain world where we cannot predict exactly what the next crisis will look like – or even what the current crisis will look like after today – diversifying your diversifiers by combining a number of complementary risk-managed strategies may be a prudent course of action.

We believe that this type of balanced approach has the potential to deliver compelling results over a full market cycle while managing the idiosyncratic risk of any one manager or strategy.

Diversification can also help to increase the odds of an investor sticking with their risk management plan as the short-term performance lows won’t be quite as low as they would be with a single strategy (conversely, the highs won’t be as high either).

Developing a plan and sticking with it is the most important first step in risk management. It is obviously desirable to keep premiums in strong markets as low as possible while having efficient hedges in down markets, but simple diversification can go a long way to provide a robust results.

Risk management is, by definition, required to be in place before risks are realized. Even when the market is currently down, risks in the future are still present. Therefore, we must periodically ask ourselves, “What risks are we willing to bear?”

One potential path has been locked into history, but the next time potential risks become reality – and they inevitably will – we must be comfortable with our answer.

Why Trend Models Diverge

By Corey Hoffstein

On March 9, 2020

In Risk & Style Premia, Trend, Weekly Commentary

This post is available as a PDF download here.

Summary

During the week of February 23^rd, the S&P 500 fell more than 10%.
After a prolonged bullish period in equities, this tumultuous decline caused many trend-following signals to turn negative.
As we would expect, short-term signals across a variety of models turned negative. However, we also saw that price-minus-moving-average models turned negative across a broad horizon of lookbacks where the same was not true for other models.
In this brief research note, we aim to explain why common trend-following models are actually mathematically linked to one another and differ mainly in how they place weight on recent versus prior price changes.
We find that price-minus-moving-average models place the greatest weight on the most recent price changes, whereas models like time-series momentum place equal-weight across their lookback horizon.

In a market note we sent out last weekend, the following graphic was embedded:

What this table intends to capture is the percentage of trend signals that are on for a given model and lookback horizon (i.e. speed) on U.S. equities. The point we were trying to establish was that despite a very bearish week, trend models remained largely mixed. For frequent readers of our commentaries, it should come as no surprise that we were attempting to highlight the potential specification risks of selecting just one trend model to implement with (especially when coupled with timing luck!).

But there is a potentially interesting second lesson to learn here which is a bit more academic. Why does it look like the price-minus (i.e. price-minus-moving-average) models turned off, the time series momentum models partially turned off, and the cross-over (i.e. dual-moving-average-cross) signals largely remained positive?

While this note will be short, it will be somewhat technical. Therefore, we’ll spoil the ending: these signals are all mathematically linked.

They can all be decomposed into a weighted average of prior log-returns and the primary difference between the signals is the weighting concentration. The price-minus model front-weights, the time-series model equal weights, and the cross-over model tends to back-weight (largely dependent upon the length of the two moving averages). Thus, we would expect a price-minus model to react more quickly to large, recent changes.

If you want the gist of the results, just jump to the section The Weight of Prior Evidence, which provides graphical evidence of these weighting schemes.

Before we begin, we want to acknowledge that absolutely nothing in this note is novel. We are, by in large, simply re-stating work pioneered by Bruder, Dao, Richard, and Roncalli (2011); Marshall, Nguyen and Visaltanachoti (2012); Levine and Pedersen (2015); Beekhuizen and Hallerbach (2015); and Zakamulin (2015).

Decomposing Time-Series Momentum

We will begin by decomposing a time-series momentum value, which we will define as:

We will begin with a simple substitution:

Which implies that:

Simply put, time-series momentum puts equal weight on all the past price changes¹ that occur.

Decomposing Dual-Moving-Average-Crossover

We define the dual-moving-average-crossover as:

We assume m is less than n (i.e. the first moving average is “faster” than the second). Then, re-writing:

Here, we can make a cheeky transformation where we add and subtract the current price, P_t:

What we find is that the double-moving-average-crossover value is the difference in two weighted averages of time-series momentum values.

Decomposing Price-Minus-Moving-Average

This decomposition is trivial given the dual-moving-average-crossover. Simply,

The Weight of Prior Evidence

We have now shown that these decompositions are all mathematically related. Just as importantly, we have shown that all three methods are simply re-weighting schemes of prior price changes. To gain a sense of how past returns are weighted to generate a current signal, we can plot normalized weightings for different hypothetical models.

For TSMOM, we can easily see that shorter lookback models apply more weight on less data and therefore are likely to react faster to recent price changes.
PMAC models apply weight in a linear, declining fashion, with the most weight applied to the most recent price changes. What is interesting is that PMAC(50) puts far more weight on recent prices changes than the TSMOM(50) model does. For equivalent lookback periods, then, we would expect PMAC to react much more quickly. This is precisely why we saw PMAC models turn off in the most recent sell-off when other models did not: they are much more front-weighted.
DMAC models create a hump-shaped weighting profile, with increasing weight applied up until the length of the shorter lookback period, and then descending weight thereafter. If we wanted to, we could even create a back-weighted model, as we have with the DMAC(150, 200) example. In practice, it is common to see that m is approximately equal to n/4 (e.g. DMAC(50, 200)). Such a model underweights the most recent information relative to slightly less recent information.

Conclusion

In this brief research note, we demonstrated that common trend-following signals – namely time-series momentum, price-minus-moving-average, and dual-moving-average-crossover – are mathematically linked to one another. We find that prior price changes are the building blocks of each signal, with the primary differences being how those prior price changes are weighted.

Time-series momentum signals equally-weight prior price changes; price-minus-moving-average models tend to forward-weight prior price changes; and dual-moving-average-crossovers create a hump-like weighting function. The choice of which model to employ, then, expresses a view as to the relative importance we want to place on recent versus past price changes.

These results align with the trend signal changes seen over the past week during the rapid sell-off in the S&P 500. Price-minus-moving-average models appeared to turn negative much faster than time-series momentum or dual-moving-average-crossover signals.

By decomposing these models into their most basic and shared form, we again highlight the potential specification risks that can arise from electing to employ just one model. This is particularly true if an investor selects just one of these models without realizing the implicit choice they have made about the relative importance they would like to place on recent versus past returns.

Ensembles and Rebalancing

By Corey Hoffstein

On February 24, 2020

In Portfolio Construction, Weekly Commentary

This post is available as a PDF download here.

Summary

While rebalancing studies typically focus on the combination of different asset classes, we evaluate a combination of two naïve trend-following strategies.
As expected, we find that a rebalanced fixed-mix of the two strategies generates a concave payoff profile.
More interestingly, deriving the optimal blend of the two strategies allows the rebalanced portfolio to out-perform either of the two underlying strategies.
While most rebalancing literature has focused on the benefits of combining asset classes, we believe this literature can be trivially extended to ensembles of strategies.

Two weeks ago, we wrote about the idea of payoff diversification. The notion is fairly trivial, though we find it is often overlooked. Put simply, any and all trading decisions – even something as trivial as rebalancing – create a “payoff profile.” These profiles often fall into two categories: concave strategies that do well in stable environments is maintained and convex strategies that do better in the tails.

For example, we saw that rebalancing a 60/40 stock/bond portfolio earned a premium against a buy-and-hold approach when the spread between stock and bond returns remained narrow. Conversely, when the spread in return between stocks and bonds was wide, rebalancing created a drag on returns. This is a fairly trivial and obvious conclusion, but we believe it is important for investors to understand these impacts and why payoff is a meaningful axis of diversification.

In our prior study, we compared two different approaches to investing: strategic rebalancing and momentum investing. In this (very brief) study, we want to demonstrate that these results are also applicable when applied to different variations of the same strategy.

Specifically, we will look at two long/short trend following strategies applied to broad U.S. equities. When trend signals are positive, the strategy will be long U.S. equities and short the risk-free rate; when trend signals are negative the strategy will be short U.S. equities and long the risk-free rate. We will use a simple time-series momentum signal. The first model (“21D”) will evaluate trailing 21-day returns and hold for 1 day and the second model (“168D”) will evaluate trailing 168-day returns and holds for 14 days (with 14 overlapping portfolios).¹ Both strategies implement a full skip day before allocating and assuming implementation at closing prices.

Source: Kenneth French Data Library. Calculations by Newfound Research. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. Past performance is not indicative of future results.

So, what happens if we create a portfolio that holds both of these strategies, allocating 50% of our capital to each? Readers of our prior note will likely be able to guess the answer easily: we create a concave payoff profile that depends upon the relative performance between the two strategies. How, specifically, that concave shape manifests will be path dependent, but will also depend upon the rebalance frequency. For example, below we plot the payoff profiles for the 50/50 blend rebalanced weekly and monthly.

If we stop thinking of these as two strategies applied to the same asset and just think of them as two assets, the results are fairly standard and intuitive. What is potentially appealing, however, is that the same literature and research that applies to the potential to create a rebalancing premium between assets can apply to a portfolio of strategies (whether a combination of distinct strategies, such as value and momentum, or an ensemble of the same strategy).

Below, we plot the annualized return of weekly rebalanced portfolios with different fixed-mix allocations to the 21D and 168D strategies. We can see that the curve peaks at approximately 45%, suggesting that a 45% allocation to the 21D strategy and a 55% allocation to the 168D strategy actually maximizes the compound annualized growth rate of the portfolio.

If we follow the process of Dubikovsky and Susinno (2017)² to derive the optimal blend of these two assets – using the benefit of hindsight to measure their annualized returns (7.28% and 7.61% respectively), volatility (17.55% and 17.97% respectively), and correlation (0.1318) – we derive an optimal weight of 45.33%.

Perhaps somewhat surprisingly, even if the correlation between these two strategies was 0.9, the optimal blend would still recommend about 10% to the 21D variation. And, as extreme as it may seem, even if the annualized return of the 21D strategy was just 5.36% – a full 225 basis points below the 168D strategy – the optimal blend would still recommend about 10%. Diversification can create interesting opportunities to harvest return; at least, in expectation.

And, as we would expect, if we have no view as to a difference in return or volatility between the two specifications, we would end up with a recommended allocation of 50% to each.

Conclusion

While most studies on rebalancing consider the potential benefits of combining assets, we believe that these benefits are trivially extended to strategies. Not just different strategies, however, but even strategies of the same style.

In this brief note, we explore the payoff profile created by combining two naïve long/short trend following strategies applied to broad U.S. equities. Unsurprisingly, rebalancing a simple mixture of the two specifications creates a concave payoff that generally profits when the spread between the two strategies is narrow and loses when the spread is wide.

More interestingly, however, we demonstrate that by rebalancing a fixed-mix of the two strategies, we can generate a return that is greater than either strategy individually. We believe that this potential benefit of ensemble approaches has been mostly overlooked by existing literature and deserves further analysis.