Month: May 2020

Defensive Equity with Machine Learning

On May 25, 2020

In Defensive, Risk & Style Premia, Weekly Commentary

This post is available as a PDF download here.

Summary

Defensive equity strategies are comprised of stocks that lose less than the market during bear markets while keeping up with the market during a bull market.
Coarse sorts on metrics such as volatility, beta, value, and momentum lead to diversified portfolios but have mixed results in terms of their defensive characteristics, especially through different crisis periods that may favor one metric over another.
Using non-linear machine learning techniques is a desirable way to identify certain combinations of factors that lead to better defensive equity strategies over multiple periods.
By applying techniques such as random forests and gradient boosting to two sample defensive equity metrics, we find that machine learning does not add significant value over a low volatility sort, given the features included in the model.
While this by no means rules out the benefits of machine learning techniques, it shows how a blanket application of it is not a panacea for investing during crisis periods.

There is no shortage of hypotheses as to what characteristics define a stock that will outperform in a bear market. Some argue that value stocks should perform well, given their relative valuation buffer (the “less far to fall” argument). Some argue for a focus on balance sheet strength while others argue that cash-flow is the ultimate life blood of a company and should be prioritized. There are even arguments for industry preferences based upon economic cyclicality.

Each recession and crisis is unique, however, and therefore the characteristics of stocks that fare best will likely change. For example, the dot-com run-up caused a large number of real-economy businesses to be sorted into the “cheap” bucket of the value factor. These companies also tended to have higher quality earnings and lower beta / volatility than the dot-com stocks.

Common sense would indicate that unconstrained value may be a natural counter-hedge towards large, speculative bubbles, but we need only look towards 2008 – a credit and liquidity event – to see that value is not a panacea for every type of crisis.

It is for this reason that some investors prefer to take their cues from market-informed metrics such as beta, volatility, momentum, or trading volume.

Regardless of approach, there are some philosophical limitations we should consider when it comes to expectations with defensive equity portfolios. First, if we were able to identify an approach that could avoid market losses, then we would expect that strategy to also have negative alpha.¹ If this were not the case, we could construct an arbitrage.

Therefore, in designing a defensive equity portfolio, our aim should be to provide ample downside protection against market losses while minimizing the relative upside participation cost of doing so.

Traditional linear sorts – such as buying the lowest volatility stocks – are coarse by design. They aim to robustly capture a general truth and hedge missed subtleties through diversification. For example, while some stocks deserve to be cheap and some stocks are expensive for good reason, naïve value sorts will do little to distinguish them from those that are unjustifiably cheap or rich.

For a defensive equity portfolio, however, this coarseness may not only reduce effectiveness, but it may also increase the implicit cost. Therefore, in this note we implement non-linear techniques in an effort to more precisely identify combinations of characteristics that may create a more effective defensive equity strategy.

The Strategy Objective

To start, we must begin by defining precisely what we mean by a “defensive equity strategy.” What are the characteristics that would make us label one security as defensive and another as not? Or, potentially better, is there a characteristic that allows us to rank securities on a gradient of defensiveness?

This is not a trivial decision, as our entire exercise will attempt to maximize the probability of correctly identifying securities with this characteristic.

As our goal is to find those securities which provide the most protection during equity market routs but bleed the least during equity market rallies, we chose a metric that scored how closely a stock’s return reflected the payoff of a call option on the S&P 500 over the next 63 trading days (approximately 3 months).

In other words, if the S&P 500 is positive over the next 63 trading days, the score of a security is equal to the squared difference between its return and the S&P 500’s return. If the market’s return is negative, the score of a security is simply its squared return.

To determine whether this metric reflects the type of profile we want, we can create a long/short portfolio. Each month we rank securities by their scores and select the quintile with the lowest scores. Securities are then weighted by their market capitalization. Securities are held for three months and the portfolio is implemented with three tranches. The short leg of the portfolio is the market rather than the highest quintile, as we are explicitly trying to identify defense against the market.

To create a scalable solution, we restrict our investable universe to those in the top 1,000 securities by market capitalization.

We plot the performance below.

Source: Sharadar Fundamentals. Calculations by Newfound Research. Returns are hypothetical and backtested. Returns are gross of all fees including, but not limited to, management fees, transaction fees, and taxes. Returns assume the reinvestment of all distributions.

We can see that the strategy is relatively flat during bull markets (1998-2000, 2003-2007, 2011-2015, 2016-2018), but rallies during bear markets and sudden market shocks (2000-2003, 2008, 2011, 2015/2016, Q4 2018, and 2020).

Interestingly, despite having no sector constraints and not explicitly targeting tracking error at the portfolio level, the resulting portfolio ends up well diversified across sectors, though it does appear to make significant short-term jumps in sector weights. We can also see an increasing tilt towards Technology over the last 3 years in the portfolio. In recent months, positions in Financials and Industrials have been almost outright eliminated.

Source: Sharadar Fundamentals. Calculations by Newfound Research.

Of course, this metric is explicitly forward looking. We’re using a crystal ball to peer into the future and identify those stocks that track the best on the way up and protect the best on the way down. Our goal, then, is to use a variety of company and security characteristics to accurately forecast this score.

We will include a variety of characteristics and features, including:

Size: Market Capitalization.
Valuation: Book-to-Price, Earnings-to-Price, Free Cash Flow-to-Price, Revenue-to-EV, and EBITDA-to-EV.
Momentum: 12-1 Month Return and 1-Month Return.
Risk: Beta, Volatility, Idiosyncratic Volatility, and Ulcer Index.
Quality: Accruals, ROA, ROE, CFOA, GPOA, Net Margin, Asset Turnover, Leverage, and Payout Ratio.
Growth: Internal Growth Rate, EPS Growth, Revenue Growth.

These 24 features are all cross-sectionally ranked at each point in time. We also include dummy variables for each security to represent sector inclusion as well as whether the company has positive Net Income and whether the company has positive Operating Cash Flow.

Note that we are not including any market regime characteristics, such information about market returns, volatility, interest rates, credit spreads, sentiment, or monetary or fiscal policy. Had we included such features, our resulting model may end up as a factor switching approach, changing which characteristics it selects based upon the market environment. This may be an interesting model in its own right, but our goal herein is simply to design a static, non-linear factor sort.

Random Forests

Our first approach will be to apply a random forest algorithm, which is an ensemble learning method. The approach uses a training data set to build a number of individual decision trees whose results are then re-combined to create the ultimate decision. By training each tree on a subset of data and considering only a subset of features for each node, we can create trees that may individually have high variance, but as an aggregate forest reduce variance without necessarily increasing bias.

As an example, this means that one tree may be built using a mixture of low volatility and quality features, while another may be built using valuation and momentum features. Each tree is able to model a non-linear relationship, but by restricting tree depth and building trees using random subsets of data and features, we can prevent overfitting.

There are a number of hyperparameters that can be set to govern the model fit. For example, we can set the maximum depth of the individual trees as well as the number of trees we want to fit. Fitting hyperparameters is an art unto itself, and rather than go down the rabbit hole of tuning hyperparameters via cross-validation, we did our best to select reasonable hyper parameters. We elected to train the model on 50% of our data (March 1998 to March 2009), with a total of 100 trees each with a maximum depth of 2.

The results of the exercise are plotted below.

Source: Sharadar Fundamentals. Calculations by Newfound Research.

The performance does appear to provide defensive properties both in- and out-of-sample, with meaningful returns generated in 2000-2002, 2008, Q3 and Q4 of 2011, June 2015 through June 2016, and Q4 2008.

We can see that the allocations also express a number of static sector concentrations (e.g. Consumer Defensive) as well as some cyclical changes (e.g. Finances pre- and post-2007).

We can also gain insight into how the portfolio composition changes by looking at the weighted characteristic scores of the long leg of the portfolio over time.

Source: Sharadar Fundamentals. Calculations by Newfound Research.

It is important to remember that characteristics are cross-sectionally ranked across stocks. For some characteristics, higher is often considered better (e.g. a higher earnings-to-price cheaper is considered cheaper), whereas for other factors lower is better (e.g. lower volatility is considered to have less risk).

We can see that some characteristics are static tilts: higher market capitalization, positive operating cash flow, positive net income, and lower risk characteristics. Other characteristics are more dynamic. By 12/2008, the portfolio has tilted heavily towards high momentum stocks. A year later, the portfolio has tilted heavily towards low momentum stocks.

What is somewhat difficult to disentangle is whether these static and dynamic effects are due to the non-linear model we have developed, or whether it’s simply that applying static tilts results in the dynamic tilts. For example, if we only applied a low volatility tilt, is it possible that the momentum tilts would emerge naturally?

Unfortunately, the answer appears to be the latter. If we plot a long/short portfolio that goes long the bottom quintile of stocks ranked on realized 1-year volatility and short the broad market, we see a very familiar equity curve.

It would appear that the random forest model effectively identified the benefits of low volatility securities. And while out-of-sample performance does appear to provide more ample defense during 2011, 2015-2016, and 2018 than the low volatility tilt, it also has significantly greater performance drag.

Gradient Boosting

One potential improvement we might consider is to apply a gradient boosting model. Rather than simply building our decision trees independently in parallel, we can build them sequentially such that each tree is built on a modified version of the original data set (e.g. increasing the weights of those data points that were harder to classify and decreasing the weights on those that were easier).

Rather than just generalize to a low-volatility proxy, gradient boosting may allow our decision tree process to pick up upon greater subtleties and conditional relationships in the data. For comparison purposes, we’ll assume the same maximum tree depth and number of trees as the random forest method.

In initially evaluating the importance of features, it does appear that low volatility remains a critical factor, but other characteristics – such as momentum, free cash flow yield, and payout ratio – are close seconds. This may be a hint that gradient boosting was able to identify more subtle relationships.

Unfortunately, in evaluating the sector characteristics over time, we see a very similar pattern. Though we can notice that sectors like Technology have received a meaningfully higher allocation with this methodology versus the random forest approach.

Source: Sharadar Fundamentals. Calculations by Newfound Research.

If we compare long/short portfolios, we find little meaningful difference to our past results. Our model simply seems to identify a (historically less effective) low volatility model.

Re-Defining Defensiveness

When we set out on this problem, we made a key decision to define a stock’s defensiveness by how closely it is able to replicate the payoff of a call option on the S&P 500. What if we had elected another definition, though? For example, we could define defensive stocks as those that minimize the depth and frequency of drawdowns using a measure like the Ulcer Index.

Below we replicate the above tests but use forward 12-month Ulcer Index as our target score (or, more precisely, a security’s forward 12-month cross-sectional Ulcer Index rank).

We again begin by constructing an index that has perfect foresight, buying a market-capitalization weighted portfolio of securities that rank in the lowest quintile of forward 12-month ulcer index. We see a very different payoff profile than before, with strong performance exhibited in both bull and bear markets.

By focusing on forward 12-month scores rather than 3-month scores, we also see a far steadier sector allocation profile over time. Interestingly, we still see meaningful sector tilts over time, with sectors like Technology, Financials, and Consumer Defensives coming in and out of favor over time.

We again use a gradient boosted random forest model to try to model our target scores. We find that five of the top six most important features are price return related, either measuring return or risk.

Despite the increased emphasis on momentum, the resulting long/short index still echoes a naïve low-volatility sort. This is likely because negative momentum and high volatility have become reasonably correlated proxies for one another in recent years.

While returns appear improved from prior attempts, the out-of-sample performance (March 2009 and onward) is almost identical to that of the low-volatility long/short.

Conclusion

In this research note we sought to apply machine learning techniques to factor portfolio construction. Our goal was to exploit the ability of machine learning models to model non-linear relationships, hoping to come up with a more nuanced definition of a defensive equity portfolio.

In our first test, we defined a security’s defensiveness by how closely it was able to replicate the payoff of a call option on the S&P 500 over rolling 63-day (approximately 3-month) periods. If the market was up, we wanted to pick stocks that closely matched the market’s performance; if the market was down, we wanted to pick stocks that minimized drawdown.

After pre-engineering a set of features to capture both company and stock dynamics, we first turned to a random forest model. We chose this model as the decision tree structure would allow us to model conditional feature dynamics. By focusing on generating a large number of shallow trees we aimed to avoid overfitting while still reducing overall model variance.

Training the model on data from 1999-2009, we found that the results strongly favored companies exhibiting positive operating cash flow, positive earnings, and low realized risk characteristics (e.g. volatility and beta). Unfortunately, the model did not appear to provide any meaningful advantage versus a simple linear sort on volatility.

We then turned to applying gradient boosting to our random forest. This approach builds trees in sequence such that each tree seeks to improve upon the last. We hoped that such an approach would allow the random forest to build more nuance than simply scoring on realized volatility.

Unfortunately, the results remained largely the same.

Finally, we decided to change our definition of defensiveness by focusing on the depth and frequency of drawdowns with the Ulcer Index. Again, after re-applying the gradient boosted random forest model, we found little difference in realized results versus a simple sort on volatility (especially out-of-sample).

One answer for these similar results may be that our objective function is highly correlated to volatility measures. For example, if stocks follow a geometric Brownian motion process, those with higher levels of volatility should have deeper drawdowns. And if the best predictor of future realized volatility is past realized volatility, then it is no huge surprise that the models ultimately fell back towards a naïve volatility sort.

Interestingly, value, quality, and growth characteristics seemed largely ignored. We see two potential reasons for this.

The first possibility is that they were simply subsumed by low volatility with respect to our objective. If this were the case, however, we would see little feature importance placed upon them, but would still expect their weighted average characteristic scores within our portfolios to be higher (or lower). While this is true for select features (e.g. payout ratio), the importance of others appears largely cyclical (e.g. earnings-to-price). In fact, during the fall out of the dot-com bubble, weighted average value scores remained between 40 and 70.

The second reason is that the fundamental drivers behind each market sell-off are different. Factors tied to company metrics (e.g. valuation, quality, or growth), therefore, may be ill-suited to navigate different types of sell offs. For example, value was the natural antithesis to the speculative dot-com bubble. However, during the recent COVID-19 crisis, it has been the already richly priced technology stocks that have fared the best. Factors based upon security characteristics (e.g. volatility, returns, or volume) may be better suited to dynamically adjust to market changes.

While our results were rather lackluster, we should acknowledge that we have really only scratched the surface of machine learning techniques. Furthermore, our results are intrinsically linked to how we’ve defined our problem and the features we engineered. A more thoughtful target score or a different set of features may lead to substantially different results.

Straddles and Trend Following

By Nathan Faber

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.