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Decomposing Trend Equity

This post is available as a PDF download here.

Summary­

  • We introduce the simple arithmetic of portfolio construction where a strategy can be broken into a strategic allocation and a self-financing trading strategy.
  • For long/flat trend equity strategies, we introduce two potential decompositions.
  • The first implementation is similar to equity exposure with a put option overlay. The second is similar to a 50% equity / 50% cash allocation with a 50% overlay to a straddle.
  • By evaluating the return profile of the active trading strategy in both decompositions, we can gain a better understanding for how we expect the strategy to perform in different environments.
  • In both cases, we can see that trend equity can be thought of as a strategic allocation to equities – seeking to benefit from the equity risk premium – plus an alternative strategy that seeks to harvest benefits from the trend premium.

The Simple Arithmetic of Portfolio Construction

In our commentary A Trend Equity Primer, we introduced the concept of trend equity, a category of strategies that aim to harvest the long-term benefits of the equity risk premium while managing downside risk through the application of trend following.  In this brief follow-up piece, we aim to provide further transparency into the behavior of trend equity strategies by decomposing this category of strategies into component pieces.

First, what do we mean by “decompose”?

As it turns out, the arithmetic of portfolios is fairly straight forward.  Consider this simple scenario: we currently hold a portfolio consisting entirely of asset A and want to hold a portfolio that is 50% A and 50% of some asset B.  What do we do?

Figure 1

No, this is not a trick question.  The straightforward answer is that we sell 50% of our exposure in A and buy 50% of our exposure in B.  As it turns out, however, this is entirely equivalent to holding our portfolio constant and simply going short 50% exposure in A and using the proceeds to purchase 50% notional portfolio exposure in B (see Figure 2).  Operationally, of course, these are very different things.  Thinking about the portfolio in this way, however, can be constructive to truly understanding the implications of the trade.

The difference in performance between our new portfolio and our old portfolio will be entirely captured by the performance of this long/short overlay. This tells us, for example, that the new portfolio will outperform the old portfolio when asset B outperforms asset A, since the long/short portfolio effectively captures the spread in performance between asset B and asset A.

Figure 2: Portfolio Arithmetic – Long/Short Overlay

Relative to our original portfolio, the long/short represents our active bets.  A slightly more nuanced view of this arithmetic requires scaling our active bets such that each leg is equal to 100%, and then only implementing a portion of that overlay.  It is important to note that the overlay is “dollar-neutral”: in other words, the dollars allocated to the short leg and the long leg add up to zero.  This is also called “self-funding” because it is presumed that we would enter the short position and then use the cash generated to purchase our long exposure, allowing us to enter the trade without utilizing any capital.

Figure 3: Portfolio Arithmetic – Scaled Long/Short Overlay

In our prior example, a portfolio that is 50% long B and 50% short A is equivalent to 50% exposure to a portfolio that is 100% long B and 100% short A.  The benefit of taking this extra step is that it allows us to decompose our trade into two pieces: the active bets we are making and the sizing of these bets.

Decomposing Trend Equity

Trend equity strategies are those strategies that seek to combine structural exposure to equities with the potential benefits of an active trend-following trading strategy.  A simple example of such a strategy is a “long/flat” strategy that invests in large-cap U.S. equities when the measured trend in large-cap U.S. equities is positive and otherwise invests in short-term U.S. Treasuries (or any other defensive asset class).

An obvious question with a potentially non-obvious answer is, “how do we benchmark such a strategy?”  This is where we believe decomposition can be informative.  Our goal should be to decompose the portfolio into two pieces: the strategic benchmark allocation and a dollar-neutral long/short trading strategy that captures the manager’s active bets.

For long/flat trend equity strategies, we believe there are two obvious decompositions, which we outline in Figure 4.

Figure 4

Strategic Position

Trend Strategy

Decomposition

Positive Trend

Negative Trend

Strategic +
Flat/Short Trend Strategy

100% Equity

No Position

-100% Equity
100% ST US Treasuries

Strategic + 50% Long/Short Trend Strategy

50% Equity
50% ST US Treasuries

100% Equity
-100% ST US Treasuries

-100% Equity
+100% ST US Treasuries

Equity + Flat/Short

The first decomposition achieves the long/flat strategy profile by assuming a strategic allocation that is allocated to U.S. equities.  This is complemented by a trading strategy that goes short large-cap U.S. equities when the trend is negative, investing the available cash in short-term U.S. Treasuries, and does nothing otherwise.

The net effect is that when trends are positive, the strategy remains fully invested in large-cap U.S. equities.  When trends are negative, the overlay nets out exposure to large-cap U.S. equities and leaves the portfolio exposed only to short-term U.S. Treasuries.

In Figures 5, we plot the return profile of a hypothetical flat/short large-cap U.S. equity strategy.

Figure 5: A Flat/Short U.S. Equity Strategy

Source: Newfound Research.  Return data relies on hypothetical indices and is exclusive of all fees and expenses.  Returns assume the reinvestment of all dividends.  Flat/Short Equity shorts U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return, investing available capital in 3-month U.S. Treasury Bills.  The strategy assumes zero cost of shorting.   The Flat/Short Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary.  It is not possible to invest in an index.  Past performance does not guarantee future results.

The flat/short strategy has historically achieved a payoff structure that looks very much like a put option: positive returns during significantly negative return regimes, and (on average) slight losses otherwise.  Of course, unlike a put option where the premium paid is known upfront, the flat/short trading strategy pays its premium in the form of “whipsaw” resulting from trend reversals.  These head-fakes cause the strategy to “short low” and “cover high,” creating realized losses.

Our expectation for future returns, then, is a combination of the two underlying strategies:

  • 100% Strategic Equity: We should expect to earn, over the long run, the equity risk premium at the risk of large losses due to economic shocks.
  • 100% Flat/Short Equity: Empirical evidence suggests that we should expect a return profile similar to a put option, with negative returns in most environments and the potential for large, positive returns during periods where large-cap U.S. equities exhibit large losses.  Historically, the premium for the trend-following “put option” has been significantly less than the premium for buying actual put options.  As a result, hedging with trend-following has delivered higher risk-adjusted returns.  Note, however, that trend-following is rarely helpful in protecting against sudden losses (e.g. October 1987) like an actual put option would be.

Taken together, our long-term return expectation should be the equity risk premium minus the whipsaw costs of the flat/short strategy. The drag in return, however, is payment for the expectation that significant left-tail events will be meaningfully offset.  In many ways, this decomposition lends itself nicely to thinking of trend equity as a “defensive equity” allocation.

Figure 6: Combination of U.S. Large-Cap Equities and a Flat/Short Trend-Following Strategy

Source: Newfound Research.  Return data relies on hypothetical indices and is exclusive of all fees and expenses.  Returns assume the reinvestment of all dividends.  Flat/Short Equity shorts U.S. Large-Cap Equity when the prior month has a negative 12-1 month total return, investing available capital in 3-month U.S. Treasury Bills.  The strategy assumes zero cost of shorting.   The Flat/Short Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary.  It is not possible to invest in an index.  Past performance does not guarantee future results.

50% Equity/50% Cash + 50% Long/Short

The second decomposition achieves the long/flat strategy profile by assuming a strategic allocation that is 50% large-cap U.S. equities and 50% short-term U.S. Treasuries.  The overlaid trend strategy now goes both long and short U.S. equities depending upon the underlying trend signal, going short and long large-cap U.S. Treasuries to keep the dollar-neutral profile of the overlay.

One difference in this approach is that to achieve the desired long/flat return profile, only 50% exposure to the long/short strategy is required.  As before, the net effect is such that when trends are positive, the portfolio is invested entirely in large-cap U.S. equities (as the short-term U.S. Treasury positions cancel out), and when trends are negative, the portfolio is entirely invested in short-term U.S. Treasuries.

In Figures 7, we plot the return profile of a hypothetical long/short large-cap U.S. equity strategy.

Figure 7: A Long/Short Equity Trend-Following Strategy

Source: Newfound Research.  Return data relies on hypothetical indices and is exclusive of all fees and expenses.  Returns assume the reinvestment of all dividends.  Long/Short Equity goes long U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return, shorting an equivalent amount in 3-month U.S. Treasury Bills.  When the prior month has a negative 12-1 month total return, the strategy goes short U.S. Large-Cap Equity, investing available capital in 3-month U.S. Treasury Bills.  The strategy assumes zero cost of shorting.   The Long/Short Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary.  It is not possible to invest in an index.  Past performance does not guarantee future results.

We can see the traditional “smile” associated with long/short trend-following strategies.  With options, this payoff profile is reminiscent of a straddle, a strategy that combines a position in a put and a call option to profit in both extremely positive and negative environments.  The premium paid to buy these options causes the strategy to lose money in more normal environments.  We see a similar result with the long/short trend-following approach.

As before, our expectation for future returns is a combination of the two underlying strategies:

  • 50% Equity / 50% Cash: We should expect to earn, over the long run, about half the equity risk premium, but only expect to suffer about half the losses associated with equities.
  • 50% Long/Short Equity: The “smile” payoff associated with trend following should increase exposure to equities in the positive tail and help offset losses in the negative tail, at the cost of whipsaw during periods of trend reversals.

Taken together, we should expect equity up-capture exceeding 50% in strongly trending years, a down-capture less than 50% in strongly negatively trending years, and a slight drag in more normal environments.  We believe that this form of decomposition is most useful when investors are planning to fund their trend equity from both stocks and bonds, effectively using it as a risk pivot within their portfolio.

In Figure 8, we plot the return combined return profile of the two component pieces. Note that it is identical to Figure 6.

Figure 8

Source: Newfound Research.  Return data relies on hypothetical indices and is exclusive of all fees and expenses.  Returns assume the reinvestment of all dividends.  Long/Short Equity goes long U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return, shorting an equivalent amount in 3-month U.S. Treasury Bills.  When the prior month has a negative 12-1 month total return, the strategy goes short U.S. Large-Cap Equity, investing available capital in 3-month U.S. Treasury Bills.  The strategy assumes zero cost of shorting.   The Long/Short Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary.  It is not possible to invest in an index.  Past performance does not guarantee future results.

Conclusion

In this commentary, we continued our exploration of trend equity strategies. To gain a better sense of how we should expect trend equity strategies to perform, we introduce the basic arithmetic of portfolio construction that we later use to decompose trend equity into a strategic allocation plus a self-funded trading strategy.

In the first decomposition, we break trend equity into a strategic, passive allocation in large-cap U.S. equities plus a self-funding flat/short trading strategy. The flat/short strategy sits in cash when trends in large-cap U.S. equities are positive and goes short large-cap U.S. equities when trends are negative.  In isolating the flat/short trading strategy, we see a return profile that is reminiscent of the payoff of a put option, exhibiting negative returns in positive market environments and large gains during negative market environments.

For investors planning on utilizing trend equity as a form of defensive equity, this decomposition is appropriate.  It clearly demonstrates that we should expect returns that are less than passive equity during almost all market environments, with the exception being extreme negative tail events, where the trading strategy aims to hedge against significant losses.  While we would expect to be able to measure manager skill by the amount of drag created to equities during positive markets (i.e. the “cost of the hedge”), we can see from the hypothetical example inn Figure 5 that there is considerable variation year-to-year, making short-term analysis difficult.

In our second decomposition, we break trend equity into a strategic portfolio that is 50% large-cap U.S. equity / 50% short-term U.S. Treasury plus a self-funding long/short trading strategy.  If the flat/short trading strategy was similar to a put option, the long/short trading strategy is similar to a straddle, exhibiting profit in the wings of the return distribution and losses near the middle.

This particular decomposition is most relevant to investors who plan on funding their trend equity exposure from both stocks and bonds, allowing the position to serve as a risk pivot within their overall allocation.  The strategic contribution provides partial exposure to the equity risk premium, but the trading strategy aims to add value in both tails, demonstrating that trend equity can potentially increase returns in both strongly positive and strongly negative environments.

In both cases, we can see that trend equity can be thought of as a strategic allocation to equities – seeking to benefit from the equity risk premium – plus an alternative strategy that seeks to harvest benefits from the trend premium.

In this sense, trend equity strategies help investors achieve capital efficiency.  Allocations to the alternative return premia, in this case trend, does not require allocating away from the strategic, long-only portfolio.  Rather, exposure to both the strategic holdings and the trend-following alternative strategy can be gained in the same package.

A Trend Equity Primer

This post is available as a PDF download here.

Summary­

  • Trend-following strategies exploit the fact that investors exhibit behavioral biases that cause trends to persist.
  • While many investment strategies have a concave payoff profile that reaps small rewards at the risk of large losses, trend-following strategies exhibit a convex payoff profile, one that pays small premiums with the potential of a large reward.
  • By implementing a trend-following strategy on equities, investors can tap into both the long-term return premium from holding equities and the convex payoff profile associated with trend following.
  • There are multiple ways to include a trend-following equity strategy in a portfolio, and the method of incorporation will affect the overall risk and return expectations in different market environments.
  • As long as careful consideration is given to whipsaw, hedging ability, and implementation costs, trend-following equity can be a potentially useful diversifier in most traditionally allocated portfolios.

A Balance of Risks

Most investors – individual and institutional alike – live in the balance of two risks: failing slow and failing fast.  Most investors are familiar with the latter: the risk of large and sudden drawdowns that can permanently impair an investor’s lifestyle or ability to meet future liabilities.  Slow failure, on the other hand, occurs when an investor fails to grow their portfolio at a speed sufficient to offset inflation and withdrawals.

Investors have traditionally managed these risks through asset allocation, balancing exposure to growth-oriented asset classes (e.g. equities) with more conservative, risk-mitigating exposures (e.g. cash or bonds).  How these assets are balanced is typically governed by where an investor falls in their investment lifecycle and which risk has the greatest impact upon the probability of their future success.

For example, younger investors who have a large proportion of their future wealth tied up in human capital often have very little risk of failing fast, as they are not presently relying upon withdrawals from their investment capital. Evidence suggests that the risk of fast failure peaks for pre- and early-retirees, whose future lifestyle will be largely predicated upon the amount of capital they are able to maintain into early retirement.  Later-stage retirees, on the other hand, once again become subject to the risk of failing slow, as longer lifespans put greater pressure upon the initial retirement capital to last.

Trend equity strategies seek to address both risks simultaneously by maintaining equity exposure when trends are positive and de-risking the portfolio when trends are negative.  Empirical evidence suggests that such strategies may allow investors to harvest a significant proportion of the long-term equity risk premium while significantly reducing the impact of severe and prolonged drawdowns.

The Potential Hedging Properties of Trend Following

When investors buy stocks and bonds, they are exposing themselves to “systematic risk factors.”  These risk factors are the un-diversifiable uncertainties associated with any investment. For bearing these risks, investors expect to earn a reward.  For example, common equity is generally considered to be riskier than fixed income because it is subordinate in the capital structure, does not have a defined payout, and does not have a defined maturity date.  A rational investor would only elect to hold stocks over bonds, then, if they expected to earn a return premium for doing so.

Similarly, the historical premium associated with many active investment strategies are also assumed to be risk-based in nature.  For example, quantitatively cheap stocks have historically outperformed expensive ones, an anomaly called the “value factor.”  Cheap stocks may be trading cheaply for a reason, however, and the potential excess return earned from buying them may simply be the premium required by investors to bear the excess risk.

In many ways, an investor bearing risk can be thought of as an insurer, expecting to collect a premium over time for their willingness to carry risk that other investors are looking to offload.  The payoff profile for premiums generated from bearing risk, however, is concave in nature: the investor expects to collect a small premium over time but is exposed to potentially large losses (see Figure 1).  This approach is often called being “short volatility,” as the manifestation of risk often coincides with large (primarily negative) swings in asset values.

Even the process of rebalancing a strategic asset allocation can create a concave payoff structure.  By reallocating back to a fixed mixture of assets, an investor sells assets that have recently outperformed and buys assets that have recently underperformed, benefiting when the relative performance of investments mean-reverts over time.

When taken together, strategically allocated portfolios – even those with exposure to alternative risk premia – tend to combine a series of concave payoff structures. This implies that a correlation-based diversification scheme may not be sufficient for managing left-tail risk during bad times, as a collection of small premiums may not offset large losses.

In contrast, trend-following strategies “cut their losers short and let their winners run” by design, creating a convex payoff structure (see Figure 1).1  Whereas concave strategies can be thought of as collecting an expected return premium for bearing risk, a convex payoff can be thought of as expecting to pay an insurance premium in order to hedge risk.  This implies that while concave payoffs benefit from stability, convex payoffs benefit from instability, potentially helping hedge portfolios against large losses at the cost of smaller negative returns during normal market environments.

Figure 1: Example Concave and Convex Payoff Structures; Profit in Blue and Loss in Orange

Source: Newfound Research.  For illustrative purposes only and not representative of any Newfound Research product or investment.

What is Trend Equity?

Trend equity strategies rely upon the empirical evidence2 that performance tends to persist in the short-run: positive performance tends to beget further positive performance and negative performance tends to beget further negative performance.  The theory behind the evidence is that behavioral biases exhibited by investors lead to the emergence of trends.

In an efficient market, changes in the underlying value of an investment should be met by an immediate, commensurate change in the price of that investment. The empirical evidence of trends suggests that investors may not be entirely efficient at processing new information.  Behavioral theory suggests that investors anchor their views on prior beliefs, causing price to underreact to new information.  As price continues to drift towards fair value, herding behavior occurs, causing price to overreact and extend beyond fair value.  Combined, these effects cause a trend.

Trend equity strategies seek to capture this potential inefficiency by systematically investing in equities when they are exhibiting positively trending characteristics and divesting when they exhibit negative trends.  The potential benefit of this approach is that it can try to exploit two sources of return: (1) the expected long-term risk premium associated with equities, and (2) the convex payoff structure typically associated with trend-following strategies.

As shown in Figure 2, a hypothetical implementation of this strategy on large-cap U.S. equities has historically matched the long-term annualized return while significantly reducing exposure to both tails of the distribution.  This is quantified in Figure 3, which demonstrates a significant reduction in both the skew and kurtosis (“fat-tailedness”) of the return distribution.

Figure 2

Figure 3

U.S. Large-Cap EquitiesTrend Equity
Annualized Return11.1%11.6%
Volatility16.9%11.3%
Skewness-1.40.0
Excess Kurtosis2.2-1.0

 Source: Newfound Research.  Return data relies on hypothetical indices and is exclusive of all fees and expenses.  Returns assume the reinvestment of all dividends.  Trend Equity invests in U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return and in 3-month U.S. Treasury Bills otherwise.  The Trend Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary.  It is not possible to invest in an index.  Past performance does not guarantee future results.

Implementing Trend Equity

With trend equity seeking to benefit from both the long-term equity risk premium and the convex payoff structure of trend-following, there are two obvious examples of how it can be implemented in the context of an existing strategic portfolio. The preference as to the approach taken will depend upon an investor’s goals.

Investors seeking to reduce risk in their portfolio may prefer to think of trend equity as a form of dynamically hedged equity, replacing a portion of their traditional equity exposure.  In this case, when trend equity is fully invested, the portfolio will match the original allocation profile; when the trend equity strategy is divested, the portfolio will be significantly underweight equity exposure.  The intent of this approach is to match the long-term return profile of equities with less realized risk.

On the other hand, investors seeking to increase their returns may prefer to treat trend equity as a pivot within their portfolio, funding the allocation by drawing upon both traditional stock and bond exposures.  In this case, when fully invested, trend equity will create an overweight to equity exposure within the portfolio; when divested, it will create an underweight.  The intent of this approach is to match the long-term realized risk profile of a blended stock/bond mix while enhancing long-term returns.

To explore these two options in the context of an investor’s lifecycle, we echo the work of Freccia, Rauseo, and Villalon (2017).  Specifically, we will begin with a naïve “own-your-age” glide path, which allocates a proportion of capital to bonds equivalent to the investor’s age.  We assume the split between domestic and international exposures is 60/40 and 70/30 respectively for stocks and bonds, selected to approximate the split between domestic and international exposures found in Vanguard’s Target Retirement Funds.

An investor seeking to reduce exposure to negative equity tail events could fund trend equity exposure entirely from their traditional equity allocation. Applying the own-your-age glide path over the horizon of June 1988 to June 2018, carving out 30% of U.S. equity exposure for trend equity (e.g. an 11.7% allocation for a 35 year old investor and an 8.1% allocation for a 55 year old investor) would have offered the same long-term return profile while reducing annualized volatility and the maximum drawdown experienced.

For an investor seeking to increase return, funding a position in trend equity from both U.S. equities and U.S. bonds may be a more applicable approach.  Again, applying the own-your-age glide-path from June 1988 to June 2018, we find that replacing 50% of existing U.S. equity exposure and 30% of existing U.S. bond exposure with trend equity would have offered a nearly identical long-term volatility profile while increasing long-term annualized returns.

Figure 4

Source: Newfound Research.  For illustrative purposes only and not representative of any Newfound Research product or investment.

 

Figure 5: Hypothetical Portfolio Statistics, June 1988 – June 2018

Original
Glidepath
Same Return,
Decrease Risk
Increase Return,
Same Risk
Annual Return8.20%8.25%8.60%
Volatility8.58%8.17%8.59%
Maximum Drawdown-28.55%-24.71%-23.80%
Sharpe Ratio0.610.640.65

 Source: Newfound Research.  Return data relies on hypothetical indices and is exclusive of all fees and expenses.  Returns assume the reinvestment of all dividends.  Trend Equity invests in U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return and in 3-month U.S. Treasury Bills otherwise.  The Trend Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary.  It is not possible to invest in an index.  Past performance does not guarantee future results.

 

Figure 6: Own-Your-Age Glide Paths Including Trend Equity

Source: Newfound Research.  For illustrative purposes only and not representative of any Newfound Research product or investment.  Allocation methodologies described in the preceding section.

A Discussion of Trade-Offs

At Newfound Research, we champion the philosophy that “risk cannot be destroyed, only transformed.”  While we believe that a convex payoff structure – like that empirically found in trend-following strategies – can introduce beneficial diversification into traditionally allocated portfolios, we believe any overview is incomplete without a discussion of the potential trade-offs of such an approach.

The perceived trade-offs will be largely dictated by how trend equity is implemented by an investor.  As in the last section, we will consider two cases: first the investor who replaces their traditional equity exposure, and second the investor that funds an allocation from both stocks and bonds.

In the first case, we believe that the convex payoff example displayed Figure 1 is important to keep in mind.  Traditionally, convex payoffs tend to pay a premium during stable environments.  When this payoff structure is combined with traditional long-only equity exposure to create a trend equity strategy, our expectation should be a return profile that is expected to lag behind traditional equity returns during calm market environments.

This is evident in Figure 7, which plots hypothetical rolling 3-year annualized returns for both large-cap U.S. equities and a hypothetical trend equity strategy. Figure 8 also demonstrates this effect, plotting rolling 1-year returns of a hypothetical trend equity strategy against large-cap U.S. equities, highlighting in orange those years when trend equity underperformed.

For the investor looking to employ trend equity as a means of enhancing return by funding exposure from both stocks and bonds, long-term risk statistics may be misleading.  It is important to keep in mind that at any given time, trend equity can be fully invested in equity exposure.  While evidence suggests that trend-following strategies may be able to act as an efficient hedge when market downturns are gradual, they are typically inefficient when prices collapse suddenly.

In both cases, it is important to keep in mind that convex payoff premium associated with trend equity strategies is not consistent, nor is the payoff guaranteed. In practice, the premium arises from losses that arrive during periods of trend reversals, an effect popularly referred to as “whipsaw.”  A trend equity strategy may go several years without experiencing whipsaw, seemingly avoiding paying any premium, then suddenly experience multiple back-to-back whipsaw events at once.  Investors who allocate immediately before a series of whipsaw events may be dismayed, but we believe that these are the costs necessary to access the convex payoff opportunity and should be considered on a multi-year, annualized basis.

Finally, it is important to consider that trend-following is an active strategy. Beyond management fees, it is important to consider the impact of transaction costs and taxes.

Figure 7Source: Newfound Research.  Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all dividends.  Trend Equity invests in U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return and in 3-month U.S. Treasury Bills otherwise.   The Trend Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary.  It is not possible to invest in an index.  Past performance does not guarantee future results.

Figure 8

Source: Newfound Research.  Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all dividends.  Trend Equity invests in U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return and in 3-month U.S. Treasury Bills otherwise.   The Trend Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary.  It is not possible to invest in an index.  Past performance does not guarantee future results.

Conclusion

In this primer, we have introduced trend equity, an active strategy that seeks to provide investors with exposure to the equity risk premium while mitigating the impacts of severe and prolonged drawdowns.  The strategy aims to achieve this objective by blending exposure to equities with the convex payoff structure traditionally exhibited by trend-following strategies.

We believe that such a strategy can be a particularly useful diversifier for most strategically allocated portfolios, which tend to be exposed to the concave payoff profile of traditional risk factors.  While relying upon correlation may be sufficient in normal market environments, we believe that the potential premiums collected can be insufficient to offset large losses generated during bad times.  It is during these occasions that we believe a convex payoff structure, like that empirically found in trend equity, can be a particularly useful diversifier.

We explored two ways in which investors can incorporate trend equity into a traditional profile depending upon their objective.  Investors looking to reduce realized risk without necessarily sacrificing long-term return can fund their trend equity exposure with their traditional equity allocation.  Investors looking to enhance returns while maintaining the same realized risk profile may be better off funding exposure from both traditional stock and bond allocations.

Finally, we discussed the trade-offs associated with incorporating trend equity into an investor’s portfolio, including (1) the lumpy and potentially large nature of whipsaw events, (2) the inability to hedge against sudden losses, and (3) the costs associated with managing an active strategy.  Despite these potential drawbacks, we believe that trend-following equity can be a potentially useful diversifier in most traditionally allocated portfolios.

Bibliography

Freccia, Maxwell, and Rauseo, Matthew, and Villalon, Daniel, DC Solutions Series: Defensive Equity, Part 2.  Available at https://www.aqr.com/Insights/Research/DC-Solutions/DC-Solutions-Series-Defensive-Equity-Part-2.  Accessed September 2018.

Hsieh, David A. and Fung, William, The Risk in Hedge Fund Strategies: Theory and Evidence from Trend Followers. The Review of Financial Studies, Vol. 14, No. 2, Summer 2001. Available at SSRN: https://ssrn.com/abstract=250542

Hurst, Brian and Ooi, Yao Hua and Pedersen, Lasse Heje, A Century of Evidence on Trend-Following Investing (June 27, 2017). Available at SSRN: https://ssrn.com/abstract=2993026 or http://dx.doi.org/10.2139/ssrn.2993026

Lempérière, Yves, and Deremble, Cyril and Seager, Philip and Potters, Marc, and Bouchaud, Jean-Phillippe. (April, 2014), Two Centuries of Trend Following, Journal of Investment Strategies, 3(3), pp. 41-61.

Factor Fimbulwinter

This post is available as a PDF download here.

Summary­

  • Value investing continues to experience a trough of sorrow. In particular, the traditional price-to-book factor has failed to establish new highs since December 2006 and sits in a 25% drawdown.
  • While price-to-book has been the academic measure of choice for 25+ years, many practitioners have begun to question its value (pun intended).
  • We have also witnessed the turning of the tides against the size premium, with many practitioners no longer considering it to be a valid stand-alone anomaly. This comes 35+ years after being first published.
  • With this in mind, we explore the evidence that would be required for us to dismiss other, already established anomalies.  Using past returns to establish prior beliefs, we simulate out forward environments and use Bayesian inference to adjust our beliefs over time, recording how long it would take for us to finally dismiss a factor.
  • We find that for most factors, we would have to live through several careers to finally witness enough evidence to dismiss them outright.
  • Thus, while factors may be established upon a foundation of evidence, their forward use requires a bit of faith.

In Norse mythology, Fimbulvetr (commonly referred to in English as “Fimbulwinter”) is a great and seemingly never-ending winter.  It continues for three seasons – long, horribly cold years that stretch on longer than normal – with no intervening summers.  It is a time of bitterly cold, sunless days where hope is abandoned and discord reigns.

This winter-to-end-all-winters is eventually punctuated by Ragnarok, a series of events leading up to a great battle that results in the ultimate death of the major gods, destruction of the cosmos, and subsequent rebirth of the world.

Investment mythology is littered with Ragnarok-styled blow-ups and we often assume the failure of a strategy will manifest as sudden catastrophe.  In most cases, however, failure may more likely resemble Fimbulwinter: a seemingly never-ending winter in performance with returns blown to-and-fro by the harsh winds of randomness.

Value investors can attest to this.  In particular, the disciples of price-to-book have suffered greatly as of late, with “expensive” stocks having outperformed “cheap” stocks for over a decade.  The academic interpretation of the factor sits nearly 25% belowits prior high-water mark seen in December 2006.

Expectedly, a large number of articles have been written about the death of the value factor.  Some question the factor itself, while others simply argue that price-to-book is a broken implementation.

But are these simply retrospective narratives, driven by a desire to have an explanation for a result that has defied our expectations?  Consider: if price-to-book had exhibited positive returns over the last decade, would we be hearing from nearly as large a number of investors explaining why it is no longer a relevant metric?

To be clear, we believe that many of the arguments proposed for why price-to-book is no longer a relevant metric are quite sound. The team at O’Shaughnessy Asset Management, for example, wrote a particularly compelling piece that explores how changes to accounting rules have led book value to become a less relevant metric in recent decades.1

Nevertheless, we think it is worth taking a step back, considering an alternate course of history, and asking ourselves how it would impact our current thinking.  Often, we look back on history as if it were the obvious course.  “If only we had better prior information,” we say to ourselves, “we would have predicted the path!”2  Rather, we find it more useful to look at the past as just one realized path of many that’s that could have happened, none of which were preordained.  Randomness happens.

With this line of thinking, the poor performance of price-to-book can just as easily be explained by a poor roll of the dice as it can be by a fundamental break in applicability.  In fact, we see several potential truths based upon performance over the last decade:

  1. This is all normal course performance variance for the factor.
  2. The value factor works, but the price-to-book measure itself is broken.
  3. The price-to-book measure is over-crowded in use, and thus the “troughs of sorrow” will need to be deeper than ever to get weak hands to fold and pass the alpha to those with the fortitude to hold.
  4. The value factor never existed in the first place; it was an unfortunate false positive that saturated the investing literature and broad narrative.

The problem at hand is two-fold: (1) the statistical evidence supporting most factors is considerable and (2) the decade-to-decade variance in factor performance is substantial.  Taken together, you run into a situation where a mere decade of underperformance likely cannot undue the previously established significance.  Just as frustrating is the opposite scenario. Consider that these two statements are not mutually exclusive: (1) price-to-book is broken, and (2) price-to-book generates positive excess return over the next decade.

In investing, factor return variance is large enough that the proof is not in the eating of the short-term return pudding.

The small-cap premium is an excellent example of the difficulty in discerning, in real time, the integrity of an established factor.  The anomaly has failed to establish a meaningful new high since it was originally published in 1981.  Only in the last decade – nearly 30 years later – have the tides of the industry finally seemed to turn against it as an established anomaly and potential source of excess return.

Thirty years.

The remaining broadly accepted factors – e.g. value, momentum, carry, defensive, and trend – have all been demonstrated to generate excess risk-adjusted returns across a variety of economic regimes, geographies, and asset classes, creating a great depth of evidence supporting their existence. What evidence, then, would make us abandon faith from the Church of Factors?

To explore this question, we ran a simple experiment for each factor.  Our goal was to estimate how long it would take to determine that a factor was no longer statistically significant.

Our assumption is that the salient features of each factor’s return pattern will remain the same (i.e. autocorrelation, conditional heteroskedasticity, skewness, kurtosis, et cetera), but the forward average annualized return will be zero since the factor no longer “works.”

Towards this end, we ran the following experiment: 

  1. Take the full history for the factor and calculate prior estimates for mean annualized return and standard error of the mean.
  2. De-mean the time-series.
  3. Randomly select a 12-month chunk of returns from the time series and use the data to perform a Bayesian update to our mean annualized return.
  4. Repeat step 3 until the annualized return is no longer statistically non-zero at a 99% confidence threshold.

For each factor, we ran this test 10,000 times, creating a distribution that tells us how many years into the future we would have to wait until we were certain, from a statistical perspective, that the factor is no longer significant.

Sixty-seven years.

Based upon this experience, sixty-seven years is median number of years we will have to wait until we officially declare price-to-book (“HML,” as it is known in the literature) to be dead.3  At the risk of being morbid, we’re far more likely to die before the industry finally sticks a fork in price-to-book.

We perform this experiment for a number of other factors – including size (“SMB” – “small-minus-big”), quality (“QMJ” – “quality-minus-junk”), low-volatility (“BAB” – “betting-against-beta”), and momentum (“UMD” – “up-minus-down”) – and see much the same result.  It will take decades before sufficient evidence mounts to dethrone these factors.

HMLSMB4QMJBABUMD
Median Years-until-Failure6743132284339

 

Now, it is worth pointing out that these figures for a factor like momentum (“UMD”) might be a bit skewed due to the design of the test.  If we examine the long-run returns, we see a fairly docile return profile punctuated by sudden and significant drawdowns (often called “momentum crashes”).

Since a large proportion of the cumulative losses are contained in these short but pronounced drawdown periods, demeaning the time-series ultimately means that the majority of 12-month periods actually exhibit positive returns.  In other words, by selecting random 12-month samples, we actually expect a high frequency of those samples to have a positive return.

For example, using this process, 49.1%, 47.6%, 46.7%, 48.8% of rolling 12-month periods are positive for HML, SMB, QMJ, and BAB factors respectively.  For UMD, that number is 54.7%.  Furthermore, if you drop the worst 5% of rolling 12-month periods for UMD, the average positive period is 1.4x larger than the average negative period.  Taken together, not only are you more likely to select a positive 12-month period, but those positive periods are, on average, 1.4x larger than the negative periods you will pick, except for the rare (<5%) cases.

The process of the test was selected to incorporate the salient features of each factor.  However, in the case of momentum, it may lead to somewhat outlandish results.

Conclusion

While an evidence-based investor should be swayed by the weight of the data, the simple fact is that most factors are so well established that the majority of current practitioners will likely go our entire careers without experiencing evidence substantial enough to dismiss any of the anomalies.

Therefore, in many ways, there is a certain faith required to use them going forward. Yes, these are ideas and concepts derived from the data.  Yes, we have done our best to test their robustness out-of-sample across time, geographies, and asset classes.  Yet we must also admit that there is a non-zero probability, however small it is, that these are false positives: a fact we may not have sufficient evidence to address until several decades hence.

And so a bit of humility is warranted.  Factors will not suddenly stand up and declare themselves broken.  And those that are broken will still appear to work from time-to-time.

Indeed, the death of a factor will be more Fimulwinter than Ragnarok: not so violent to be the end of days, but enough to cause pain and frustration among investors.

 

Addendum

We have received a large number of inbound notes about this commentary, which fall upon two primary lines of questions.  We want to address these points.

How were the tests impacted by the Bayesian inference process?

The results of the tests within this commentary are rather astounding.  We did seek to address some of the potential flaws of the methodology we employed, but by-in-large we feel the overarching conclusion remains on a solid foundation.

While we only presented the results of the Bayesian inference approach in this commentary, as a check we actually tested two other approaches:

  1. A Bayesian inference approach assuming that forward returns would be a random walk with constant variance (based upon historical variance) and zero mean.
  2. Forward returns were simulated using the same bootstrap approach, but the factor was being discovered for the first time and the entire history was being evaluated for its significance.

The two tests were in effort to isolate the effects of the different components of our test.

What we found was that while the reported figures changed, the overall  magnitude did not.  In other words, the median death-date of HML may not have been 67 years, but the order of magnitude remained much the same: decades.

Stepping back, these results were somewhat a foregone conclusion.  We would not expect an effect that has been determined to be statistically significant over a hundred year period to unravel in a few years.  Furthermore, we would expect a number of scenarios that continue to bolster the statistical strength just due to randomness alone.

Why are we defending price-to-book?

The point of this commentary was not to defend price-to-book as a measure.  Rather, it was to bring up a larger point.

As a community, quantitative investors often leverage statistical significance as a defense for the way we invest.

We think that is a good thing.  We should look at the weight of the evidence.  We should be data driven.  We should try to find ideas that have proven to be robust over decades of time and when applied in different markets or with different asset classes.  We should want to find strategies that are robust to small changes in parameterization.

Many quants would argue (including us among them), however, that there also needs to be a why.  Why does this factor work?  Without the why, we run the risk of glorified data mining.  With the why, we can choose for ourselves whether we believe the effect will continue going forward.

Of course, there is nothing that prevents the why from being pure narrative fallacy.  Perhaps we have simply weaved a story into a pattern of facts.

With price-to-book, one might argue we have done the exact opposite.  The effect, technically, remains statistically significant and yet plenty of ink has been spilled as to why it shouldn’t work in the future.

The question we must answer, then, is, “when does statistically significant apply and when does it not?”  How can we use it as a justification in one place and completely ignore it in others?

Furthermore, if we are going to rely on hundreds of years of data to establish significance, how can we determine when something is “broken” if the statistical evidence does not support it?

Price-to-book may very well be broken.  But that is not the point of this commentary.  The point is simply that the same tools we use to establish and defend factors may prevent us from tearing them down.

 

How to Benchmark Trend-Following

This post is available as a PDF download here.

Summary­

  • Benchmarking a trend-following strategy can be a difficult exercise in managing behavioral biases.
  • While the natural tendency is often to benchmark equity trend-following to all-equities (e.g. the S&P 500), this does not accurately give the strategy credit for choosing to be invested when the market is going up.
  • A 50/50 portfolio of equities and cash is generally an appropriate benchmark for long/flat trend-following strategies, both for setting expectations and for gauging current relative performance.
  • If we acknowledge that for a strategy to outperform over the long-run, it must undergo shorter periods of underperformance, using this symmetric benchmark can isolate market environments that underperformance should be expected.
  • Diversifying risk-management approaches (e.g. pairing strategic allocation with tactical trend-following) can manage events that are unfavorable to one strategy, and benchmarking is a tool to set expectations around the level of risk management necessary in different market environments.

Any strategy that deviates from the most basic is compared to a benchmark. But how do you choose an appropriate benchmark?

The complicated nature of benchmarking can be easily seen by considering something as simple as a value stock strategy.

You may pit your concentrated value manager you currently use up against the more diversified value manager you used previously. At that time, you may have compared that value manager to a systematic smart-beta ETF like the iShares S&P 500 Value ETF (ticker: IVE). And if you were invested in that ETF, you might compare its performance to the S&P 500.

What prevents you from benchmarking them all to the S&P 500? Or from benchmarking the concentrated value strategy to all of the other three?

Benchmark choices are not unique and are highly dependent on what aspect of performance you wish to measure.

Benchmarking is one of the most frequently abused facets of investing. It can be extremely useful when applied in the correct manner, but most of the time, it is simply a hurdle to sticking with an investment plan.

In an ideal world, the only benchmark for an investor would be whether or not they are on track for hitting their financial goals. However, in an industry obsessed with relative performance, choosing a benchmark is a necessary exercise.

This commentary will explore some of the important considerations when choosing a benchmark for trend-following strategies.

The Purpose of a Trend-Following Benchmark

As an investment manager, our goal with benchmarking is to check that a strategy’s performance is in line with our expectations. Performance versus a benchmark can answer questions such as:

  • Is the out- or underperformance appropriate for the given market environment?
  • Is the magnitude of out- or underperformance typical?
  • How is the strategy behaving in the context of other ways of managing risk?

With long/flat trend-following strategies, the appropriate benchmark should gauge when the manager is making correct or incorrect calls in either direction.

Unfortunately, we frequently see long/flat equity trend-following strategies benchmarked to an all-equity index like the S&P 500. This is similar to the coinflip game we outlined in our previous commentary about protecting and participating with trend-following.[1]

The behavioral implications of this kind of benchmarking are summarized in the table below.

The two cases with wrong calls – to move to cash when the market goes up or remain invested when the market goes down – are appropriately labeled, as is the correct call to move to cash when the market is going down. However, when the market is going up and the strategy is invested, it is merely keeping up with its benchmark even though it is behaving just as one would want it to.

To reward the strategy in either correct call case, the benchmark should consist of allocations to both equity and cash.

A benchmark like this can provide objective answers to the questions outlined above.

Deriving a Trend-Following Benchmark

Sticking with the trend-following strategy example we outlined in our previous commentary[2], we can look at some of the consequences of choosing different benchmarks in terms of how much the trend-following strategy deviates from them over time.

The chart below shows the annualized tracking error of the strategy to the range of strategic proportions of equity and cash.

Source: Kenneth French Data Library. Data from July 1926 – February 2018. Calculations by Newfound Research. Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions.  This document does not reflect the actual performance results of any Newfound investment strategy or index.  All returns are backtested and hypothetical.  Past performance is not a guarantee of future results.

The benchmark that minimizes the tracking error is a 47% allocation to equities and 53% to cash. This 0.47 is also the beta of the trend-following strategy, so we can think of this benchmark as accounting for the risk profile of the strategy over the entire 92-year period.

But what if we took a narrower view by constraining this analysis to recent performance?

The chart below shows the equity allocation of the benchmark that minimizes the tracking error to the trend-following strategy over rolling 1-year periods.

Source: Kenneth French Data Library. Data from July 1926 – February 2018. Calculations by Newfound Research. Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions.  This document does not reflect the actual performance results of any Newfound investment strategy or index.  All returns are backtested and hypothetical.  Past performance is not a guarantee of future results.

A couple of features stand out here.

First, if we constrain our lookback period to one year, a time-period over which many investors exhibit anchoring bias, then the “benchmark” that we may think we will closely track – the one we are mentally tied to – might be the one that we deviate the most from over the next year.

And secondly, the approximately 50/50 benchmark calculated using the entire history of the strategy is rarely the one that minimizes tracking error over the short term.

The median equity allocation in these benchmarks is 80%, the average is 67%, and the data is highly clustered at the extremes of 100% equity and 100% cash.

Source: Kenneth French Data Library. Data from July 1926 – February 2018. Calculations by Newfound Research. Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions. This document does not reflect the actual performance results of any Newfound investment strategy or index.  All returns are backtested and hypothetical.  Past performance is not a guarantee of future results.

The Intuitive Trend-Following Benchmark

Is there a problem in determining a benchmark using the tracking error over the entire period?

One issue is that it is being calculated with the benefit of hindsight. If you had started a trend-following strategy back in the 1930s, you would have arrived at a different equity allocation for the benchmark based on this analysis given the available data (e.g. using data up until the end of 1935 yields an equity allocation of 37%).

To remove this reliance on having a sufficiently long backtest, our preference is to rely more on the strategy’s rules and how we would use it in a portfolio to determine our trend-following benchmarks.

For a trend following strategy that pivots between stocks and cash, a 50/50 benchmark is a natural choice.

It is broad enough to include the assets in the trend-following strategy’s investment universe while being neutral to the calls to be long or flat.

Seeing the 50/50 portfolio be the answer to the tracking error minimization problem over the entire data simply provides empirical evidence for its use.

One argument against using a 50/50 blend could focus on the fact that the market is generally up more frequently than it is down, at least historically. While this is true, the magnitude of down moves has often been larger than the magnitude of up moves. Since this strategy is explicitly meant as a risk management tool, accounting for both the magnitude and the frequency is prudent.

Another argument against its use could be the belief that we are entering a different market environment where history will not be an accurate guide going forward. However, given the random nature of market moves coupled with the behavioral tendencies of investors to overreact, herd, and anchor, a benchmark close to a 50/50 is likely still a fitting choice.

Setting Expectations with a Trend-Following Benchmark

Now that we have a benchmark to use, how do we use it to set our expectations?

Neglecting the historical data for the moment, from the ex-ante perspective, it is helpful to decompose a typical market cycle into four different segments and assess how we expect trend-following to behave:

  • Initial decline – Equity markets begin to sell off, and the fully invested trend-following strategy underperforms the 50/50 benchmark.
  • Prolonged drawdown – The trend-following strategy adapts to the decline and moves to cash. The trend-following strategy outperforms.
  • Initial recovery – The trend-following strategy is still in cash and lags the benchmark as prices rebound off the bottom.
  • Sustained recovery – The trend-following strategy reinvests and captures more of the upside than the benchmark.

Of course, this is a somewhat ideal scenario that rarely plays out perfectly. Whipsaw events occur as prices recover (decline) before declining (recovering) again.

But it is important to note how the level of risk relative to this 50/50 benchmark varies over time.

Contrast this with something like an all equity strategy benchmarked to the S&P 500 where the risk is likely to be similar during most market environments.

Now, if we look at the historical data, we can see this borne out in the graph of the drawdowns for trend-following and the 50/50 benchmark.

Source: Kenneth French Data Library. Data from July 1926 – February 2018. Calculations by Newfound Research. Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions.  This document does not reflect the actual performance results of any Newfound investment strategy or index.  All returns are backtested and hypothetical.  Past performance is not a guarantee of future results.

In most prolonged and major (>20%) drawdowns, trend-following first underperforms the benchmark, then outperforms, then lags as equities improve, and then outperform again.

Using the most recent example of the Financial Crisis, we can see the capture ratios verses the benchmark in each regime.

Source: Kenneth French Data Library. Data from October 2007 – February 2018. Calculations by Newfound Research. Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions.  This document does not reflect the actual performance results of any Newfound investment strategy or index.  All returns are backtested and hypothetical.  Past performance is not a guarantee of future results.

The underperformance of the trend-following strategy verses the benchmark is in line with expectations based on how the strategy is desired to work.

Another way to use the benchmark to set expectations is to look at rolling returns historically. This gives context for the current out- or underperformance relative to the benchmark.

From this we can see which percentile the current return falls into or check to see how many standard deviations it is away from the average level of relative performance.

Source: Kenneth French Data Library. Data from July 1926 – February 2018. Calculations by Newfound Research. Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions.  This document does not reflect the actual performance results of any Newfound investment strategy or index.  All returns are backtested and hypothetical.  Past performance is not a guarantee of future results.

In all this, there are a few important points to keep in mind:

  • Price moves that occur faster than the scope of the trend-following measurement can be one source of the largest underperformance events.
  • Along a similar vein, whipsaw is a key risk of trend-following. Highly oscillatory markets will not be favorable to trend-following. In these scenarios, trend following can underperform even fully invested equities.
  • With percentile analysis, there is always a first time for anything. Having a rich data history covering a variety of market scenarios mitigates this, but setting new percentiles, either on the low end or high end, is always possible.
  • Sometimes a strategy is expected to lag its benchmark in a given market environment. A primary goal with benchmarking is it accurately set these expectations for the potential magnitude of relative performance and design the portfolio accordingly.

Conclusion

Benchmarking a trend-following strategy can be a difficult exercise in managing behavioral biases. With the tendency to benchmark all equity-based strategies to an all-equity index, investors often set themselves up for a let-down in a bull market with trend-following.

With benchmarking, the focus is often on lagging the benchmark by “too much.” This is what an all-equity benchmark can do to trend-following. However, the issue is symmetric: beating the benchmark by “too much” can also signal either an issue with the strategy or with the benchmark choice. This is why we would not benchmark a long/flat trend-following strategy to cash.

A 50/50 portfolio of equities and cash is generally an appropriate benchmark for long/flat trend-following strategies. This benchmark allows us to measure the strategy’s ability to correctly allocate when equities are both increasing or decreasing.

Too often, investors use benchmarking solely to see which strategy is beating the benchmark by the most. While this can be a use for very similar strategies (e.g. a set of different value managers), we must always be careful not to compare apples to oranges.

A benchmark should not conjure up an image of a dog race where the set of investment strategies are the dogs and the benchmark is the bunny out ahead, always leading the way.

We must always acknowledge that for a strategy to outperform over the long-run, it must undergo shorter periods of underperformance. Diversifying approaches can manage events that are unfavorable to one strategy, and benchmarking is a tool to set expectations around the level of risk management necessary in different market environments.

 

[1] https://blog.thinknewfound.com/2018/05/leverage-and-trend-following/

[2] https://blog.thinknewfound.com/2018/03/protect-participate-managing-drawdowns-with-trend-following/

Leverage and Trend Following

This post is available as a PDF download here.

Summary­

  • We typically discuss trend following in the context of risk management for investors looking to diversify their diversifiers.
  • While we believe that trend following is most appropriate for investors concerned about sequence risk, levered trend following may have use for investors pursuing growth.
  • In a simple back-test, a naïve levered trend following considerably increases annualized returns and reduces negative skew and kurtosis (“fat tails”).
  • The introduced leverage, however, significantly increases annualized volatility, meaning that the strategy still exhibits significant and large drawdown profiles.
  • Nevertheless, trend following may be a way to allow for the incorporation of leverage with reduced risk of permanent portfolio impairment that would otherwise occur from large drawdowns.

In an industry obsessed with alpha, our view here at Newfound has long been to take a risk-first approach to investing.  In light of this, when we discuss trend following techniques, it is often with an eye towards explicitly managing drawdowns.  Our aim is to help investors diversify their diversifiers and better manage the potentially devastation that sequence risk can wreak upon their portfolios.

Thus, we often discuss the application of trend following for soon-to-be and recent retirees who are in peak sequence risk years.

  • Empirical evidence suggests that trend following can be a highly effective means of limiting exposure to significant and prolonged drawdowns.
  • Trend following is complementary to other diversifiers like fixed income, which can theoretically increase the Sharpe ratio of the diversification bucket as a whole.
  • Instead of acting as a static hedge, the dynamic approach of trend following can also help investors take advantage of market tailwinds. This may be particularly important if real interest rates remain low.
  • The potential tax inefficiency of trend following is significantly lower when the alternative risk management technique is fixed income.

Despite our focus on using trend following to manage sequence risk, we often receive questions from investors still within their accumulation phase asking whether trend following can be appropriate for them as well.  Most frequently, the question is, “If trend following can manage downside risk, can I use a levered approach to trend following in hopes of boosting returns?”

This commentary explores that idea, specifically in the context of available levered ETFs.

Does Naïve Levered Trend Following Work?

In an effort to avoid overfitting our results to any one particular model or parameterization of trend following, we have constructed our signals employing a model-of-models approach [1] Specifically, we use four different definitions of trend for a given N-period lookback:

  • Price-Minus-Moving-Average: When price is above its N-period simple moving average, invest.Otherwise, divest.
  • EWMA Cross-Over: When the (N/4)-length exponentially-weighted moving average is above the (N/2)-length exponentially-weighted moving average, invest.Otherwise, divest.
  • EWMA Slope: When the (N/2)-length exponentially-weighted moving average is positively sloped, invest. Otherwise, divest.
  • Percentile Channel: When price crossed above the trailing 75thpercentile over the prior N-periods, invest. Stay invested until it crosses below its trailing 25thpercentile over the prior N-periods.  Stay divested until it crosses back above the 75th

For each of these four models, we also run a number of parameterizations covering 6-to-18-month lookbacks.  In grand total, there are 4 models with 5 parameterizations each, giving us 30 variations of trend signals.

Using these signals, we construct three models. In the first model, we simply invest in U.S. equities in proportion to the number of signals that are positive. For example, if 75% of the trend following signals are positive, the portfolio is 75% invested in U.S. equities and 25% in the risk-free asset.

For our leveraged model, we simply multiply the percentage of signals by 2x and invest that proportion of our portfolio in U.S. equities and the remainder in the risk-free asset.  In those cases where the amount invested in U.S. equities exceeds 100% of the portfolio, we assume a negative allocation to the risk-free asset (e.g. if we invest 150% of our assets in U.S. equities, we assume a -50% allocation to the risk-free asset).

With the benefit of hindsight, we should not be surprised at the results.  If we know that trend following is effective at limiting severe and prolonged drawdowns (the kryptonite to levered investors), then it should come as no surprise that a levered trend following strategy does quite well.

It is well worth pointing out, however, that a highly levered strategy can be quickly wiped out by a sudden and immediate drawdown that trend following is unable to sidestep.  Assuming a 2x levered position, our portfolio would be quickly wiped out by a sharp 50% correction.  While such an event did not happen during the 1900s for U.S. equities, that does not mean it cannot happen in the future.  Caveat emptor.

Logarithmically-plotted equity curves can be deceiving, so it is important that we also compare the annual return characteristics.

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

While we can see that a simple trend following approach effectively “clips” the tails of the underlying distribution – giving up both the best and the worst annual returns – the levered strategy still has significant mass in both directions.  Evaluating the first several moments of the distributions, however, we see that both simple and levered trend following significantly reduce the skew and kurtosis of the return distribution.

MeanStandard DeviationSkewKurtosis
U.S. Equities9.4%19%-1.011.36
Trend Following9.5%13%0.09-0.92
Levered Trend Following14.4%26%0.11-0.78

 

Nevertheless, the standard deviation of the levered trend following strategy exceeds even that of the underlying asset, a potential indication that expectations for the approach may be less about, “Can I avoid large drawdowns?” and more about, “Can I use leverage for growth and still avoid catastrophe?”  We can see this by plotting the joint annual log-return distributions.

We can see that for U.S. equity returns between 0% and -20%, the Levered Trend Following strategy can exhibit returns between -20% and -40%.  About 11% of the observations fall into this category, making it an occurrence that a levered trend follower should expect to experience multiple times in their investment lifecycle.  We can even see one year where U.S. equities are slightly positive and the levered model exhibits a near -30% return.  It is in the most extreme U.S. equity years – those exceeding -20% – that the trend following aspect appears to come into play.

We must also ask the question, “can this idea survive associated fees?”  If investors are looking to apply this approach using levered ETFs, they must consider the expense ratios of the ETFs themselves, transaction costs, and bid/ask spreads.  Here we will use the ProShares Ultra S&P 500 ETF (“SSO”) as a data proxy.  The expense ratio is 0.90% and the average bid/ask spread is 0.03%.  Since transactions costs vary, we will assume an added annual 0.20% fee for asset-based pricing.

In comparison, for the naïve model, we will use the SPDR S&P 500 ETF (“SPY”) as the data proxy and assume an expense ratio of 0.09% and an average bid/ask spread 0.004%.  Since most platforms have a vanilla S&P 500 ETF on their no-transaction fee list, we will not add any explicit transaction costs.

We plot the strategy equity curves below net of these assumed fees.

The annualized return for the Levered Trend Following strategy declines from 15.9% to 14.5%, while the unlevered version only falls from 10.1% to 10.0%.  While the overall return of the levered version declines by 140 basis points per year, it still far exceeds the total return performance of the unlevered version. 

Conclusion

Based upon this initial analysis, it would appear that a simple, levered trend following approach may be worth further consideration for investors in the accumulation phase of their investment lifecycle.

Do-it-yourself investors may have no problem implementing this idea on their own using levered ETFs, but other investors may prefer a simple, packaged approach.  Unfortunately, as far as we are aware, no such packaged product exists in the marketplace today.

However, one workaround may be to utilize levered ETFs to “make room” for an unlevered trend following strategy.  For example, if a growth-oriented investor currently holdings an 80/20 stock/bond mix and wanted to introduce a 20% allocation to trend following, they could re-orient their portfolio to be 60% stocks, 10% 2x levered stocks, 10% 2x levered bonds, and 20% trend following.  This would have the effect of being an 80/20 stock/bond portfolio with 20% leverage applied to introduce the trend following strategy.  While there are the nuances of daily reset to consider in the levered ETF solutions, this approach may allow for the modest introduction of levered trend following into the portfolio.

It is worth noting that while we employed up to 2x leverage in this commentary, there is no reason investors could not apply a lower amount, either by mixing levered and unlevered ETFs, or by using a solution like the new Portfolio+ line-up from Direxion, which applies 1.25x leverage to underlying indices.

As we like to say here at Newfound, “risk cannot be destroyed, only transformed.” While this commentary explored levered trend following in comparison to unlevered exposure, a more apt comparison might simply be to levered market exposure.  We suspect that the trend following overlay creates the same transformation: a reduction of the best and worst years at the cost of whipsaw. However, the introduction of leverage further heightens the risk of sudden and immediate drawdowns: the exact loss profile trend following is ill-suited to avoid.

 


 

[1] Nothing in this commentary reflects an actual investment strategy or model managed by Newfound and any investment strategies or investment approaches reflected herein are constructed solely for purposes of analyzing and evaluating the topics herein.

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