The Research Library of Newfound Research

Month: September 2018

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.

Timing Equity Returns Using Monetary Policy

This post is available as PDF download here.

Summary

  • Can the monetary policy environment be used to predict global equity market returns? Should we overweight/buy countries with expansionary monetary policy regimes and underweight/sell countries with contractionary monetary policy regimes?
  • In twelve of the fourteen countries studied, both nominal and real equity returns are higher (lower) when the central banks most recent action was to cut (hike) rates. For example, nominal U.S. equity returns are 1.8% higher during expansionary environments.  Real U.S. equity returns are 3.6% higher during expansionary environments.  The gap is even larger outside the United States.
  • However, the monetary policy regime explains very little of the overall variation in equity returns from a statistical standpoint.
  • While many of the return differentials during expansionary vs. contractionary regimes seem large at first glance, few are statistically significant once we realistically account for the salient features of equity returns and monetary policy. In other words, we can’t be sure the return differentials didn’t arise simply due to luck.
  • As a result, evidence suggests that making buy/sell decisions on the equity markets of a given country using monetary policy regime as the lone signal is overly ambitious.

Can the monetary policy environment be used to predict global equity market returns?  Should we overweight/buy countries with expansionary monetary policy and underweight/sell countries with contractionary monetary policy?

Such are the softball questions that our readers tend to send in.

Intuitively, it’s clear that monetary policy has some type of impact on equity returns.  After all, if the Fed raised rates to 10% tomorrow, that would clearly impact stocks.

The more pertinent question though is if these impacts always tend to be in one direction.  It’s relatively straightforward to build a narrative around why this could be the case.  After all, the Fed’s primary tool to manage its unemployment and inflation mandates is the discount rate.  Typically, we think about the Fed hiking interest rates when the economy gets “too hot” and cutting them when it gets “too cold.”  If hiking (cutting) rates has the goal of slowing (stimulating) the economy, it’s plausible to think that equity returns would be pushed lower (higher).

There are a number of good academic papers on the subject. Ioannadis and Kontonikas (2006) is a good place to start. The paper investigates the impact of monetary policy shifts on equity returns in thirteen OECD countries1 from 1972 to 2002.

Their analysis can be split into two parts.  First, they explore whether there is a contemporaneous relationship between equity returns and short-term interest rates (i.e. how do equity returns respond to interest rate changes?)2.  If there is a relationship, are returns likely to be higher or lower in months where rates increase?

Source: “Monetary Policy and the Stock Market: Some International Evidence” by Ioannadis and Kontonikas (2006).

 

In twelve of the thirteen countries, there is a negative relationship between interest rate changes and equity returns.  Equity returns tend to be lower in months where short-term rates increase.  The relationship is statistically significant at the 5% level in eight of the countries, including the United States.

While these results are interesting, they aren’t of much direct use for investors because, as mentioned earlier, they are contemporaneous.  Knowing that equity returns are lower in months where short-term interest rates rise is actionable only if we can accurately predict the interest rate movements ahead of time.

As an aside, if there is one predictive interest rate model we subscribe to, it’s that height matters.

Fortunately, this is where the authors’ second avenue of analysis comes into play.  In this section, they first classify each month as being part of either a contractionary or an expansionary monetary policy regime.  A month is part of a contractionary regime if the last change in the discount rate was positive (i.e. the last action by that country’s central bank was a hike).  Similarly, a month is part of an expansionary regime if the last central bank action was a rate cut.

We illustrate this classification for the United States below.  Orange shading indicates contractionary regimes and gray shading indicates expansionary regimes.

The authors then regress monthly equity returns on a dummy variable representing which regime a month belongs to.  Importantly, this is not a contemporaneous analysis: we know whether the last rate change was positive or negative heading into the month.  Quoting the paper:

“The estimated beta coefficients associated with the local monetary environment variable are negative and statistically significant in six countries (Finland, France, Italy, Switzerland, UK, US).  Hence, for those countries our measure of the stance of monetary policy contains significant information, which can be used to forecast expected stock returns.  Particularly, we find that restrictive (expansive) monetary policy stance decreases (increases) expected stock returns.”

Do we agree?

Partially.  When we analyze the data using a similar methodology and with data updated through 20183, we indeed find a negative relationship between monetary policy environment and forward 1-month equity returns.  For example, annualized nominal returns in the United States were 10.6% and 8.8% in expansionary and contractionary regimes, respectively.  The gap is larger for real returns – 7.5% in expansionary environments and 3.9% in contractionary environments.

Source: Bloomberg, MSCI, Newfound Research. Past performance does not guarantee future results. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of dividends.

 

A similar, albeit more pronounced, pattern emerges when we go outside the United States and consider thirteen other countries.

 

Source: Bloomberg, MSCI, Newfound Research. Past performance does not guarantee future results. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of dividends.

 

The results are especially striking in ten of the fourteen countries examined. The effect in the U.S. was smaller compared to many of these.

 

Source: Bloomberg, MSCI, Newfound Research. Past performance does not guarantee future results. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of dividends.

 

That being said, we think the statistical significance (and therefore investing merit) is less obvious.  Now, it is certainly the case that many of these differences are statistically significant when measured traditionally.  In this sense, our results agree with Ioannadis and Kontonikas (2006).

However, there are two issues to consider.  First, the R2 values for the regressions are very low.  For example, the highest R2 in the paper is 0.037 for Finland.  In other words, the monetary regime models do not do a particularly great job explaining stock returns.

Second, it’s important to take a step back and think about how monetary regimes evolve.  Central banks, especially today, typically don’t raise rates one month, cut the next, raise the next, etc.  Instead, these regimes tend to last multiple months or years.  The traditional significance testing assumes the former type of behavior, when the latter better reflects reality.

Now, this wouldn’t be a major issue if stock returns were what statisticians call “IID” (independent and identically distributed).  The results of a coin flip are IID.  The probability of heads and tails are unchanged across trials and the result of one flip doesn’t impact the odds for the next.

Daily temperatures are not IID.  The distribution of temperatures is very different for a day in December than they are for a day in July, at least for most of us.  They are not identical.  Nor are they independent.  Today’s high temperature gives us some information that tomorrow’s temperature has a good chance of hitting that value as well.

Needless to say, stock returns behave more like temperatures than they do coin flips.  This combination of facts – stock returns being non-IID (exhibiting both heteroskedasticity4 and autocorrelation) and monetary policy regimes having the tendency to persist over the medium term – leads to false positives.  What at first glance look like statistically significant relationships are no longer up to snuff because the model was poorly constructed in the first place.

To flush out these issues, we used two different simulation-based approaches to test for the significance of return differences across regimes.5

The first approach works as follows for each country:

  1. Compute the probability of expansionary and contractionary regimes using that country’ actual history.
  2. Randomly classify each month into one of the two regimes using the probabilities from #1.
  3. Compute the difference between annualized returns in expansionary vs. contractionary regimes using that country’s actual equity returns.
  4. Return to #2, repeating 10,000 times total.

This approach assumes that today’s monetary policy regime says nothing about what tomorrow’s may be. We have transformed monetary policy into an IID variable.  Below, we plot the regime produced by a single iteration of the simulation. Clearly, this is not realistic.

Source: Newfound Research

 

The second approach is similar to the first in all ways except how the monetary policy regimes are simulated.  The algorithm is:

  1. Compute the transition matrix for each country using that country’s actual history of monetary policy shifts. A transition matrix specifies the likelihood of moving to each regime state given that we were in a given regime the prior month.  For example, if last month was contractionary, we may have a 95% probability of staying contractionary and a 5% probability of moving to an expansionary state.
  2. Randomly classify each month into one of the two regimes using the transition matrix from #1. We have to determine how to seed the simulation (i.e. which state do we start off in).  We do this randomly using the overall historical probability of contractionary/expansionary regimes for that country.
  3. Compute the difference between annualized returns in expansionary vs. contractionary regimes using that country’s actual equity returns.
  4. Return to #2, repeating 10,000 times total.

The regimes produced by this simulation look much more realistic.

Source: Newfound Research

 

When we compare the distribution of return differentials produced by each of the simulation approaches, we see that the second produces a wider range of outcomes.

 

Source: Newfound Research

 

In the table below, we present the confidence intervals for return differentials using each algorithm.  We see that the differentials are statistically significant in six of the fourteen countries when we use the first methodology that produces unrealistic monetary regimes.  Only four countries show statistically significant results with the improved second method.

 

CountrySpread Between Annualized Real Returns95% CI
First Method
P-Value
First Method
95% CI
Second Method
P-Value
Second Method
Australia+9.8%-1.1% to +20.7%7.8%-1.5% to +21.1%8.9%
Belgium+14.6%+4.1% to +25.1%0.6%+0.7% to +28.5%3.9%
Canada-0.7%-12.2% to +10.8%90.5%-14.2% to +12.8%91.9%
Finland+29.0%+6.5% to +51.5%1.2%-2.4% to +60.4%7.1%
France+17.3%-0.5% to +35.1%5.7%-10.8% to +45.4%22.7%
Germany+10.8%-1.1% to +22.7%7.5%-2.8% to +24.4%12.0%
Italy+17.3%+3.6% to +31.0%1.3%-0.2% to +34.8%5.3%
Japan+26.5%+12.1% to +40.9%0.0%+3.4% to +49.6%2.5%
Netherlands+16.8%-1.8% to +35.4%7.6%-11.6% to +45.2%24.7%
Spain+23.8%+11.3% to +36.3%0.0%+9.9% to +37.7%0.1%
Sweden+30.4%+12.7% to +48.1%0.1%+4.7% to +56.1%2.1%
Switzerland+2.3%-11.5% to +16.1%74.4%-26.3% to +30.9%87.5%
United Kingdom-0.6%-11.5% to +10.3%91.4%-12.0% to +10.8%91.8%
United States+3.6%-5.0% to +12.2%41.1%-6.0% to +13.2%46.2%

Source: Bloomberg, MSCI, Newfound Research

 

Conclusion

We find that global equity returns have been more than 10% higher during expansionary regimes.  At first glance, such a large differential suggests there may be an opportunity to profitably trade stocks based on what regime a given country is in.

Unfortunately, the return differentials, while large, are generally not statistically significant when we account for the realistic features of equity returns and monetary policy regimes. In plain English, we can’t be sure that the return differentials didn’t arise simply due to randomness.

This result isn’t too surprising when we consider the complexity of the relationship between equity returns and interest rates (despite what financial commentators may have you believe).  Interest rate changes can impact both the numerator (dividends/dividend growth) and denominator (discount rate) of the dividend discount model in complex ways.  In addition, there are numerous other factors that impact equity returns and are unrelated / only loosely related to interest rates.

When such complexity reigns, it is probably a bit ambitious to rely on a standalone measure of monetary policy regime as a predictor of equity returns.

 


 

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