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Category: Weekly Commentary Page 8 of 21

Tactical Credit

By

On June 3, 2019

In Credit, Momentum, Popular, Risk & Style Premia, Weekly Commentary

This post is available as a PDF download here.

Summary­

  • In this commentary we explore tactical credit strategies that switch between high yield bonds and core fixed income exposures.
  • We find that short-term momentum signals generate statistically significant annualized excess returns.
  • We use a cross-section of statistically significant strategy parameterizations to generate an ensemble strategy.Consistent with past research, we find that this ensemble approach helps reduce idiosyncratic specification risk and dramatically increases the strategy’s information ratio above the median underlying strategy information ratio.
  • To gain a better understanding of the strategy, we attempt to determine the source of strategy returns. We find that a significant proportion of returns are generated as price returns occurring during periods when credit spreads are above their median value and are expanding.
  • Excluding the 2000-2003 and 2008-2009 sub-periods reduces gross-of-cost strategy returns from 2.9% to 1.5%, bringing into question how effective post-of-cost implementation can be if we do not necessarily expect another crisis period to unfold.

There is a certain class of strategies we get asked about quite frequently but have never written much on: tactical credit.

The signals driving these strategies can vary significantly (including momentum, valuation, carry, macro-economic, et cetera) and implementation can range from individual bonds to broad index exposure to credit default swaps.  The simplest approach we see, however, are high yield switching strategies.  The strategies typically allocate between high yield corporate bonds and core fixed income (or short-to-medium-term U.S. Treasuries) predominately based upon some sort of momentum-driven signal.

It is easy to see why this seemingly naïve approach has been attractive.  Implementing a simple rotation between –high-yield corporates– and –core U.S. fixed income– with a 3-month lookback with 1-month hold creates a fairly attractive looking –tactical credit– strategy.

Source: Tiingo.  Calculations by Newfound Research.   Tactical Credit strategy returns are hypothetical and backtested.  Returns gross of all management fees and taxes, but net of underlying fund fees.  HY Corporates represents the Vanguard High-Yield Corporate Fund (VWEHX).  Core Bonds is represented by the Vanguard Total. Bond Market Index Fund (VBMFX).  Returns assume the reinvestment of all distributions.

Visualizing the ratio of the equity curves over time, we see a return profile that is reminiscent of past writings on tactical and trend equity strategies. The tactical credit strategy tends to outperform core bonds during most periods, with the exception of periods of economic stress (e.g. 2000-2002 or 2008).  On the other hand, the tactical credit strategy tends to underperform high yield corporates in most environments, but has historically added significant value in those same periods of economic stress.

Source: Tiingo.  Calculations by Newfound Research.   Tactical Credit strategy returns are hypothetical and backtested.  Returns gross of all management fees and taxes, but net of underlying fund fees.  HY Corporates represents the Vanguard High-Yield Corporate Fund (VWEHX).  Core Bonds is represented by the Vanguard Total. Bond Market Index Fund (VBMFX).  Returns assume the reinvestment of all distributions.

This is akin to tactical equity strategies, which have historically out-performed the safety asset (e.g. cash) during periods of equity market tailwinds, but under-performed buy-and-hold equity during those periods due to switching costs and whipsaw. As the most aggressive stance the tactical credit strategy can take is a 100% position in high yield corporates, it would be unrealistic for us to expect such a strategy to out-perform in an environment that is conducive to strong high yield performance.

What makes this strategy different than tactical equity, however, is that the vast majority of total return in these asset classes comes from income rather than growth.  In fact, since the 1990s, the price return of high yield bonds has annualized at -0.8%.  This loss reflects defaults occurring within the portfolio offset by recovery rates.1

This is potentially problematic for a tactical strategy as it implies a significant potential opportunity cost of switching out of high yield.  However, we can also see that the price return is volatile.  In years like 2008, the price return was -27%, more than offsetting the 7%+ yield you would have achieved just holding the fund.

Source: Tiingo.  Calculations by Newfound Research.   Returns gross of all management fees and taxes, but net of underlying fund fees.

Like trend equity, we can think of this tactical credit strategy as being a combination of two portfolios:

  • A fixed-mix of 50% high yield corporates and 50% core bonds; and
  • 50% exposure to a dollar-neutral long/short portfolio that captures the tactical bet.

For example, when the tactical credit portfolio is 100% in high yield corporates, we can think of this as being a 50/50 strategy portfolio with a 50% overlay that is 100% long high yield corporates and 100% short core bonds, leading to a net exposure that is 100% long high yield corporates.

Thinking in this manner allows us to isolate the active returns of the portfolio actually being generated by the tactical signals and determine value-add beyond a diversified buy-and-hold core.  Thus, for the remainder of this commentary we will focus our exploration on the long/short component.

Before we go any further, we do want to address that a naïve comparison between high yield corporates and core fixed income may be plagued by changing composition in the underlying portfolios as well as unintended bets.  For example, without specifically duration matching the legs of the portfolio, it is likely that a dollar-neutral long/short portfolio will have residual interest rate exposure and will not represent an isolated credit bet.  Thus, naïve total return comparisons will capture both interest rate and credit-driven effects.

This is further complicated by the fact that sensitivity to these factors will change over time due both to the math of fixed income (e.g. interest rate sensitivity changing over time due to higher order effects like convexity) as well as changes in the underlying portfolio composition.  If we are not going to specifically measure and hedge out these unintended bets, we will likely want to rely on faster signals such that the bet our portfolio was attempting to capture is no longer reflected by the holdings.

We will begin by first evaluating the stability of our momentum signals.  We do this by varying formation period (i.e. lookback) and holding period of our momentum rotation strategy and calculating the corresponding t-statistic of the equity curve’s returns.  We plot the t-statistics below and specifically highlight those regions were t-statistics exceed 2, a common threshold for significance.

Source: Tiingo.  Calculations by Newfound Research.

It should be noted that data for this study only goes back to 1990, so achieving statistical significance is more difficult as the sample size is significantly reduced. Nevertheless, unlike trend equity which tends to exhibit strong significance across formation periods ranging 6-to-18 months, we see a much more limited region with tactical credit. Only formation periods from 3-to-5 months appear significant, and only with holding periods where the total period (formation plus holding period) is less than 6-months.

Note that our original choice of 63-day (approximately 3 months) formation and 21-day (approximately 1 month) hold falls within this region.

We can also see that very short formation and holding period combinations (e.g. less than one month) also appear significant.  This may be due to the design of our test.  To achieve the longest history for this study, we employed mutual funds.  However, mutual funds holding less liquid underlying securities tend to exhibit positive autocorrelation. While we adjusted realized volatility levels for this autocorrelation effect in an effort to create more realistic t-statistics, it is likely that positive results in this hyper short-term region emerge from this effect.

Finally, we can see another rather robust region representing the same formation period of 3-to-5 months, but a much longer holding length of 10-to-12 months.  For the remainder of this commentary, we’ll ignore this region, though it warrants further study.

Assuming formation and holding periods going to a daily granularity, the left-most region represents over 1,800 possible strategy combinations.  Without any particular reason for choosing one over another, we will embrace an ensemble approach, calculating the target weights for all possible combinations and averaging them together in a virtual portfolio-of-portfolios configuration.

Below we plot the long/short allocations as well as the equity curve for the ensemble long/short tactical credit strategy.

Source: Tiingo.  Calculations by Newfound Research.   Tactical Credit strategy returns are hypothetical and backtested.  Returns gross of all management fees and taxes, but net of underlying fund fees.  Returns assume the reinvestment of all distributions.

Note that each leg of the long/short portfolio does not necessarily equal 100% notional.  This reflects conflicting signals in the underlying portfolios, causing the ensemble strategy to reduce its gross allocation as a reflection of uncertainty.

As a quick aside, we do want to highlight how the performance of the ensemble compares to the performance of the underlying strategies.

Below we plot the annualized return, annualized volatility, maximum drawdown, and information ratio of all the underlying equity curves of the strategies that make up the ensemble.  We also identify the –ensemble approach–.  While we can see that the ensemble approach brings the annualized return in-line with the median annualized return, its annualized volatility is in the 14thpercentile and its maximum drawdown is in the 8thpercentile.

Source: Tiingo.  Calculations by Newfound Research.   Tactical Credit strategy returns are hypothetical and backtested.  Returns gross of all management fees and taxes, but net of underlying fund fees.  Returns assume the reinvestment of all distributions.

By maintaining the median annualized return and significantly reducing annualized volatility, the ensemble has an information ratio in the 78thpercentile.  As we’ve demonstrated in prior commentaries, by diversifying idiosyncratic specification risk, the ensemble approach is able to generate an information ratio significantly higher than the median without having to explicitly choose which specification we believe will necessarily outperform.

Given this ensemble implementation, we can now ask, “what is the driving force of strategy returns?”  In other words, does the strategy create returns by harvesting price return differences or through carry (yield) differences?

One simple way of evaluating this question is by evaluating the strategy’s sensitivity to changes in credit spreads.  Specifically, we can calculate daily changes in the ICE BofAML US High Yield Master II Option-Adjusted Spread and multiply it against the strategy’s exposure to high yield bonds on the prior day.

By accumulating these weighted changes over time, we can determine how much spread change the strategy has captured.  We can break this down further by isolating positive and negative change days and trying to figure out whether the strategy has benefited from avoiding spread expansion or from harvesting spread contraction.

In the graph below, we can see that the strategy harvested approximately 35,000 basis points (“bps”) from 12/1996 to present (the period for which credit spread data was available). Point-to-point, credit spreads actually widened by 100bps over the period, indicating that tactical changes were able to harvest significant changes in spreads.

Source: St. Louis Federal Reserve.  Calculations by Newfound Research.  

We can see that over the full period, the strategy predominately benefited from harvesting contracting spreads, as exposure to expanding spreads had a cumulative net zero impact.  This analysis is incredibly regime dependent, however, and we can see that periods like 2000-2003 and 2008 saw a large benefit from short-exposure in high yield during a period when spreads were expanding.

We can even see that in the case of post-2008, switching to long high yield exposure allowed the strategy to benefit from subsequent credit spread declines.

While this analysis provides some indication that the strategy benefits from harvesting credit spread changes, we can dig deeper by taking a regime-dependent view of performance. Specifically, we can look at strategy returns conditional upon whether spreads are above or below their long-term median, as well as whether they expand or contract in a given month.

Source: St. Louis Federal Reserve.  Calculations by Newfound Research.  Tactical Credit strategy returns are hypothetical and backtested.  Returns gross of all management fees and taxes, but net of underlying fund fees.  Returns assume the reinvestment of all distributions.

Most of the strategy return appears to occur during times when spreads are above their long-term median. Calculating regime-conditional annualized returns confirms this view.

Above

Below

Expanding

10.88%

-2.79%

Contracting

1.59%

4.22%

 

The strategy appears to perform best during periods when credit spreads are expanding above their long-term median level (e.g. crisis periods like 2008).  The strategy appears to do its worst when spreads are below their median and begin to expand, likely representing periods when the strategy is generally long high yield but has not had a chance to make a tactical switch.

This all points to the fact that the strategy harvests almost all of its returns in crisis periods.  In fact, if we remove 2000-2003 and 2008-2009, we can see that the captured credit spread declines dramatically.

Source: St. Louis Federal Reserve.  Calculations by Newfound Research.  

Capturing price returns due to changes in credit spreads are not responsible for all of the strategy’s returns, however.

Below we explicitly calculate the yield generated by the long/short strategy over time.  As high yield corporates tend to offer higher yields, when the strategy is net long high yield, the strategy’s yield is positive.  On the other hand, when the strategy is net short high yield, the strategy’s yield is negative.

This is consistent with our initial view about why these sorts of tactical strategies can be so difficult.  During the latter stages of the 2008 crisis, the long/short strategy had a net negative yield of close to -0.5% per month.2   Thus, the cost of carrying this tactical position is rather expensive and places a larger burden on the strategy accurately timing price return.

Source: Tiingo.  Calculations by Newfound Research.  Tactical Credit strategy returns are hypothetical and backtested.  Returns gross of all management fees and taxes, but net of underlying fund fees.

From this graph, we believe there are two interesting things worth calling out:

  • The long-run average yield is positive, representing the strategy’s ability to capture carry differences between high yield and core bonds.
  • In the post-crisis environments, the strategy generates yields in excess of one standard deviation of the full-period sample, indicating that the strategy may have benefited from allocating to high yield when yields were abnormally large.

To better determine whether capturing changes in credit spreads or carry differences had a larger impact on strategy returns, we can explicitly calculate the –price– and –total return– indices of the ensemble strategy.

Source: St. Louis Federal Reserve.  Calculations by Newfound Research.  Tactical Credit strategy returns are hypothetical and backtested.  Returns gross of all management fees and taxes, but net of underlying fund fees.  Total return series assumes the reinvestment of all distributions.

The –price return– and –total return– series return 2.1% and 2.9% annualized respectively, implying that capturing price return effects account for approximately 75% of the strategy’s total return.

This is potentially concerning, because we have seen that the majority of the price return comes from a single regime: when credit spreads are above their long-term median and expanding.  As we further saw, simply removing the 2000-2003 and 2008-2009 periods significantly reduced the strategy’s ability to harvest these credit spread changes.

While the strategy may appear to be supported by nearly 30-years of empirical evidence, in reality we have a situation where the vast majority of the strategy’s returns were generated in just two regimes.

If we remove 2000-2003 and 2008-2009 from the return series, however, we can see that the total return of the strategy only falls to 0.7% and. 1.6% annualized for –price return– and –total return– respectively.  While this may appear to be a precipitous decline, it indicates that there may be potential to capture both changes in credit spread and net carry differences even in normal market environments so long as implementation costs are kept low enough.

Source: Tiingo.  Calculations by Newfound Research.  Tactical Credit strategy returns are hypothetical and backtested.  Returns gross of all management fees and taxes, but net of underlying fund fees.  Total return series assumes the reinvestment of all distributions.

Conclusion

In this commentary, we explored a tactical credit strategy that switched between high yield corporate bonds and core fixed income.  We decompose these strategies into a 50% high yield / 50% core fixed income portfolio that is overlaid with 50% exposure to a dollar-neutral long/short strategy that captures the tactical tilts.  We focus our exploration on the dollar-neutral long/short portfolio, as it isolates the active bets of the strategy.

Using cross-sectional momentum, we found that short-term signals with formation periods ranging from 3-to-5 months were statistically significant, so long as the holding period was sufficiently short.

We used this information to construct an ensemble strategy made out of more than 1,800 underlying strategy specifications.  Consistent with past research, we found that the ensemble closely tracked the median annualized return of the underlying strategies, but had significantly lower volatility and maximum drawdown, leading to a higher information ratio.

We then attempted to deconstruct where the strategy generated its returns from.  We found that a significant proportion of total returns were achieved during periods when credit spreads were above their long-term median and expanding.  This is consistent with periods of economic volatility such as 2000-2003 and 2008-2009.

The strategy also benefited from harvesting net carry differences between high yield and core fixed income.  Explicitly calculating strategy price and total return, we find that this carry component accounts for approximately 25% of strategy returns.

The impact of the 2000-2003 and 2008-2009 periods on strategy returns should not be understated.   Removing these time periods reduced strategy returns from 2.9% to 1.6% annualized. Interestingly, however, the proportion of total return explained by net carry only increased from 25% to 50%, potentially indicating that the strategy was still able to harvest some opportunities in changing credit spreads.

For investors evaluating these types of strategies, cost will be an important component.  While environments like 2008 may lead to opportunities for significant out-performance, without them the strategy may offer anemic returns.  This is especially true when we recall that a long-only implementation only has 50% implicit exposure to the long/short strategy we evaluated in this piece.

Thus, the 2.9% annualized return is really closer to a 1.5% annualized excess return above the 50/50 portfolio.  For the ex-crisis periods, the number is closer to 0.8% annualized.  When we consider that this analysis was done without explicit consideration for management costs or trading costs and we have yet to apply an appropriate expectation haircut given the fact that this analysis was all backtested, there may not be sufficient juice to squeeze.

That said, we only evaluated a single signal in this piece.  Combining momentum with valuation, carry, or even macro-economic signals may lead to significantly better performance.  Further, high yield corporates is a space where empirical evidence suggests that security selection can make a large difference.  Careful selection of funds may lead to meaningfully better performance than just broad asset class exposure.

 

 

Tactical Portable Beta

By

On May 6, 2019

In Carry, Portfolio Construction, Risk & Style Premia, Term, Trend, Value, Weekly Commentary

This post is available as a PDF download here.

Summary­

  • In this commentary, we revisit the idea of portable beta: utilizing leverage to overlay traditional risk premia on existing strategic allocations.
  • While a 1.5x levered 60/40 portfolio has historically out-performed an all equity blend with similar risk levels, it can suffer through prolonged periods of under-performance.
  • Positive correlations between stocks and bonds, inverted yield curves, and rising interest rate environments can make simply adding bond exposure on top of equity exposure a non-trivial pursuit.
  • We rely on prior research to introduce a tactical 90/60 model, which uses trend signals to govern equity exposure and value, momentum, and carry signals to govern bond exposure.
  • We find that such a model has historically exhibited returns in-line with equities with significantly lower maximum drawdown.

In November 2017, I was invited to participate in a Bloomberg roundtable discussion with Barry Ritholtz, Dave Nadig, and Ben Fulton about the future of ETFs.  I was quoted as saying,

Most of the industry agrees that we are entering a period of much lower returns for stocks and fixed income. That’s a problem for younger generations. The innovation needs to be around efficient use of capital. Instead of an ETF that holds intermediate-term Treasuries, I would like to see a U.S. Treasury ETF that uses Treasuries as collateral to buy S&P 500 futures, so you end up getting both stock and bond exposure.  By introducing a modest amount of leverage, you can take $1 and trade it as if the investor has $1.50. After 2008, people became skittish around derivatives, shorting, and leverage. But these aren’t bad things when used appropriately.

Shortly after the publication of the discussion, we penned a research commentary titled Portable Beta which extolled the potential virtues of employing prudent leverage to better exploit diversification opportunities.  For investors seeking to enhance returns, increasing beta exposure may be a more reliable approach than the pursuit of alpha.

In August 2018, WisdomTree introduced the 90/60 U.S. Balanced Fund (ticker: NTSX), which blends core equity exposure with a U.S. Treasury futures ladder to create the equivalent of a 1.5x levered 60/40 portfolio.  On March 27, 2019, NTSX was awarded ETF.com’s Most Innovative New ETF of 2018.

The idea of portable beta was not even remotely uniquely ours.  Two anonymous Twitter users – “Jake” (@EconomPic) and “Unrelated Nonsense” (@Nonrelatedsense) – had discussed the idea several times prior to my round-table in 2017.  They argued that such a product could be useful to free up space in a portfolio for alpha-generating ideas.  For example, an investor could hold 66.6% of their wealth in a 90/60 portfolio and use the other 33.3% of their portfolio for alpha ideas.  While the leverage is technically applied to the 60/40, the net effect would be a 60/40 portfolio with a set of alpha ideas overlaid on the portfolio. Portable beta becomes portable alpha.

Even then, the idea was not new.  After NTSX launched, Cliff Asness, co-founder and principal of AQR Capital Management, commented on Twitter that even though he had a “22-year head start,” WisdomTree had beat him to launching a fund.  In the tweet, he linked to an article he wrote in 1996, titled Why Not 100% Equities, wherein Cliff demonstrated that from 1926 to 1993 a 60/40 portfolio levered to the same volatility as equities achieved an excess return of 0.8% annualized above U.S. equities.  Interestingly, the appropriate amount of leverage utilized to match equities was 155%, almost perfectly matching the 90/60 concept.

Source: Asness, Cliff. Why Not 100% Equities.  Journal of Portfolio Management, Winter 1996, Volume 22 Number 2.

Following up on Cliff’s Tweet, Jeremy Schwartz from WisdomTree extended the research out-of-sample, covering the quarter century that followed Cliff’s initial publishing date.  Over the subsequent 25 years, Jeremy found that a levered 60/40 outperformed U.S. equities by 2.6% annualized.

NTSX is not the first product to try to exploit the idea of diversification and leverage.  These ideas have been the backbone of managed futures and risk parity strategies for decades. The entire PIMCO’s StocksPLUS suite – which traces its history back to 1986 – is built on these foundations.  The core strategy combines an actively managed portfolio of fixed income with 100% notional exposure in S&P 500 futures to create a 2x levered 50/50 portfolio.

The concept traces its roots back to the earliest eras of modern financial theory. Finding the maximum Sharpe ratio portfolio and gearing it to the appropriate risk level has always been considered to be the theoretically optimal solution for investors.

Nevertheless, after 2008, the words “leverage” and “derivatives” have largely been terms non gratisin the realm of investment products. But that may be to the detriment of investors.

90/60 Through the Decades

While we are proponents of the foundational concepts of the 90/60 portfolio, frequent readers of our commentary will not be surprised to learn that we believe there may be opportunities to enhance the idea through tactical asset allocation.  After all, while a 90/60 may have out-performed over the long run, the short-run opportunities available to investors can deviate significantly.  The prudent allocation at the top of the dot-com bubble may have looked quite different than that at the bottom of the 2008 crisis.

To broadly demonstrate this idea, we can examine the how the realized efficient frontier of stock/bond mixes has changed shape over time.  In the table below, we calculate the Sharpe ratio for different stock/bond mixes realized in each decade from the 1920s through present.

Source: Global Financial Data.  Calculations by Newfound Research.  Returns are hypothetical and backtested.  Returns are gross of all fees, transaction costs, and taxes.  Returns assume the reinvestment of all distributions.   Bonds are the GFD Indices USA 10-Year Government Bond Total Return Index and Stocks are the S&P 500 Total Return Index (with GFD Extension).  Sharpe ratios are calculated with returns excess of the GFD Indices USA Total Return T-Bill Index.  You cannot invest in an index.  2010s reflect a partial decade through 4/2019.

We should note here that the original research proposed by Asness (1996) assumed a bond allocation to an Ibbotson corporate bond series while we employ a constant maturity 10-year U.S. Treasury index.  While this leads to lower total returns in our bond series, we do not believe it meaningfully changes the conclusions of our analysis.

We can see that while the 60/40 portfolio has a higher realized Sharpe ratio than the 100% equity portfolio in eight of ten decades, it has a lower Sharpe ratio in two consecutive decades from 1950 – 1960.  And the 1970s were not a ringing endorsement.

In theory, a higher Sharpe ratio for a 60/40 portfolio would imply that an appropriately levered version would lead to higher realized returns than equities at the same risk level.  Knowing the appropriate leverage level, however, is non-trivial, requiring an estimate of equity volatility.  Furthermore, leverage requires margin collateral and the application of borrowing rates, which can create a drag on returns.

Even if we conveniently ignore these points and assume a constant 90/60, we can still see that such an approach can go through lengthy periods of relative under-performance compared to buy-and-hold equity.  Below we plot the annualized rolling 3-year returns of a 90/60 portfolio (assuming U.S. T-Bill rates for leverage costs) minus 100% equity returns.  We can clearly see that the 1950s through the 1980s were largely a period where applying such an approach would have been frustrating.

Source: Global Financial Data.  Calculations by Newfound Research.  Returns are hypothetical and backtested.  Returns are gross of all fees, transaction costs, and taxes.   Bonds are the GFD Indices USA 10-Year Government Bond Total Return Index and Stocks are the S&P 500 Total Return Index (with GFD Extension).  The 90/60 portfolio invests 150% each month in the 60/40 portfolio and -50% in the GFD Indices USA Total Return T-Bill Index.  You cannot invest in an index.

Poor performance of the 90/60 portfolio in this era is due to two effects.

First, 10-year U.S. Treasury rates rose from approximately 4% to north of 15%.  While a constant maturity index would constantly roll into higher interest bonds, it would have to do so by selling old holdings at a loss.  Constantly harvesting price losses created a headwind for the index.

This is compounded in the 90/60 by the fact that the yield curve over this period spent significant time in an inverted state, meaning that the cost of leverage exceeded the yield earned on 40% of the portfolio, leading to negative carry. This is illustrated in the chart below, with –T-Bills– realizing a higher total return over the period than –Bonds–.

Source: Global Financial Data.  Calculations by Newfound Research.  Returns are hypothetical and backtested.  Returns are gross of all fees, transaction costs, and taxes.  Returns assume the reinvestment of all distributions.   T-Bills are the GFD Indices USA Total Return T-Bill Index, Bonds are the GFD Indices USA 10-Year Government Bond Total Return Index, and Stocks are the S&P 500 Total Return Index (with GFD Extension). You cannot invest in an index.

This is all arguably further complicated by the fact that while a 1.5x levered 60/40 may closely approximate the risk level of a 100% equity portfolio over the long run, it may be a far cry from it over the short-run.  This may be particularly true during periods where stocks and bonds exhibit positive realized correlations as they did during the 1960s through 1980s.  This can occur when markets are more pre-occupied with inflation risk than economic risk.  As inflationary fears abated and economic risk become the foremost concern in the 1990s, correlations between stocks and bonds flipped.

Thus, during the 1960s-1980s, a 90/60 portfolio exhibited realized volatility levels in excess of an all-equity portfolio, while in the 2000s it has been below.

This all invites the question: should our levered allocation necessarily be static?

Getting Tactical with a 90/60

We might consider two approaches to creating a tactical 90/60.

The first is to abandon the 90/60 model outright for a more theoretically sound approach. Specifically, we could attempt to estimate the maximum Sharpe ratio portfolio, and then apply the appropriate leverage such that we either hit a (1) constant target volatility or (2) the volatility of equities.  This would require us to not only accurately estimate the expected excess returns of stocks and bonds, but also their volatilities and correlations. Furthermore, when the Sharpe optimal portfolio is highly conservative, notional exposure far exceeding 200% may be necessary to hit target volatility levels.

In the second approach, equity and bond exposure would each be adjusted tactically, without regard for the other exposure.  While less theoretically sound, one might interpret this approach as saying, “we generally want exposure to the equity and bond risk premia over the long run, and we like the 60/40 framework, but there might be certain scenarios whereby we believe the expected return does not justify the risk.”  The downside to this approach is that it may sacrifice potential diversification benefits between stocks and bonds.

Given the original concept of portable beta is to increase exposure to the risk premia we’re already exposed to, we prefer the second approach.  We believe it more accurately reflects the notion of trying to provide long-term exposure to return-generating risk premia while trying to avoid the significant and prolonged drawdowns that can be realized with buy-and-hold approaches.

Equity Signals

To manage exposure to the equity risk premium, our preferred method is the application of trend following signals in an approach we call trend equity.  We will approximate this class of strategies with our Newfound Research U.S. Trend Equity Index.

To determine whether our signals are able to achieve their goal of “protect and participate” with the underlying risk premia, we will plot their regime-conditional betas.  To do this, we construct a simple linear model:

We define a bear regime as the worst 16% of monthly returns, a bull regime as the best 16% of monthly returns, and a normal regime as the remaining 68% of months. Note that the bottom and top 16thpercentiles are selected to reflect one standard deviation.

Below we plot the strategy conditional betas relative to U.S. equity

We can see that trend equity has a normal regime beta to U.S. equities of approximately 0.75 and a bear market beta of 0.5, in-line with expectations that such a strategy might capture 70-80% of the upside of U.S. equities in a bull market and 40-50% of the downside in a prolonged bear market. Trend equity beta of U.S. equities in a bull regime is close to the bear market beta, which is consistent with the idea that trend equity as a style has historically sacrificed the best returns to avoid the worst.

Bond Signals

To govern exposure to the bond risk premium, we prefer an approach based upon a combination of quantitative, factor-based signals.  We’ve written about many of these signals over the last two years; specifically in Duration Timing with Style Premia (June 2017), Timing Bonds with Value, Momentum, and Carry (January 2018), and A Carry-Trend-Hedge Approach to Duration Timing (October 2018).  In these three articles we explore various mixes of value, momentum, carry, flight-to-safety, and bond risk premium measures as potential signals for timing duration exposure.

We will not belabor this commentary unnecessarily by repeating past research.  Suffice it to say that we believe there is sufficient evidence that value (deviation in real yield), momentum (prior returns), and carry (term spread) can be utilized as effective timing signals and in this commentary are used to construct bond indices where allocations are varied between 0-100%.  Curious readers can pursue further details of how we construct these signals in the commentaries above.

As before, we can determine conditional regime betas for strategies based upon our signals.

We can see that our value, momentum, and carry signals all exhibit an asymmetric beta profile with respect to 10-year U.S. Treasury returns.  Carry and momentum exhibit an increase in bull market betas while value exhibits a decrease in bear market beta.

Combining Equity and Bond Signals into a Tactical 90/60

Given these signals, we will construct a tactical 90/60 portfolio as being comprised of 90% trend equity, 20% bond value, 20% bond momentum, and 20% bond carry. When notional exposure exceeds 100%, leverage cost is assumed to be U.S. T-Bills.  Taken together, the portfolio has a large breadth of potential configurations, ranging from 100% T-Bills to a 1.5x levered 60/40 portfolio.

But what is the appropriate benchmark for such a model?

In the past, we have argued that the appropriate benchmark for trend equity is a 50% stock / 50% cash benchmark, as it not only reflects the strategic allocation to equities empirically seen in return decompositions, but it also allows both positive and negative trend calls to contribute to active returns.

Similarly, we would argue that the appropriate benchmark for our tactical 90/60 model is not a 90/60 itself – which reflects the upper limit of potential capital allocation – but rather a 45% stock / 30% bond / 25% cash mix.  Though, for good measure we might also consider a bit of hand-waving and just use a 60/40 as a generic benchmark as well.

Below we plot the annualized returns versus maximum drawdown for different passive and active portfolio combinations from 1974 to present (reflecting the full period of time when strategy data is available for all tactical signals).  We can see that not only does the tactical 90/60 model (with both trend equity and tactical bonds) offer a return in line with U.S. equities over the period, it does so with significantly less drawdown (approximately half).  Furthermore, the tactical 90/60 exceeded trend equity and 60/40 annualized returns by 102 and 161 basis points respectively.

These improvements to the return and risk were achieved with the same amount of capital commitment as in the other allocations. That’s the beauty of portable beta.

Source: Federal Reserve of St. Louis, Kenneth French Data Library, and Newfound Research.  Calculations by Newfound Research.  Returns are hypothetical and backtested.  Returns are gross of all fees, transaction costs, and taxes.  Returns assume the reinvestment of all distributions.   You cannot invest in an index.

Of course, full-period metrics can deceive what an investor’s experience may actually be like.  Below we plot rolling 3-year annualized returns of U.S. equities, the 60/40 mix, trend equity, and the tactical 90/60.

Source: Federal Reserve of St. Louis, Kenneth French Data Library, and Newfound Research.  Calculations by Newfound Research.  Returns are hypothetical and backtested.  Returns are gross of all fees, transaction costs, and taxes.  Returns assume the reinvestment of all distributions.   You cannot invest in an index.

The tactical 90/60 model out-performed a 60/40 in 68% of rolling 3-year periods and the trend equity model in 71% of rolling 3-year periods.  The tactical 90/60, however, only out-performs U.S. equities in 35% of rolling 3-year periods, with the vast majority of relative out-performance emerging during significant equity drawdown periods.

For investors already allocated to trend equity strategies, portable beta – or portable tactical beta – may represent an alternative source of potential return enhancement.  Rather than seeking opportunities for alpha, portable beta allows for an overlay of more traditional risk premia, which may be more reliable from an empirical and academic standpoint.

The potential for increased returns is illustrated below in the rolling 3-year annualized return difference between the tactical 90/60 model and the Newfound U.S. Trend Equity Index.

Source: Federal Reserve of St. Louis, Kenneth French Data Library, and Newfound Research.  Calculations by Newfound Research.  Returns are hypothetical and backtested.  Returns are gross of all fees, transaction costs, and taxes.  Returns assume the reinvestment of all distributions.   You cannot invest in an index.

From Theory to Implementation

In practice, it may be easier to acquire leverage through the use of futures contracts. For example, applying portable bond beta on-top of an existing trend equity strategy may be achieved through the use of 10-year U.S. Treasury futures.

Below we plot the growth of $1 in the Newfound U.S. Trend Equity Index and a tactical 90/60 model implemented with Treasury futures.  Annualized return increases from 7.7% to 8.9% and annualized volatility declines from 9.7% to 8.5%.  Finally, maximum drawdown decreases from 18.1% to 14.3%.

We believe the increased return reflects the potential return enhancement benefits from introducing further exposure to traditional risk premia, while the reduction in risk reflects the benefit achieved through greater portfolio diversification.

Source: Quandl and Newfound Research.  Calculations by Newfound Research.  Returns are hypothetical and backtested.  Returns are gross of all fees, transaction costs, and taxes.  Returns assume the reinvestment of all distributions.   You cannot invest in an index.

It should be noted, however, that a levered constant maturity 10-year U.S. Treasury index and 10-year U.S. Treasury futures are not the same.  The futures contracts are specified such that eligible securities for delivery include Treasury notes with a remaining term to maturity of between 6.5 and 10 years.  This means that the investor short the futures contract has the option of which Treasury note to deliver across a wide spectrum of securities with potentially varying characteristics.

In theory, this investor will always choose to deliver the bond that is cheapest. Thus, Treasury futures prices will reflect price changes of this so-calledcheapest-to-deliver bond, which often does not reflect an actual on-the-run 10-year Treasury note.

Treasury futures therefore utilize a “conversion factor” invoicing system referenced to the 6% futures contract standard.  Pricing also reflects a basis adjustment that reflects the coupon income a cash bond holder would receive minus financing costs (i.e. the cost of carry) as well as the value of optionality provided to the futures seller.

Below we plot monthly returns of 10-year U.S. Treasury futures versus the excess returns of a constant maturity 10-year U.S. Treasury index.  We can see that the futures had a beta of approximately 0.76 over the nearly 20-year period, which closely aligns with the conversion factor over the period.

Source: Quandl and the Federal Reserve of St. Louis.  Calculations by Newfound Research.

Despite these differences, futures can represent a highly liquid and cost-effective means of implementing a portable beta strategy.  It should be further noted that having a lower “beta” over the last two decades has not necessarily implied a lower return as the basis adjustment can have a considerable impact.  We demonstrate this in the graph below by plotting the returns of continuously-rolled 10-year U.S. Treasury futures (rolled on open interest) and the excess return of a constant maturity 10-year U.S. Treasury index.

Source: Quandl and Newfound Research.  Calculations by Newfound Research.  Returns are hypothetical and backtested.  Returns are gross of all fees, transaction costs, and taxes.  Returns assume the reinvestment of all distributions.   You cannot invest in an index.

Conclusion

In a low return environment, portable beta may be a necessary tool for investors to generate the returns they need to hit their financial goals and reduce their risk of failing slow.

Historically, a 90/60 portfolio has outperformed equities with a similar level of risk. However, the short-term dynamics between stocks and bonds can make the volatility of a 90/60 portfolio significantly higher than a simple buy-and-hold equity portfolio. Rising interest rates and inverted yield curves can further confound the potential benefits versus an all-equity portfolio.

Since constant leverage is not a guarantee and we do not know how the future will play out, moving beyond standard portable beta implementations to tactical solutions may augment the potential for risk management and lead to a smoother ride over the short-term.

Getting over the fear of using leverage and derivatives may be an uphill battle for investors, but when used appropriately, these tools can make portfolios work harder. Risks that are known and compensated with premiums can be prudent to take for those willing to venture out and bear them.

If you are interested in learning how Newfound applies the concepts of tactical portable beta to its mandates, please reach out (info@thinknewfound.com).

Style Surfing the Business Cycle

By

On April 29, 2019

In Risk & Style Premia, Weekly Commentary

This post is available as a PDF download here.

Summary­

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

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

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

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

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

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

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

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

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

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

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

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

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

Which Factors and When?

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

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

Model #1

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

Model #2

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

Defining the Business Cycle

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

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

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

Definition #1

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

Definition #2

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

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

Implementing Factor Rotation

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

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

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

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

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

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

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

Data-Mining Our Way to Success

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

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

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

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

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

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

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

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

A few more important things to note.

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

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

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

Conclusion

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

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

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

The Path-Dependent Nature of Perfect Withdrawal Rates

By

On April 22, 2019

In Risk Management, Sequence Risk, Weekly Commentary

This post is available as a PDF download here.

Summary

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

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

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

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

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

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

Perfect Withdrawal Rates

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

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

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

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

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

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

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

The relationship is difficult to pin down.

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

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

The Risk in Withdrawal Rates

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Conclusion

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

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

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

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

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

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

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

The Speed Limit of Trend

By

On April 15, 2019

In Trend, Weekly Commentary

This post is available as a PDF download here.

Summary­

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

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

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

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

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

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

Below we re-create this test.  Specifically,

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

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

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

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

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

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

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

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

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

Varying Drawdown Size

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

We can see some interesting patterns emerge.

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

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

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

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

Varying Volatility

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

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

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

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

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

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

Conclusion

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

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

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

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

If only reality were that simple!

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

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

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

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

 

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