The prototypical example at the time was a 1.5x levered 60% stock / 40% bond portfolio (also referred to as a “90/60”). Such a portfolio would allow investors to achieve the exposure of a 60/40 using just two-thirds of their capital, freeing up valuable portfolio real estate for diversifying alternatives.
Implementing such a portfolio in practice was also trivial: for every $1 invested, $0.9 could be invested in stocks and $0.1 held aside as cash collateral for a $0.6 notional position in U.S. Treasury futures.
Figure 1: One Possible Implementation of a 90/60 Portfolio
Today, the 13-week Treasury Bill rate hovers near 4.5% and the yield curve is severely inverted, causing many to ask, “does return stackingTM still make sense, particularly if we use Treasury futures to achieve our leverage?”
We believe the answer is a resounding “yes,” with four key points to consider.
It’s the portfolio, not the asset
With the yield curve severely inverted, paying short-term financing costs to invest in long-term Treasuries to achieve our leverage may seem like a losing prospect. We believe this line of thinking is misguided, however; it misses the forest for the trees.
Using U.S. Treasury futures is simply a means to an end. Sticking with our 90/60 example, what we actually care about is achieving 1.5x levered 60/40 exposure and the flexibility that creates for us in portfolio construction.
Would we have the same concern about an inverted yield curve if for every $1 invested we purchased $0.6 of U.S. Treasuries and held $0.4 in cash as collateral for $0.9 in S&P 500 futures exposure? What if we simply borrowed money to lever an entire 60/40 portfolio up 1.5x?
Figure 2 plots that the annual returns of these three different approaches. We can see that they are nearly identical to one another.
Figure 2: Annual Returns for Varying Approaches to Implementing a Levered 60/40 Portfolio
Source: Tiingo, Bloomberg, Barcharts. Calculations by Newfound Research. Past performance is backtested and hypothetical. Returns are gross of all fees, costs, and taxes except for underlying expense ratios. Returns assume the reinvestment of all distributions. Past performance is not indicative of future results. Starting date based upon the availability of pricing data.
To draw this point out further, consider the case of explicitly borrowing money to lever the 60/40 portfolio up 1.5x and the following ways we could implement this portfolio:
Hold 90% in stocks, 10% in U.S. Treasuries, and borrow to buy another 50% in U.S. Treasuries;
Hold 60% in U.S. Treasuries, 40% in stocks, and borrow to buy another 50% in stocks;
Hold 60% in stocks, 40% in U.S. Treasuries, and borrow to buy another 30% in stocks and 20% in U.S. Treasuries.
Figure 3: Different Approaches to Creating a 90/60 Portfolio
Does it matter which we choose? Does an inverted yield curve make the first choice less attractive than the second?
In theory, we should be indifferent to these choices. If we are concerned about using U.S. Treasury futures to achieve a levered 60/40, we should be equally concerned about using equity futures (“invert, always invert!”),
Sourcing cheap leverage.
In practice, we do care how we implement a return stackedTM portfolio. Not because the yield curve is inverted, but because explicitly borrowing at the short-term Treasury Bill rate is difficult for all but the largest institutions.
Treasury futures have historically allowed us to do just that, giving us a very cost-effective source of leverage. Figure 4 plots the embedded cost of leverage in 10-Year U.S. Treasury Futures relative to 3-Month U.S. Treasury Bill rates. By contrast, at the time of this writing, the current base margin rate is 10.75% at Schwab, 11.33% at Fidelity, and 12.50% at TD Ameritrade.
Figure 4: Embedded Financing Cost in 10-Year U.S. Treasury Futures versus 3-Month U.S. Treasury Bill Rate
Source: Bloomberg.
It’s the excess returns that matter.
But what about the fact that short-term rates have climbed from near-zero to north of 4%. Is leverage now unattractive because the cost of financing is so high?
Let us return, for a moment, back to basic portfolio theory which says the expected return of an asset can be decomposed into two parts: the risk-free rate and the asset’s risk premium. For example, the expected return of stocks should be equal to the risk-free rate plus the equity risk premium (“ERP”). Similarly, the expected return of bonds should be equal to the risk-free rate plus the bond risk premium (“BRP”).
Figure 5: Decomposing Expected Returns into the Risk-Free Rate and Risk Premia
The expected return of a portfolio, then, can simply be thought of as the risk-free rate plus the blended return of risk premia. For example, the expected return of a 60/40 is:
What about a 45% Stock / 30% Bond / 25% Cash portfolio? No surprise:
30% ERP + 20% BRP + 100% Risk-Free Rate
= 0.5x (60% ERP + 40% BRP) + 100% Risk-Free Rate
Whether we’re holding cash, fully invested, or levered, all we are doing is scaling the risk premium exposure! It is the returns in excess of the risk-free rate that matter.
The important implication here is that if we believe the levered portfolio is unattractive to invest in, it must also mean we believe the unlevered portfolio is unattractive to invest in.1 If 60% ERP + 40% BRP is negative, no amount of scaling up or down will change it; we’d be better off just holding cash.
The null hypothesis is that markets are efficient.
None of this negates the fact that an investor may hold the active view that intermediate- to long-term U.S. Treasuries are unattractive to hold relative to cash today. Such a view, however, is not unique to a levered portfolio: it would affect levered and unlevered portfolios alike. To remain consistent with such a view, an investor should sell down their long-duration bonds in preference for short-duration exposure, regardless of leverage.
The only point we will stress here is that we believe the prudent approach is to assume, as a null hypothesis, that markets are generally efficient. After all, if everyone held the same active view that long duration bonds are currently unattractive, they would sell those bonds, driving up the yield until the point they are attractive. If we believe markets are generally in equilibrium, the current long-term yield should be equally attractive as the short yield when appropriately adjusted for their risks.
How can that be the case when the short-term rate is higher than the long-term rate? The pure expectations hypothesis states that the yield curve embeds the expected path of short rates. It is important to remember that the expected return of a longer-dated Treasury should be compared to the expected return of a constantly rolled shorter-dated Treasury. An inverted yield curve, then, expresses the aggregate view that short rates should be lower in the future, which would bring down the return of the constantly rolled short-rate series.
Nevertheless, if an investor does have an active view about the relative expected returns of short- versus longer-dated Treasuries, that view would be expressed regardless of whether the portfolio is levered or not.
Conclusion
In this note we have attempted to address the question as to whether return stackingTM still makes sense when the cost of financing goes up, particularly if we’re accessing that financing through longer-dated Treasury futures during an inverted yield curve environment.
We believe the answer is ‘yes’, and four key points help illustrate this fact. First, philosophically, we care less about the specific asset we are levering than the make-up of the levered portfolio. Second, in practice we want to choose an asset to lever that provides us with a cost of financing as close to the risk-free rate as possible. Third, it is the return in excess of the risk-free rate that ultimately matters. Finally, an active view about the relative attractiveness of Treasuries applies regardless of whether the portfolio is levered or not.
As a final point, we want to zoom out once more to emphasize the portfolio view. Consider the investor who uses a 90/60 portfolio to free up capital, and that freed up capital is invested for alpha exposure. Very frequently, alpha exposures are packaged in a way they provide cash plus alpha returns. For example, a managed futures fund is effectively U.S. T-Bills plus the return of an active futures trading strategy.
Which means the cash positions effectively net out. Assume we put 66.6% of our portfolio in a 90/60 and 33.3% of our portfolio in a managed futures fund. If we x-ray the former position, we effectively have 60% stocks plus 40% bonds minus 33.3% U.S. T-Bills. If we x-ray the latter, we effectively have 33.3% T-Bills plus 33.3% of the active futures strategy. Taken together, we’re left with 60% stocks plus 40% bonds plus 33.3% of the active futures strategy.
More than anything, it’s the net portfolio allocation that matters.
This paper is unlike any research we’ve shared in the past. Within we dive into the circumstantial evidence surrounding the “weird” behavior many investors believe markets are exhibiting. We tackle narratives such as the impact of central bank intervention, the growing scale of passive / indexed investing, and asymmetric liquidity provisioning.
Spoiler: Individually, the evidence for these narratives may be nothing more than circumstantial. In conjunction, however, they share pro-cyclical patterns that put pressure upon the same latent risk: liquidity.
In the last part of the paper we discuss some ideas for how investors might try to build portfolios that can both seek to exploit these dynamics as well as remain resilient to them.
The convex payoff profile of trend following strategies naturally lends itself to comparative analysis with option strategies. Unlike options, however, the payout of trend following is not guaranteed.
To compare and contrast the two approaches, we replicate simple trend following strategies with corresponding option straddle strategies.
While trend-following has no explicit up-front cost, it also bears the full brunt of any price reversals. The straddle-based approach, on the other hand, pays an explicit cost to insure against sudden and large reversals.
This transformation of whipsaw risk into an up-front option premium can be costly during strongly trending market environments where the option buyer would have been rewarded more for setting a higher deductible for their implicit insurance policy and paying a lower premium.
From 2005-2020, avoiding this upfront premium was beneficial. The sudden loss of equity markets in March 2020, however, allowed straddle-based approaches to make up for 15-years of relative underperformance in a single month.
Whether an investor wishes to avoid these up-front costs or pay them is ultimately a function of the risks they are willing to bear. As we like to say, “risk cannot be destroyed, only transformed.”
We often repeat the mantra that, “risk cannot be destroyed, only transformed.” While not being able to destroy risk seems like a limitation, the assertion that risk can be transformed is nearly limitless.
With a wide variety of investment options, investors have the ability to mold, shape, skew, and shift their risks to fit their preferences and investing requirements (e.g. cash flows, liquidity, growth, etc.).
The payoff profile of a strategy is a key way in which this transformation of risk manifests, and the profile of trend following is one example that we have written much on historically. The convex payoff of many long/short trend following strategies is evident from the historical payoff diagram.
Source: Newfound Research. Payoff Diversification (February 10th, 2020). Source: Kenneth French Data Library; Federal Reserve Bank of St. Louis. Calculations by Newfound Research. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. The 60/40 portfolio is comprised of a 60% allocation to broad U.S. equities and a 40% allocation to a constant maturity 10-Year U.S. Treasury index. The momentum portfolio is rebalanced monthly and selects the asset with the highest prior 12-month returns whereas the buy-and-hold variation is allowed to drift over the 1-year period.The 10-Year U.S. Treasuries index is a constant maturity index calculated by assuming a 10-year bond is purchased at the beginning of every month and sold at the end of that month to purchase a new bond at par at the beginning of the next month. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results.
This characteristic “V” shape in the diagram is reminiscent of an option straddle, where an investor buys a put and call option of the same maturity struck at the same price. This position allows the investor to profit if the price of the underlying security moves significantly in either direction, but they pay for this opportunity in the option premiums.
Source: theoptionsguide.com
The similarity of these payoff profiles is no coincidence. As we demonstrated in Trend – Convexity and Premium (February 11th, 2019), simple total return trend following signals coarsely approximate the delta of the straddle. For those less familiar with the parlance of options, delta is the sensitivity in the value of the options to changes in the underlying stock. For example, if delta is +1, then the value of the option position will match price changes in the underlying dollar-for-dollar. If delta is -1, then the position will lose $1 for every dollar gained in the underlying and vice versa (i.e. the position is effectively short).
How does this connection arise? Consider a naïve S&P 500 trend strategy that rebalances monthly and uses 12-month total returns as a trend signal, buying when prior returns are positive and shorting when prior returns are negative. The key components of this strategy are today’s S&P 500 level and the level 12 months ago.
Now consider a strategy that buys a 1-month straddle with a strike equal to the level of the S&P 500 12 months ago. When the current level is above the strike, the strategy’s delta will be positive and when the level is below the strike, the delta will be negative. What we can see is that the sensitivity of our options trade to changes in the S&P 500 will match the sign of the trend strategy!
There are two key differences, however. First, our trend strategy was designed to always be 100% long or 100% short, whereas the straddle’s sensitivity can vary between -100% and 100%. Second, the trend strategy cannot change its exposure intramonth whereas the straddle will. In fact, if price starts above the strike price (a positive trend) but ultimately ends below – so far as it is sufficiently far that we can make up for the premium paid for our options – the straddle can still profit!
In this commentary, we will compare and contrast the trend and option-based approaches for a variety of lookback horizons.
Methodology and Data
For this analysis, we will use the S&P 500 index for equity returns, the iShares Short-term U.S. Treasury Bond ETF (ticker: SHV) as the risk-free rate, and monthly options data on the S&P 500 (SPX options).
The long/short trend equity strategy looks at total returns of equities over a given number of months. If this return is positive, the strategy invests in equities for the following month. If the return is negative, the strategy shorts equities for the following month and earns the short-term Treasury rate on the cash. The strategy is rebalanced monthly on the third Friday of each month to coincide with the options expiration dates.
For the (semi-equivalent) straddle replication, at the end of each month we purchase a call option and a put option struck at the level of the S&P 500 at the beginning of the lookback window of the trend following strategy. We can also back out the strike price using the current trend signal value and S&P 500. For example, if the trend signal is 25% and the S&P 500 is trading at $3000, we would set the strike of the options at $2400.
The options account is assumed to be fully cash collateralized. Any premium is paid on the options roll date, interest is earned on the remaining account balance, and the option payout is realized on the next roll date.
To value the options, we employ Black-Scholes pricing on an implied volatility surface derived from available out-of-the money options. Specifically, on a given day we fit a parabola to the implied variances versus log-moneyness (i.e. log(strike/price)) of the options for each time to maturity.
In prior research, we created straddle-derived trend-following models by purchasing S&P 500 exposure in proportion to the delta of the strategy. To calculate delta, we had previously priced the options using 21-day realized volatility as a proxy for implied volatility. This generally leads to over-pricing the options during crisis times and underpricing during more tame market environments, especially for deeper out of the money puts. In this commentary we are actually purchasing the straddles and holding them for one month.
Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.
Straddle vs. Trend Following
Below we plot the ratio of the equity curves for the straddle strategies versus their corresponding trend following strategies. When the line is increasing, the straddle strategy is out-performing, and when the line is decreasing the trend strategy is out-performing.
Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.
We can see, generally, that trend following out-performed the explicit purchase of options for almost all lookback periods for the majority of the 15-year test period.
It is only with the most recent expiration – March 20, 2020 – that many of the straddle strategies came to out-perform their respective trend strategies. With the straddle strategy, we pay an explicit premium to help insure our position against sudden and large intra-month price reversals. This did not occur very frequently during the 15 year history, but was very valuable protection in March when the trend strategies were largely still long coming off markets hitting all-time-highs in late February.
Shorter-term lookbacks fared particularly well during that month, as the trend following strategy was in a long position on the February 2020 options expiry date, and the straddles set by the short-term lookback window were relatively cheap from a historical perspective.
Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.
Note the curious case of the 14-month lookback. Entering March, the S&P 500 was +45% over a 14-month lookback (almost perfectly anchored to December 2018 lows). Therefore, the straddle was struck so deep in the money that it did not create any protection against the market’s sudden and large drawdown.
Prior to March 2020, only the 8- and 15-month lookback window strategies had outperformed their corresponding trend following strategies. In both cases, it was just barely and just recently.
Another interesting point to note is that longer-term straddle strategies (lookbacks greater than 9 months) shared similar movements during many periods while shorter-term lookbacks (3-6 months) showed more dispersion over time.
Overall, many of the straddles exhibit more “crisis alpha” than their trend following counterparts. This is an explicit risk we pay to hedge with the straddle approach and a fact we will discuss in more detail later on.
How Equity Movements Affect Straddles
Before we move into a discussion of how we can frame the straddle strategies, it will be helpful to revisit how straddles are affected by changing equity prices and how this effect changes with different lookback windows for the strategies.
Consider the delta of a straddle versus how far away price is from the strike (normalized by volatility).
Naively, we might consider that the longer our trend lookback window – and therefore the further back in time we set our strike price – the further away from the strike that price has had the opportunity to move. Consider two extremes: a strike set equal to the price of the S&P 500 10 years ago versus one set a day ago. We would expect that today’s price is much closer to that from a day ago than 10 years ago.
Therefore, for a longer lookback horizon we might expect that there is a greater chance that the straddle is currently deeper in the money, leading to a delta closer to +/- 1. In the case of straddles struck at index levels more recently realized, it is more likely that price is close to at the money, leading to deltas closer to 0.
This also means that while the trend following strategy is taking a binary bet, the straddle is able to modulate exposure to equity moves when the trend is less pronounced. For example, if a 12-month trend signal is +1%, the trend model will retain a +1 exposure while the delta of the straddle may be closer to 0.
Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.
Additionally, when the delta of a straddle is closer to zero, its gamma is higher. Gamma reflects how quickly the straddle’s sensitivity to changes in the underlying asset – i.e. the delta – will change. The trend strategy has no intra-month gamma, as once the position is set it remains static until the next rebalance.
As we generally expect the straddles struck longer ago to be deeper in the money than those struck more recently, we would also expect them to have lower gamma.
This also serves to nicely connect trend speed with the length of the lookback window. Shorter lookback windows are associated with trend models that change signals more rapidly while longer lookback windows are slower. Given that a total return trend signal can be thought of as the average of daily log returns, we would expect a longer lookback to react more slowly to recent changes than a shorter lookback because the longer lookback is averaging over more data.
But if we think of it through the lens of options – that the shorter lookback is coarsely replicating the delta of a straddle struck more recently – then the ideas of speed and gamma become linked.
Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.
The Straddle Strategy as an Insurance Policy
One of the key differences between the trend strategy and the straddle is that the straddle has features that act as insurance against price reversals. As an example, consider a case where the trend strategy has a positive signal. To first replicate the payoff, the straddle strategy buys an in-the-money call option. This is the first form of insurance, as the total amount this position can lose is the premium paid for the option, while the trend strategy can lose significantly more.
The straddle strategy goes one step further, though, and would also buy a put option. So not only does it have a fixed loss on the call if price reverses course, but it can also profit if it reverses sufficiently.
One way to model the straddle strategies, then, is as insurance policies with varying deductibles. There is an up-front premium that is paid, and the strategy does not pay out until the deductible – the distance that the option is struck in the money – is met.
When the deductible is high – that is, when the trend is very strong in either direction – the premium for the insurance policy tends to be low. On the other hand, a strategy that purchases at the money straddles would be equivalent to buying insurance with no deductible.
Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.
On average, the 3-month straddle strategy pays annual premiums of about 14% for the benefit of only having to wait for a price reversal of 6% before protection kicks in. Toward the other end of the spectrum, the 12-month strategy has an annual average premium of under 6% with a 16% deductible.
We can also visualize how often each straddle strategy pays higher premiums by looking at the deltas of the straddles over time. When these values deviate significantly from +1 or -1, then the straddle is lowering its insurance deductible in favor of paying more in premium. When the delta is nearly +1 or -1, then the straddle is buying higher deductible insurance that will take a larger whipsaw to payout.
The charts below show the delta over time in the straddle strategies vs. the trend allocation for 3-, 6-, and 12-month lookback windows.
There is significant overlap, especially as trends get longer. The differences in the deltas in the 3-month straddle model highlight its tradeoff between lower deductibles and higher insurance premiums. However, this leads it to be more adaptive at capitalizing on equity moves in the opposite direction that lead to losses in the binary trend-following model.
Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.
Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.
Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.
Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.
The chart below shows the annualized performance of the straddle strategies when they underperform trend following (premium) and the annualized performance of the straddle strategies when they outperform trend following (payout). As the lookback window increases, both of these figures generally decline in absolute value.
Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.
Even though we saw previously that the 3-month straddle strategy had the highest annual premium, its overall payout when it outperforms trend following is substantial. The longer lookbacks do not provide as much of a buffer due to their higher deductible levels, despite their lower premiums.
When the naïve trend strategy is right, it captures the full price change with no up-front premium. When it is wrong, however, it bears the full brunt of losses.
With the straddle strategy, the cost is paid up front for the benefit to not only protect against price reversals, but even potentially profit from them.
As a brief aside, a simpler options strategy with similar characteristics would be to buy only either a call option or put option depending on the trend signal. This strategy would not profit from a reversion of the trend, but it would cap losses. Comparing it to the straddle strategies highlights the cost and benefit of the added protection.
Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.
Buying only puts or calls generally helped both of the strategies shown in the chart. This came in reduced premiums over a time period when trimming premiums whenever possible paid off, especially for the 12-month lookback strategy. However, there are some notable instances where the extra protection of the straddle was very helpful, e.g. August 2011 and late 2014 for the 3-month lookback strategy and March 2020 for both.
Despite the similarities between the options and trend strategies, this difference in when the payment is made – either up-front in the straddle strategy or after-the fact in whipsaw in the trend following strategy – ends up being the key differentiator.
The relative performance of the strategies shows that investors mostly benefitted over the past 15 years by bearing this risk of whipsaw and large, sudden price-reversals. However, as the final moths of data indicates, option strategies can provide benefits that option-like strategies cannot.
Ultimately, the choice between risks is up to investor preferences, and a diversified approach that pairs strategies different convex strategies such as trend following and options is likely most appropriate.
Conclusion
The convex payoff profile of trend following strategies naturally lends itself to comparative analysis with option strategies, which also have a convex payoff profile. In fact, we would argue – as we have many times in the past – that trend following strategies coarsely replicate the delta profile of option straddles.
In this commentary, we sought to make that connection more explicit by building option straddle strategies that correspond to a naïve trend following strategies of varying lookback lengths.
While the trend following approach has no explicit up-front cost, it risks bearing the full brunt of sudden and large price reversals. With the straddle-based approach, an investor explicitly pays an up-front premium to insure against these risks.
When evaluated through the lens of an insurance policy, the straddle strategy dynamically adjusts its associated premium and deductible over time. When trends are strong, for example, premiums paid tend to be lower, but the cost is a higher deductible. Conversely, when trends are flat, the premium is much higher, but the deductible is much lower.
We found that over the 2005-2020 test period, the cost of the option premiums exceeded the cost of whipsaw in the trend strategies in almost all cases. That is, until March 2020, when a significant and sudden market reversal allowed the straddle strategies to make up for 15 years of relative losses in a single month.
As we like to say: risk cannot be destroyed, only transformed. In this case, the trend strategy was willing to bear the risk of large intra-month price reversals to avoid paying any up-front premium. This was a benefit to the trend investor for 15 years. And then it wasn’t.
By constructing straddle strategies, we believe that we can better measure the trade-offs of trend following versus the explicit cost of insurance. While trend following may approximate the profile of a straddle, it sacrifices some of the intra-month insurance qualities to avoid an up-front premium. Whether this risk trade-off is ultimately worth it depends upon the risks an investor is willing to bear.
In past research we have explored the potential benefits of how-based diversification through the lens of pay-off functions.
Specifically, we explored how strategic rebalancing created a concave payoff while momentum / trend-following created a convex payoff. By combining these two approaches, total portfolio payoff became more neutral to the dispersion in return of underlying assets.
We have also spent considerable time exploring when-based diversification through our writing on rebalance timing luck.
To manage rebalance timing luck, we advocate for a tranching methodology that can be best distilled as rebalancing “a little but frequently.”
Herein, we demonstrate that the resulting payoff profile of a tranche-based rebalancing strategy closely resembles that of a portfolio that combines both strategic rebalancing and momentum/trend-following.
While we typically think of tranching as simply a way to de-emphasize the impact of a specific rebalancing date choice, this research suggests that for certain horizons, tranching may also be effective because it naturally introduces momentum/trend-following into the portfolio.
In Payoff Diversification (February 10th, 2020), we explored the idea of combining concave and convex payoff profiles. Specifically, we demonstrated that rebalancing a strategic asset allocation was inherently concave (i.e. mean reversionary) whereas trend-following and momentum was inherently convex. By combining the two approaches together, we could neutralize the implicit payoff profile of our portfolio with respect to performance of the underlying assets.
Source: Newfound Research. Payoff Diversification (February 10th, 2020). Source: Kenneth French Data Library; Federal Reserve Bank of St. Louis. Calculations by Newfound Research. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. The 60/40 portfolio is comprised of a 60% allocation to broad U.S. equities and a 40% allocation to a constant maturity 10-Year U.S. Treasury index. The rebalanced variation is rebalanced at the end of each month whereas the buy-and-hold variation is allowed to drift over the 1-year period. The momentum portfolio is rebalanced monthly and selects the asset with the highest prior 12-month returns whereas the buy-and-hold variation is allowed to drift over the 1-year period.The 10-Year U.S. Treasuries index is a constant maturity index calculated by assuming a 10-year bond is purchased at the beginning of every month and sold at the end of that month to purchase a new bond at par at the beginning of the next month. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results.
The intuition behind why rebalancing is inherently mean-reversionary is fairly simple. Consider a simple 50% stock / 50% bond portfolio. Between rebalances, this allocation will drift based upon the relative performance of stocks and bonds. When we rebalance, to right-size our relative allocations we must sell the asset that has out-performed and buy the one that has under-performed. “Sell your winners and buy your losers” certainly sounds mean-reversionary to us.
In fact, one way to think about a rebalance is as the application of a long/short overlay on your portfolio. For example, if the 50/50 portfolio drifted to a 45/55, we could think about rebalancing as holding the 45/55 and overlaying it with a +5/-5 long/short portfolio. This perspective explicitly expresses the “buy the loser, short the winner” strategy. In other words, we’re actively placing a trade that benefits when future returns between the two assets reverts.
While we may not be actively trying to express a view or forecast about future returns when we rebalance, we should consider the performance implications of our choice based upon whether the relative performance of these two assets continues to expand or contract:
Relative Performance Expands
Relative Performance Contracts
Rebalance
–
+
Do Not Rebalance
+
–
Our argument in Payoff Diversification was that by combining strategic rebalancing and momentum / trend following, we could help neutralize this implicit bet.
What we can also see in the table above, though, is that the simple act of not rebalancing benefits from a continuation of relative returns just as trend/momentum does.
Let’s keep that in the back of our minds and switch gears, for a moment, to portfolio tranching. Frequent readers of our research notes will know we have spent considerable time researching the implications of rebalance timing luck. We won’t go into great detail here, but the research can be broadly summarized as, “when you rebalance your portfolio can have meaningful implications for performance.”
Given the discussion above, why that result holds true follows naturally. If two people hold 60/40 portfolios but rebalance them at different times in the year, their results will diverge based upon the relative performance of stocks and bonds between the rebalance periods.
As a trivial example, consider two 60/40 investors who each rebalance once a year. One chooses to rebalance every March and one chooses to rebalance every September. In 2008, the September investor would have re-upped his allocation to equities only to watch them sell-off for the next six months. The March investor, on the other hand, would have rebalanced earlier that year and her equity allocation would have drifted lower as the 2008 crisis wore on.
Even better, she would rebalance in March 2009, re-upping her equity allocation near the market bottom and almost perfectly timing the performance mean-reversion that would unfold. The September investor, on the other hand, would be underweight equities due to drift at this point.
Below we plot hypothetical drifted equity allocations for these investors over time.
Source: Tiingo. Calculations by Newfound Research.
The implications are that rebalancing can imbed large, albeit unintentional, market-timing bets.
The whole concept of tranching can be summarized with the phrase: “a little but frequently.” In other words, rebalance your portfolio more frequently, but only make small changes. As an example, rather than rebalance once a year, we could rebalance 1/12th of our portfolio every month. If our portfolio had drifted from a 60/40 to a 55/45, rather than rebalancing all the way back, we would just correct 1/12th of the drift, trading to a 55.42/44.58.1
Another way to think about this approach is as a collection of sub-portfolios. For example, if we elected to implement a 12-month tranche, we might think of it as 12 separate sub-portfolios, each of which rebalances every 12 months but does so at the end of a different month (e.g. one rebalances in January, one in February, et cetera).
But why does this approach work? It helps de-emphasize the mean-reversion bet for any given rebalance date. We can see this by constructing the same payoff plots as before for different tranching speeds. The 1-month tranche reflects a full monthly rebalance; a 3-month tranche reflects rebalancing 33.33% of the portfolio; a 6-month tranche reflects rebalancing 16.66% of the portfolio each month; et cetera.
Source: Newfound Research. Payoff Diversification (February 10th, 2020). Source: Kenneth French Data Library; Federal Reserve Bank of St. Louis. Calculations by Newfound Research. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. The 60/40 portfolio is comprised of a 60% allocation to broad U.S. equities and a 40% allocation to a constant maturity 10-Year U.S. Treasury index. The rebalanced variation is rebalanced partially at the end of each month whereas the buy-and-hold variation is allowed to drift over the 1-year period. The 10-Year U.S. Treasuries index is a constant maturity index calculated by assuming a 10-year bond is purchased at the beginning of every month and sold at the end of that month to purchase a new bond at par at the beginning of the next month. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results.
Note how the concave payoff function appears to “unbend” and the 12-month tranche appears similar in shape to payoff of the 90% strategic rebalance / 10% momentum strategy portfolio we plotted in the introduction.
Why might this be the case? Recall that not rebalancing can be effective so long as there is continuation (i.e. momentum / trend) in the relative performance between stocks and bonds. By allowing our portfolio to drift, our portfolio will naturally tilt itself towards the out-performing asset. Furthermore, drift serves as an interesting amplifier to the momentum signal: the more persistent the relative out-performance, and the larger the relative out-performance in magnitude, the greater the resulting tilt.
While tranching naturally helps reduce rebalance timing luck by de-emphasizing each specific rebalance, we can also see that we may be able to naturally embed momentum into our process.
Conclusion
In portfolio management research, the answer we find is often a reflection of the angle by which a question is asked.
For example, in prior research notes, we have spent considerable time documenting the impact of rebalance timing luck in strategic asset allocation, tactical asset allocation, and factor investing. The simple choice of when, though often overlooked in analysis, can have a significant impact upon realized results. Therefore, in order to de-emphasize the choice of when, we introduce portfolio tranching.
We have also spent a good deal of time discussing the how axis of diversification (i.e. process). Not only have we research this topic through the lens of ensemble techniques, but we have also explored it through the payoff profiles generated by each process. We find that by combining diversifying concave and convex profiles – e.g. mean-reversion and momentum – we can potentially create a return profile that is more robust to different outcomes.
Herein, we found that tranching the rebalance of a strategic asset allocation may, in fact, allow us to naturally embed momentum without having to explicitly introduce a momentum strategy. What we find, then, is that the two topics may not actually be independent avenues of research about when and how. Rather, they may just different ways of exploring how to diversify the impacts of convexity and concavity in portfolio construction.
About two years ago, we compared and contrasted different approaches to risk managing equity exposure; including fixed income, risk parity, managed futures, tactical equity, and options-based strategies.
Given the recent market events as the world navigates through the COVID-19 crisis, we revisit this analysis to see how these strategies would have fared over the past two years.
We find that all eight strategies studied have continued to successfully reduce risk, with two of the previously underperforming options-based strategies now jumping to the forefront of the pack.
Over time, performance of the risk management strategies still varies significantly both relative to the S&P 500 and compared to the other strategies. Generally, risk-managed strategies tend to behave like insurance, underperforming on the upside and outperforming on the downside.
Diversifying your diversifiers by blending a number of complementary risk-managed strategies together – even at random – can be a powerful method of improving long-term outcomes.
“The primary requirement of historical time is that inly one of the possible alternatives coming at you from the future can be actualized in the present where it will flow into the pat and remain forever after unalterable. You may sometimes have “another chance” and be able to make a different choice in some later present, but this can in no way change the choice you did in fact make in the first instance.”
– Dr. William G. Pollard, Prof. of Physics, Manhattan Project
23 trading days.
In a little over a month, the S&P 500 dropped nearly 35% from all-time highs in a sell-off that was one of the fastest in history. Many investors experienced the largest drawdowns their portfolios had seen since the Financial Crisis.
While the market currently sits in a drawdown closer to 25% (as of the time of this writing), the future remains could take any path. Following the relative calm in the market over the preceding year, we are now living through a historic time with the uncertainty and severity of the growing COVID-19 pandemic and its far-reaching ramifications.
However, as a firm that focuses on managing risk, we are used to not knowing the answers.
In the summer of 2018, we published a piece entitled The State of Risk Management where we examined the historical trade-offs in terms of returns during market downturns versus returns during calm market environments of a variety of risk management methods.
Since that time, especially with the benefit of hindsight, one might argue that risk management was unnecessary until this past month. While the S&P 500 experienced a 19% drawdown in Q4 of 2018, it quickly recovered and went on to post a gain of 32% in 2019, rewarding those who stayed the course (or, better yet, bought the dip).
Source: Tiingo. Returns are gross of all management fees, transaction fees, and taxes, but net of underlying fund fees. Total return series assumes the reinvestment of all distributions. Data through 3/27/2020.
With the future poised to follow a variety of uncertain paths, we think it is a prudent time to check in on some of the more popular ways to manage risk and see how they are handling the current events.
The Updated Historical Track Record
For risk management, we examine eight strategies that roughly fit into four categories:
Options Strategies: equity collar3, protective put4, and put-write5,6
Equity Strategies: long-only defensive equity that blends a minimum volatility strategy7, a quality strategy8, and a dividend growth strategy9 in equal weights
Trend-Following Strategies: managed futures10 and tactical equity11
Index data was used prior to fund inception when necessary, and the common inception data is December 1997.
The following charts show the return and risk characteristics of the strategies over the entire historical period. Previously, we had used maximum drawdown as a measure of risk but have now switched to using the ulcer index to quantify both the duration and severity of drawdowns.
Data Source: CBOE, Tiingo, S&P. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. Data is from December 1997 to 3/27/2020.
Data Source: CBOE, Tiingo, S&P. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. Data is from December 1997 to 3/27/2020.
Relative to when we previously presented these statistics (as of July 2018), the most notable changes are that the 95-100 Collar index and Risk Parity have improved and that Managed Futures moved into the top-performing spot up from the middle of the pack. Trend Equity dropped slightly in the rankings, which is partially attributable to our switching over to using the Newfound Trend Equity Index, which includes exposure to small- and mid-cap companies and invests in cash rather than corporate bonds for the defensive position.
Six of the eight strategies still exhibit strong risk-adjusted performance relative to the S&P over the entire time period.
But as we also showed in 2018, the dispersion in strategy performance is significant.
Data Source: CBOE, Tiingo, S&P. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. Data is from December 1997 to 3/27/2020.
This chart also highlights the current trailing one-year performance for each strategy as of 3/27/2020.
Both the 95-110 Collar and the 5% Put Protection indices are in the top 10% of their historical one-year returns, with the put protection index forging new maximum territory. Trend equity and defensive equity have exhibited returns closer to their median levels, while managed futures, strategic diversification with bonds, and risk parity have had returns above their medians.
When we examine the current market environment, this makes sense. Many options were relatively cheap (i.e. implied volatility was low) heading into and early in February, and the option rollover date was close to when the drawdown began (positive timing luck). Equity trends were also very strong coming out of 2019.
With the sharp reversal in equity prices, option strategies provided a strong static hedge that any investors had been paying premiums for through the previous years of bull market returns.
Trend equity strategies were slower to act as trends took time to reverse before cash was introduced into the portfolio, and managed futures were eventually able to capitalize on short positions and diversification once these trends were established.
Zooming in more granularly, we can see the trade-offs between the hedging performance of each strategy in down markets and the premiums paid through negative returns in up-markets. This chart shows the returns relative to the S&P 500 (SPY). When the lines are increasing (decreasing), the hedge is outperforming (underperforming). A flatter line during periods of calm markets indicates lower premiums if we think of these strategies as insurance policies.
Data Source: CBOE, Tiingo, S&P. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. Data is through 3/27/2020.
All eight strategies have provided hedging in both Q4 2018 and the current downturn. The -95-100 Collar- provided some of the lowest premiums. -Trend Equity- also provided low premiums but had a slower time getting back in the market after the hedging period in 2018.
-Managed Futures- have provided some of the best hedging through both down periods but had the highest premium during the strong market of 2019.
With the continued dispersion in performance, especially with the “new” market crisis, this highlights the importance of diversification.
Diversifying Your Diversifiers
Not every risk management strategy will perfectly hedge every downturn while also having a low cost during up markets.
We see the power of diversifying your diversifiers when we test simple equal-weight blends of the risk management strategies. In our 2018 update, we had used an equal weight blend of all eight strategies and a blend of the six strategies that had historical Sharpe ratios above the S&P 500. This latter selection was admittedly biased with hindsight. The two excluded strategies – the 95-110 Collar and the 5% Put Protection indices – were some of the best performing over the period from August 2018 to March 2020!
Our own biases notwithstanding, we still include both blends for comparison.
Both blends have higher Sharpe ratios than 6 of the 8 individual strategies and higher excess return to ulcer index ratios than all of the eight individual strategies.
This is a very powerful result, indicating that naïve diversification is nearly as good as being able to pick the best individual strategies with perfect foresight.
Data Source: CBOE, Tiingo, S&P. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. Data is through 3/27/2020.
But holding eight – or even six – strategies can be daunting, especially for more aggressive investors who may only want to allocate a small portion of their portfolio to a risk management sleeve.
How much diversification is enough?
The following charts show the distribution of risk-adjusted returns from randomly choosing any number of the 8 strategies and holding them in equal weight.
As is to be expected, the cost of choosing the “wrong” blend of strategies decreases as the number of strategies held increases. The potential benefits initially increase and then back off as the luck of choosing the “right” strategy blend is reduced through holding a greater number of strategies.
Both charts show the distributions converging for the single choice for an 8-strategy portfolio.
Data Source: CBOE, Tiingo, S&P. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. Data is through 3/27/2020.
Data Source: CBOE, Tiingo, S&P. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. Data is through 3/27/2020.
Even holding 3 or 4 of the eight risk management strategies, chosen at random, leads to robust results, in general, with narrowed bands in the distribution (e.g. 25th to 75th percentiles).
Blending strategies from each of the different categories – static diversification, options, equity, and trend-following – can further reduce concentration risk verses selection at random and ensure that a variety of risk factors within the hedging strategies (e.g. interest rates from bonds, volatility from options, beta from equity, and whipsaw from trend-following) are mitigated.
Conclusion
We’ve said it many times before: There is no holy grail when it comes to risk management. While finding the perfect hedge that beats all others in every environment is enticing, it is impossible via the simple fact that risk cannot be destroyed, only transformed.
In an uncertain world where we cannot predict exactly what the next crisis will look like – or even what the current crisis will look like after today – diversifying your diversifiers by combining a number of complementary risk-managed strategies may be a prudent course of action.
We believe that this type of balanced approach has the potential to deliver compelling results over a full market cycle while managing the idiosyncratic risk of any one manager or strategy.
Diversification can also help to increase the odds of an investor sticking with their risk management plan as the short-term performance lows won’t be quite as low as they would be with a single strategy (conversely, the highs won’t be as high either).
Developing a plan and sticking with it is the most important first step in risk management. It is obviously desirable to keep premiums in strong markets as low as possible while having efficient hedges in down markets, but simple diversification can go a long way to provide a robust results.
Risk management is, by definition, required to be in place before risks are realized. Even when the market is currently down, risks in the future are still present. Therefore, we must periodically ask ourselves, “What risks are we willing to bear?”
One potential path has been locked into history, but the next time potential risks become reality – and they inevitably will – we must be comfortable with our answer.
Source: Tiingo, Bloomberg, Barcharts. Calculations by Newfound Research. Past performance is backtested and hypothetical. Returns are gross of all fees, costs, and taxes except for underlying expense ratios. Returns assume the reinvestment of all distributions. Past performance is not indicative of future results. Starting date based upon the availability of pricing data.
Does it matter which we choose? Does an inverted yield curve make the first choice less attractive than the second?
Source: Bloomberg.
The expected return of a portfolio, then, can simply be thought of as the risk-free rate plus the blended return of risk premia. For example, the expected return of a 60/40 is:
Liquidity Cascades: The Coordinated Risk of Uncoordinated Market Participants
By Corey Hoffstein
On September 11, 2020
In Portfolio Construction, Risk Management, Weekly Commentary
This paper is unlike any research we’ve shared in the past. Within we dive into the circumstantial evidence surrounding the “weird” behavior many investors believe markets are exhibiting. We tackle narratives such as the impact of central bank intervention, the growing scale of passive / indexed investing, and asymmetric liquidity provisioning.
Spoiler: Individually, the evidence for these narratives may be nothing more than circumstantial. In conjunction, however, they share pro-cyclical patterns that put pressure upon the same latent risk: liquidity.
In the last part of the paper we discuss some ideas for how investors might try to build portfolios that can both seek to exploit these dynamics as well as remain resilient to them.
Read it now.