Prior research and empirical investment results demonstrate that strategy performance can be highly sensitive to rebalance schedules, an effect called rebalance timing luck (“RTL”). In this paper we extend the empirical analysis to option-based strategies. As a case study, we replicate a popular strategy – the self-financing, three-month put-spread collar – with three implementations that vary only in their rebalance schedule. We find that the annualized tracking error between any two implementations is in excess of 400 basis points. We also decompose the empirically-derived rebalance timing luck for this strategy into its linear and non-linear components. Finally, we provide intuition for the driving causes of rebalance timing luck in option-based strategies.
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.
Prior research and empirical investment results have shown that portfolio construction choices related to rebalance schedules may have non-trivial impacts on realized performance. We construct long-only indices that provide exposures to popular U.S. equity factors (value, size, momentum, quality, and low volatility) and vary their rebalance schedules to isolate the effects of “rebalance timing luck.” Our constructed indices exhibit high levels of rebalance timing luck, often exceeding 100 basis points annualized, with total impact dependent upon the frequency of rebalancing, portfolio concentration, and the nature of the underlying strategy. As a case study, we replicate popular factor-based index funds and similarly find meaningful performance impacts due to rebalance timing luck. For example, a strategy replicating the S&P Enhanced Value index saw calendar year return differentials above 40% strictly due to the rebalance schedule implemented. Our results suggest substantial problems for analyzing any investment when the strategy, its peer group, or its benchmark is susceptible to performance impacts driven by the choice of rebalance schedule.
For hedging strategies, there is often a trade-off between degree, certainty, and cost.
Put options have high certainty and typically offer a high degree of protection, making them costly to hold and roll over the long run.
In this note, we briefly explore the application of different tactical signals to a 9-month, 25-delta rolling put strategy in an effort to reduce long-term costs.
We find that signals based upon volatility appear to perform significantly better than signals based upon price changes, likely due, at least in part, to the nature of the put we are purchasing, which has significant sensitivity to changes in implied volatilities.
These results must be taken with a significant grain of salt due to the low number of actual crisis events to measure against. Furthermore, these results are not applicable for investors for whom a certain degree of loss would be disruptive to their financial plan or needs (e.g. impacting withdrawal / spending plans or forcing the liquidation of assets). For other investors, however, the tactical application of put options may represent an interesting pay-off profile.
In managing risk, there are three primary trade-offs to consider: degree, cost, and certainty.
Degree measures how much protection we are looking too get. Rather than thinking of degree as how much of our portfolio we’re looking to protect (e.g. 10% vs 100% of our notional exposure), we want to think of this more in terms of the loss level we want the protection to begin at. For example, degree captures whether we want to protect against all losses or just losses greater than 30%.
Cost captures how much we must pay for our protection. This cost can be explicit (i.e. we pay a known, up-front premium) or implicit (e.g. whipsaw cost in trend following).
Finally, certainty captures how reliable the hedge is. A centrally cleared put option, for example, has a very high degree of certainty. Buying a call option on Treasury bonds (perhaps to benefit from the materialization of a flight-to-safety trade or as a bet on Fed policy during a crisis) carries with it some basis risk if our primary goal is to protect against equity losses.
Like many trade-offs in life, this is one of those “pick two” cases. You can have a high degree of protection with high reliability, but it will cost you a lot. If you want to reduce the cost, you’ll need to either reduce the degree of protection or the certainty.
Rather than trying to find the holy grail of high degree, high certainty, and low cost, our time is likely better spent first considering the axis by which we are constrained. For example, if a 50% loss represents a catastrophic outcome (e.g. impacting withdrawal / spending plans and potentially having knock-on effects in creating forced asset sales), then we can seek to maximize certainty and minimize cost for this specific scenario. On the other hand, if we cannot afford to spend more than 300 basis points a year on risk management, then we can try to maximize degree and certainty for that budget.
Put options, by definition, have a high degree of certainty, and therefore tend to carry a fairly substantial cost. For example, below we plot the return of a put option strategy that rolls 9-month, 25-delta puts each month, purchasing enough puts to cover 100% of the S&P 500.
Source: DiscountOptionsData.com. Calculations by Newfound Research. Returns are hypothetical and backtested. Returns are gross of all fees including, but not limited to, management fees, transaction fees, and taxes. Returns assume the reinvestment of all distributions.
Despite offering meaningful returns during the 2008 economic crisis and the recent March 2020 COVID-19 panic, this strategy has still lost -2.3% annualized.
To be fair, this is a very naïve tail hedging strategy. There are no considerations for generating offsetting carry (e.g. a put ratio approach), pro-active monetization, trade conversion (e.g. puts to put spreads), reasonable basis risk trades, or exchanging between linear and non-linear trades.
And it may not be wholly fair to evaluate the returns of a tail risk strategy in isolation. After all, it may help increase the geometric returns of an equity portfolio substantially if appropriately rebalanced.
Nevertheless, this example highlights that if we want to combine a high degree of protection with certainty, it should carry relatively high cost.
In this commentary we will explore a few ideas for dynamically employing put options, attempting to maintain relatively high certainty while minimizing cost.
Tactical Signals
Using tactical signals to identify when to buy put options is akin to waiting to smell smoke before calling your agent to buy fire insurance. It may save significant cost over the long run, but you risk failing to have protection in periods where you cannot get to the phone fast enough or by the time that you do, the cost of insurance is prohibitive.
Nevertheless, in cases where a tail hedge is not necessary (i.e. true knock-out conditions) but simply preferred, tactical tail hedging may provide an attractive payoff.
Below we explore a variety of signals which may indicate elevated risk going forward. At the core of our approach will be the 9-month 25-delta put strategy we introduced above. For each of our signals, when the signal indicates rising risk, we will buy into the put strategy. Otherwise, we will assume a 0% return cash position.
It should be stressed that this is a rather general approach to what can be a highly specific problem for allocators. By rolling far-dated puts each month, our strategy will have exhibit substantial convexity to changes in implied volatility, whereas a short-dated put would exhibit greater convexity to changes in the S&P 500 itself. This means that our approach may not be suitable for protecting against slow, tepid market declines.
Fortunately, market declines and changes in volatility have historically exhibited significant negative correlation. Therefore, for large and rapid declines, we can generally expect the value of our long-dated, deep out-of-the-money puts to appreciate significantly.
Given that our options will be highly sensitive to changes in implied volatility, we explore signals that are not only potentially related to losses in U.S. equities, but also appreciation of expected volatility.
Indicator
Measure
Thesis
S&P 500 Returns
63-Day Return
Negative returns in the S&P 500 may forecast negative returns going forward.
S&P 500 Returns
Z-Score of 63-Day Return (126-Day)
Below average returns in the S&P 500 may forecast negative returns going forward.
S&P 500 Trend
30×120 EWMA
Negative trend signals in the S&P 500 may forecast negative returns going forward.
1M IV
63-Day Change
Increasing implied volatility may be a sign that investors believe risk is increasing.
1M RV
63-Day Change
Increasing realized volatility may be a sign that volatility will increase in the future.
1M RV – IV
63-Day Change
If realized volatility is increasing beyond implied volatility, it may be a sign that protection is underpriced.
1M – 3-Month RV
63-Day Change
If short-term volatility is higher than medium-term volatility, it may be a sign that risk is increasing.
Skew (1M 25 Delta Put – Call)
63-Day Change
If the skew of the volatility curve is increasing, it may be a sign that investor demand for protection has gone up.
Short Volatility Strategy
63-Day Return
If the return of a short volatility strategy is negative, it may be a sign that risk is increasing.
High Yield Credit Spreads
63-Day Change
If markets are demanding an increasing premium for credit risk, it may be a sign that economic risk is increasing.
Why would we expect tactical signals to work? The core thesis is partially behavioral and partially structural. On the behavioral side, we expect investors to first under- and then over-react to regime changes in the market. Ideally tactical signals can cue us into these changes before the herd catches on, and then we can benefit as the herd reprices markets.
From a less irrational perspective, we expect investors to exhibit “knock-out” conditions whereby they become forced sellers. For example, as prices fall and volatility picks up, collateral requirements may go up. This can cause forced de-leveraging, further driving down prices and further driving up collateral requirements. This type of positive feedback loop can create liquidity and credit spirals in markets. Therefore, by buying protection at the early signs of a potential market dislocation, we can potentially protect ourselves from the non-economically driven behavior of other market participants.
Note that we focus on fairly short measurement periods. This is for two reasons. First, risk can reprice rapidly, so we want to make sure. Secondly, put options allow us to explicitly measure, per day, how much we’ll pay in premium for the non-linear payoff we are purchasing. This massively asymmetric payoff profile means that we may be able to afford more false positives, unlike trend following where our capital may be meaningfully eroded by whipsaw or jump risk.
Below we plot the returns of applying each signal. When a signal indicates heightened risk (e.g. increasing volatility or declining prices), we purchase the put strategy index. We tranche positions over a 20-trading-day period, meaning that if a signal stays constant, we’ll increase our position by 5% a day. If a signal turns on and then immediately off, we’ll carry at least a 5% position for 20 trading days.
Source: DiscountOptionsData.com; Tiingo.com; St. Louis Federal Reserve. Calculations by Newfound Research. Returns are hypothetical and backtested. Returns are gross of all fees including, but not limited to, management fees, transaction fees, and taxes. Returns assume the reinvestment of all distributions.
We can see that all of the approaches significantly cut down on the premium paid for protection. The “worst” performing strategy – the 63-day return z-score – had a loss of -1.0% annualized compared to the -2.3% for the constant put strategy.
Of course, just sitting in cash the entire time would have reduced the cost. The question we should ask is: how much did we forego in protection?
Below we plot the performance of these approaches over several of the larger market loss scenarios over the last 15 years.
Source: DiscountOptionsData.com; Tiingo.com; St. Louis Federal Reserve. Calculations by Newfound Research. Returns are hypothetical and backtested. Returns are gross of all fees including, but not limited to, management fees, transaction fees, and taxes. Returns assume the reinvestment of all distributions.
We can see that the volatility-based models (e.g. changes in 1M IV, RV, RV – IV, and Skew) tend to do a fairly consistent job their up-capture, whereas performance-based measures on the S&P 500 (e.g. 63-day returns or 30×120 EWMA) are much less consistent. This is particularly apparent in the recent COVID-19 crisis, where return-based signals were too delayed. Interestingly, this lower upside capture was not met with decreased cost: the return-based signals were some of the worst performing models. Only the high yield credit spread model seemed to offer a balanced trade-off.
Interestingly, signals derived from a short-volatility strategy were negative in 2008. In this strategy we are short an at-the-money call and put. Calling this strategy short-volatility may be a bit of a misnomer, as it will profit when realized returns stay range-bound, which is different than explicitly generating a return from declining volatility. Nevertheless, we can see that the return profile of this approach, plotted below, looks very much like “picking up pennies in front of a steam roller.” Unfortunately, the steam roller seems to manifest rather quickly, so the 63-day return signal may be too slow in this case.
Source: DiscountOptionsData.com; Tiingo.com; St. Louis Federal Reserve. Calculations by Newfound Research. Returns are hypothetical and backtested. Returns are gross of all fees including, but not limited to, management fees, transaction fees, and taxes. Returns assume the reinvestment of all distributions.
Conclusion
Given their high certainty and degree of protection offered, put options can be prohibitively expensive (particularly after a significant market decline, when demand for protection often goes up). For investors for whom a certain level of loss is truly disruptive to operations or creates a knock-out condition, protection is not an option. For others, though, the selective use of put options may provide an interesting, diversifying payoff profile.
In this commentary, we briefly explored the application of different tactical signals to a far-dated, deep out-of-the-money put strategy. Not surprisingly, we found that all of the approaches helped reduce the annualized cost of the put strategy. However, not all of the signals provided meaningful upside capture. Given that there are few actual periods where the put strategy offers positive returns, missing these gains defeats the whole purpose of the exercise.
We found that volatility-based signals worked best. This may be due to a combination of two facts: (1) the put strategy has meaningful sensitivity to changes in implied volatility, and (2) the put strategy has an asymmetric payoff profile, reducing the cost of false positives.
These results should taken with a large grain of salt, however, as the number of meaningful payoff periods is very low. Future research should explore how these signals work when applied to different equity indices, ETFs, or even individual stocks.
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.