Reducing the Risk of Black Swans

by Larry Swedroe

  Further Evidence

  In his paper “Do Financial Markets Reward Buying or Selling Insurance and Lottery Tickets?”, which appeared in the September 2012 issue of the CFA Institute’s Financial Analysts Journal, Antti Ilmanen found that:

  Selling volatility on either the left tail (insurance) or the right tail (lottery tickets) adds value in the long run.

  As with holding high-volatility, lottery-like investments, buying options-based tail risk insurance against asymmetric payoffs earns poor long-term results.

  The evidence is not restricted to options trading. Carry-seeking and other strategies with asymmetric payoffs are closely related to volatility-selling—all are variants of selling tail risk insurance and have earned positive long-run returns. Furthermore, they often have produced Sharpe ratios higher than that of the equity risk premium.

  Speculative, lottery-like investments have delivered lower risk-adjusted returns than their defensive peers in all major asset classes. The more speculative the strategy, the worse the risk-to-reward ratio becomes.

  The use of leverage in low-volatility strategies appears to boost long-run returns.

  Ilmanen concluded: “To interpret the long-run gains from selling financial catastrophe insurance as rational risk premiums seems natural. In contrast, the gains from lottery selling seem better explained by investor irrationality or by such nonstandard preferences as lottery seeking or leverage aversion.” He noted that the demand for left tail insurance “focuses on portfolio-level downside protection and is guided by covariance with market and other systematic factors. On the right tail, lottery seeking is best served by more idiosyncratic investments and is guided by asset characteristics.”

  William Fallon, James Park and Danny Yu contribute to the literature on the VRP with their study “Asset Allocation Implications of the Global Volatility Premium,” which appears in the September/October 2015 issue of the CFA Institute’s Financial Analysts Journal. The purpose of their study was “to provide a comprehensive statistical and economic analysis of the global volatility risk premium, with a special emphasis on its practical role as an institutional holding.”

  The authors developed a grand volatility composite portfolio (GVCP), which was derived from a dynamic trading strategy applied to a variety of instruments, mainly derivatives. Their dataset consisted of nearly two decades of volatility marks gathered through an assortment of options exchanges and investment dealers. Their research accounts for transaction costs, which have a material impact on performance.

  The GVCP is an equal-risk-weighted blend of returns on 34 volatility-sensitive instruments in markets across four asset classes: equities (covering 11 markets that make up almost 90 percent of the MSCI World Index), bonds (covering four 10-year interest rate swaps, denominated in U.S. dollars, euros, sterling and yen, that make up approximately 95 percent of the J.P. Morgan GBI Global Index), currencies (covering nine major currencies, traded against the U.S. dollar, that make up more than three-quarters of non-U.S. global GDP) and commodities (10 contracts covering four major commodity sectors—industrial metals, precious metals, energy and agricultural products—that make up more than half of the S&P GSCI). The authors based their volatility returns primarily on two instruments: variance swaps and options. Their data series has an earliest start date of 1995, with other starting dates varying depending on data availability.

  To create series that were comparable across both assets and time, the authors scaled each of the 34 volatility return series to target an annualized volatility of 1 percent each month at trade inception. The scaling was ex-ante, using historical realized volatility calculated monthly with an expanding window and a minimum of 36 observations. To facilitate comparison across asset classes, they then combined the scaled volatility return series on an equal-weighted basis by asset within each asset class. They chose an equal-weighting scheme because of its simplicity and transparency. This approach resulted in four composite volatility return series—for equities, fixed income, currencies and commodities—each of which they then scaled to target 1 percent risk on an ex-ante basis using the methodology described previously. Finally, to facilitate the statistical and economic evaluation of volatility as an asset class, Fallon, Park and Yu combined the four asset class return composites on an equal-weighted basis into a single composite scaled to target 1 percent annualized risk, again using the methodology previously outlined. They called this series the GVCP. The following is a summary of their findings:

  Negative (short) volatility premiums are widespread, statistically significant and economically meaningful. A consistently positive mean for the spread between implied and realized volatility existed in all asset classes and components.

  Selling volatility is profitable in virtually all markets nearly all the time, including the five-year period surrounding September 2008, with a consistently positive mean for volatility returns (but with fat left tails).

  Adding the GVCP in small amounts to typical institutional portfolios would have substantially enhanced long-term returns (increasing the combined Sharpe ratio by as much as 12 percent in the authors’ sample) but at the cost of increased short-term tail risk.

  The means of all 34 volatility return series were positive. The annual mean return to the 11 stock components ranged from 2.8 percent to 4.5 percent, and the annual standard deviation ranged from 5.4 percent to 7.9 percent. For the four bond components, the annual mean return ranged from 1.8 percent to 4.0 percent, and the annual standard deviation ranged from 4.6 percent to 14.1 percent. For the nine currencies, the annual mean return ranged from 0.6 percent to 1.3 percent, with the annual standard deviation ranging from 2.1 percent to 4.5 percent. For the 10 commodities, the annual mean return ranged from 0.7 percent to 3.5 percent, with the annual standard deviation ranging from 3.4 percent to 13.4 percent.

  With all 34 means positive, and with 32 of them significant at the 1 percent level of confidence and two at the 10 percent level, Fallon, Park and Yu concluded: “This consistency suggests a reliable risk premium whose basis is the persistent excess of implied over realized volatility.”

  They also concluded: “Equally consistent are the patterns in higher moments, with skewness values often large and negative and excess kurtosis figures large and positive. Taken together, these results indicate that buyers offer insurance-like economic rents to sellers, who earn a steady monthly income in exchange for bearing ‘crash’ risk—the possibility of severe but empirically infrequent losses.” In other words, there is a trade-off between average returns and tail risk, with the worst cases coming in at more than double the magnitude of the best-case positive observations.

  It is important to note Fallon, Park and Yu found that, on average, “transaction costs reduce gross returns by 47%, a significant reduction.” Thus, patient trading is critical to successfully implement the strategy because investors should want to be a seller, not a buyer, of liquidity. That means accepting tracking-error risk.

  The authors also observed that the correlations between the GVCP and each of their volatility return series indicate the possibility for diversification benefits across asset classes—pooling enhances the risk and reward trade-off. Correlations are higher in equities and currencies (composite correlations of 0.88 and 0.83) and lower in fixed income and commodities (composite correlations of 0.54 and 0.69). They found that the Sharpe ratio of the GVCP, which pools by asset class and is the broadest composite, remains more than 31 percent higher than the average Sharpe ratio of the composites (1.02 versus 0.78) and 94 percent higher than the average Sharpe ratio across assets (1.02 versus 0.53). However, they found no improvement in tail risk. In fact, they determined that tail risk events in their sample were “more highly correlated than typical month-to-month returns.”

  Fallon, Park and Yu concluded that what the GVCP offers is largely distinct from standard explanatory factors (market beta, size and value). The authors write: “Therefore, it may offer unique and additive diversification benefits to trad
itional portfolios.”

  The Performance of the VRP in Calm Markets

  In an earlier study on the VRP, “Still Not Cheap: Portfolio Protection in Calm Markets,” which appeared in the Summer 2015 issue of The Journal of Portfolio Management, Israelov and Nielsen investigated whether equity portfolio insurance was, historically, a good purchase when the cost of that insurance was relatively cheap—the flip side of selling volatility insurance (earning the VRP). The premise, or theory, behind buying volatility insurance when the cost is relatively cheap is as follows:

  Historically, volatility is mean-reverting.

  Buying put options provides long volatility exposure.

  Go long volatility when it is at historically low levels because volatility is likely to revert to the mean.

  Presented in this light, buying put options in calm markets might appear to be a compelling strategy. But does hard data actually support the theory? Israelov and Nielsen begin by noting: “It is well-known that portfolio insurance is expensive on average.” Translation: Being persistently long volatility is a bad and expensive strategy, and there are more efficient ways to reduce tail risk than buying insurance. For example, for the period from March 15, 2006, through June 20, 2014, Israelov and Nielsen found that buying 5 percent out-of-the-money S&P 500 puts lowered returns by 2.5 percentage points (from 5.2 percent to 2.7 percent) and reduced the Sharpe ratio from 0.37 to 0.21, a decrease of more than 40 percent. The authors also showed that a standalone strategy of buying 5 percent out-of-the-money S&P 500 puts provided an excess return of -2.0 percent per year, and the strategy produced a Sharpe ratio of -0.83. However, such insurance lowered downside market beta considerably, from 0.85 to 0.47. Simply lowering equity exposure would have been a more efficient alternative. But we have yet to answer our question about the VRP in calm markets.

  Regarding whether it makes sense to take a tactical approach to volatility (only going long, or to avoid selling when the insurance is cheap), Israelov and Nielsen provided this important insight: “It doesn’t matter if implied volatility is at or near its historical low. It doesn’t matter if realized volatility is expected to increase. It doesn’t even matter if realized volatility actually does increase over the option’s life. What does matter is the option’s purchase price (implied volatility) relative to its fundamental value (ex-post realized volatility).”

  They found that, over the full period for which VIX data was available (from January 2, 1990, through June 30, 2014), the ex-post realized risk premium was 3.4 percent. What’s more, it was positive 88 percent of the time. The authors concluded: “Investors who heed analysts’ recommendation to purchase options are not only long volatility—they also face long odds of benefiting from the option purchase.”

  Having determined that being long volatility all the time is a bad strategy, the authors then sought to discover whether it is a good strategy to be long volatility when volatility is low and options prices are historically cheap. Israelov and Nielsen found not only that the realized ex-post variance risk premium was positive in every decile of volatility, but also that the realized premium in the three lowest-volatility buckets, at 3.1 percent, is not much different from the 3.4 percent average from all buckets. Even in the lowest VIX decile, the realized premium was 2.5 percent. They write: “Option prices may be lower, but they remain expensive in the sense that the long volatility component of one-month options is expected to have negative returns.”

  Upon examining the data, Israelov and Nielsen presented some additional interesting findings. For example: “The volatility risk premium is more variable when implied volatility is high. Its 80% confidence interval is 5% wide in the lowest implied volatility decile and 19% wide in the highest decile. In the lowest risk environment, the most extreme outcome had realized volatility 8% higher than implied volatility. In the highest risk environment, the most extreme outcome occurred when realized volatility was 49% higher than implied volatility. Although owning a put option provides the same contractual protection in each decile per se, the distribution of outcomes across volatility environments has been very different.”

  In other words, while a 5 percent out-of-the-money put provides the same protection at all times, historically investors have needed the insurance most when volatility is high, not low. The authors concluded that, while the ex-post cost of insurance was lower during times when volatility remained in the lowest three deciles, “less expensive options in calm markets do not necessarily mean that investors are getting a good deal.”

  They also noted that the maximum 21-day return from the lowest four deciles of volatility was only 1.7 percent. Given that the cost of the options used in their test was more than 1 percent per year, the authors reason that buying them “hardly seems like money well spent.”

  To examine the robustness of their findings, Israelov and Nielsen also tested whether their results held over a larger universe of equity indices. Specifically, they analyzed index options on the DAX (Germany), Euro Stoxx 50, FTSE (U.K.), Hang Seng (Hong Kong), KOSPI (Korea), NASDAQ, Nikkei (Japan), Russell 2000 and Swiss Market. Internationally, the evidence was very similar to what they found in the United States. For example, from the lowest to the highest volatility quintile, the realized risk premium persistently increased from 1.6 percent to 3.8 percent. They also found similar Sharpe ratios, of about -0.9, across quintiles, with the exception of the highest quintile, where it was much worse at -1.4.

  The takeaway is that buying insurance (put options) when volatility is low (the cost is “cheap”) is only a good strategy if investors compare it to buying insurance when volatility is high (the cost is expensive).

  As a final test, the authors examined the effectiveness of buying insurance against the risk of black swans. They concluded that black swans would need to occur with much greater frequency than they have in the past to make buying insurance an effective strategy. Israelov and Nielsen write: “If you believe that the type of black swan event … is significantly under-represented in our historical record and you are also willing to pay out more than 1% of NAV per year in order to buy protection for such an event, then purchasing put options may be rationalized.” They added this caution: “While it is certainly possible that black swans are under-represented and put options are less expensive than they appear (or even cheaply priced!), we should similarly be willing to also entertain the possibility that black swan events are over-represented in our sample … and put options are even more expensive than they appear.”

  The research presented by Israelov and Nielsen demonstrates that “put options’ low prices during calm periods give the illusion of value.” The authors close with this warning: “Buying an option is not a bet that realized volatility will increase; it is a bet that realized volatility will increase above the option’s implied volatility. Buying an option is expected to lose money even when volatility is low and rising if the spread between realized and implied volatility is sufficiently high.” Said another way, the winning strategy is to be a consistent seller of volatility insurance.

  Summary

  Diversification has been called the only free lunch in investing. And diversification is investors’ only relief from systemic and unforecastable market risks. Effective diversification requires uncorrelated investments, as well as a look beyond traditional stock and bond indices to other areas of risk and return, such as reinsurance, alternative lending and the VRP. Thus, a key to successful investing is pursuing a combination of strategies across low-correlating assets to produce a broadly diversified portfolio.

  While the VRP is best known in U.S. equities, and so most volatility products focus on them, diversification across many asset classes has the potential to improve VRP returns through reducing portfolio volatility. This is both intuitive and empirically observable in historical data, which shows low correlations of the VRP across asset classes, including commodities, currencies and credit.

  Before investing in the VRP, or any strategy exhibiting negative skewness,
you should be aware that, while such strategies can consistently accrue small and regular gains over many years, rare, large losses disproportionately occur in bad times. It is this poor timing of losses that helps explain the large required risk premiums. For example, a simple strategy that involves capturing S&P 500 volatility premium lost more than 48 percent in October 2008. However, volatility premium strategies tend to recover quickly, more so than other asset classes, because it is precisely in the immediate aftermath of a crisis event when the volatility premium is richest. This is similar to how insurance companies, which raise premiums after incurring large losses from catastrophic events, operate.

  The potential for large losses means that attempting to monetize the variance risk premium may not be suitable for all investors. However, investors with long-term investment horizons, including institutional investors or high-net-worth individuals, who are willing and able to bear the unique risks involved may be in a good position to take advantage of the VRP and potentially harvest superior risk-adjusted, long-term returns. The VRP provides another unique source of risk and return that investors can access, and one that has the potential to improve the efficiency of diversified portfolios. To access the VRP, our preferred vehicle is the Stone Ridge All Asset Variance Risk Premium Interval Fund (AVRPX). It provides exposure to the VRP across global markets and multiple asset classes, using patient trading strategies to act as a provider, rather than a taker, of liquidity.