It has long been known that investors have asymmetric preferences when it comes to bearing downside risk versus participating in the upside.
The term “loss aversion” refers to an investor’s tendency to prefer avoiding losses more strongly than acquiring gains. Most studies suggest a loss is twice as powerful, psychologically, as an equal-sized gain. This aversion helps explain why the equity risk premium has been so large; the risk of owning equities is highly correlated with the risks of the economic cycle.
Thus, in recessions, investors who earn wages or own businesses are exposed to the double whammy of bear markets and either job layoffs or reduced business income (or even bankruptcy).
Because investors are, on average, highly risk averse, it should be no surprise they have demanded a large equity premium as compensation for accepting the risks of this double whammy, especially when considering that the risk of unemployment or the loss of business income are basically uninsurable. Investors might be forced to sell stocks (because of the diminution of earned income) at the worst possible time.
A Study On Accepting Risk
Roni Israelov, Lars Nielsen and Daniel Villalon contribute to the literature on investors’ asymmetric preference for risk with their paper “Embracing Downside Risk,” which appears in the Winter 2017 issue of The Journal of Alternative Investments.
Using equity index options prices, they showed that the vast majority of the equity risk premium derives from accepting downside risk versus seeking participation in the upside. They found that, over the period 1986 through 2014, greater than 80% of the equity risk premium was explained by the willingness to accept downside risk.
The conclusion we can draw is that investors who seek to maximize upside potential while minimizing downside risk through options (buying call and put options) are highly likely to underperform due to the cost of that insurance, the size of which is related to the asymmetric preference for risk.
In other words, demand for upside participation is strong, while the tolerance for accepting downside risk is weak. The result is that the volatilities implied in the options tend to be greater than realized volatility. In fact, Israelov, Nielsen and Villalon found that the ex-post variance risk premium (VRP) was positive 88% of the time and averaged 3.4% per year.
Behavioral finance provides us with an explanation for this phenomenon. Investors have a preference for the positive skewness (meaning there is the potential for large gains) offered by buying puts, and they dislike the negative skewness (meaning there is the potential for large losses) that results in selling puts.
Israelov, Nielsen and Villalon found a similar result when they examined the upside and downside risk premium in Treasury bonds, with 62% of the excess return coming from the downside.
The lower percentage they found in bonds shouldn’t be surprising, because Treasuries have less downside risk than stocks. When they examined gold, the authors found 100% of the excess return was from downside risk.
They also found very strong results when they looked at credit default swaps, with the return for accepting downside risk accounting for more than 100% of the excess return. However, they note this result could be heavily influenced by the recent financial crisis, as the data only covered the period July 2007 through June 2015.
These findings are consistent with other research on the VRP.
In the paper “Option Markets and Implied Volatility: Past Versus Present,” which was published in the Journal of Financial Economics’ November 2009 issue, Scott Mixon presented the results of his hand-collected data set from newspapers published between 1873 and 1875.
He calculated implied and subsequently realized volatility and found option prices reflected a persistent, large and positive spread between implied and realized volatility of 11.8% for the most liquid options. That’s a huge risk premium. Today the market is more liquid, more transparent and more efficient. Thus, we should not expect to see such a large premium.
Additionally, Stone Ridge Asset Management examined the VRP for the 10 largest stocks for the period 1996 through 2012, breaking down the period into three subperiods. The firm’s researchers found a persistent and stable premium.
From 1996 through 1999, the VRP was 4.3%. From 2000 through 2009, the premium was 3.9%. And from 2010 through 2012, it was 4.1%. Stone Ridge also found strikingly similar patterns in implied volatility curves around the world.
In international markets, just as in the U.S., more short-dated and more out-of-the-money options have higher expected VRP returns in both single-stock and index options. (Full disclosure: My firm, Buckingham, recommends Stone Ridge funds in the construction of client portfolios.)
In his November 2011 paper, “The Variance Risk Premium Around the World” (a Federal Reserve System Board of Governors International Finance Discussion Paper), Juan Londono reported similar results for the VRP.
For example, the implied volatility of S&P 500 Index options exceeded realized index volatility 85% of the time from January 1990 to September 2014. And options historically have traded about 4.4 percentage points above subsequent realized volatility.
It’s important to understand that this should not be interpreted to mean the option market tends to overestimate future volatility. Instead, the more likely explanation is that option prices incorporate a risk, or insurance, premium.
Most investors are risk-averse, and so they are willing to pay a premium to hedge downside risk. Buying volatility insurance options provides that hedge or insurance. The large premium also exists because of an imbalance in supply and demand. There are likely far more natural buyers of volatility insurance options than sellers.
Lotteries Vs. Insurance
In his paper “Do Financial Markets Reward Buying or Selling Insurance and Lottery Tickets?”, which appeared in the September/October 2012 issue of 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.
- Purchasing options-based tail risk insurance against financial asymmetric payoffs is a close cousin of volatility selling and, like holding high-volatility, lotterylike investments, earns poor long-term results.
- The evidence is not restricted just 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. They have often produced Sharpe ratios higher than that of the equity risk premium.
- Speculative, lotterylike 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.
- Levering up low-volatility opportunities 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.”
Finally, we have a study by Roni Israelov and Lars Nielsen, “Still Not Cheap: Portfolio Protection in Calm Markets,” which was published in the Summer 2015 issue of The Journal of Portfolio Management. They researched whether equity portfolio insurance, historically, was a good purchase at times when the cost of that insurance is relatively cheap—the flip side of selling volatility insurance (earning the VRP).
The theory behind buying volatility insurance when its cost is relatively inexpensive is as follows:
- Historically, volatility is mean-reverting.
- Buying put options provides long volatility exposure.
- Go long volatility when it’s 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 quite a compelling strategy. 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 by buying insurance.
For example, from March 15, 2006 through June 20, 2014, Israelov and Nielsen found buying puts lowered returns by 2.5 percentage points and lowered the Sharpe ratio from 0.37 to 0.21, a relative decrease of more than 40%.
The authors also demonstrate that long volatility exposure reduces performance by 2.0 percentage points per year, and the strategy produces a Sharpe ratio of negative 0.83.
However, the insurance did lower downside beta considerably, from 0.85 to 0.47. Simply lowering equity exposure would have been a more efficient alternative. But we’ve yet to answer our question about the VRP in calm markets.
A Tactical Approach
Regarding whether or not it makes sense to take a tactical approach to volatility (only going long, or avoiding 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 (Jan. 2, 1990 through June 30, 2014), the ex-post realized risk premium paid was 3.4%. What’s more, the premium was positive 88% of the time.
They 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 of the time has been a bad strategy, Israelov and Nielsen then sought to discover whether it was a good strategy to be long volatility when volatility is low and options prices are historically cheap.
The authors found not only that the realized ex-post volatility risk premium was positive in every decile, but that the realized premium in the three lowest-volatility buckets, at 3.1%, isn’t really much different than the 3.4% average from all buckets. Even in the lowest VIX Index decile, the realized premium was 2.5%.
The authors 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% out-of-the-money put provides the same protection at all times, historically, investors have needed the insurance the most when volatility has been high, not low.
The authors concluded that, while the ex-post cost of insurance was lower at 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 was only 1.7%. Given that the cost of the options was more than 1% per year, “to buy these options hardly seems like money well spent.”
Testing For Robustness
To examine the robustness of their findings, Israelov and Nielsen tested whether their results held over a larger universe of international equity indexes. Specifically, they analyzed index options on the DAX (Germany), Euro Stoxx 50, FTSE (U.K.), Hang Seng (Hong Kong), KOSPI (Korea), the Nasdaq, Nikkei (Japan), Russell 2000 and Swiss Market.
The evidence internationally was very similar to what they found in the U.S. For example, from the lowest to the highest volatility quintile, the realized risk premium persistently increased from 1.6% to 3.8%. The authors 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 bottom line 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 so-called black swans. They concluded black swans would have 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.”
Puts More Expensive?
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 offered by Israelov and Nielsen demonstrates that “put options’ low prices during calm periods give the illusion of value.”
The authors end 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.”
In other words, the winning strategy is to be a consistent seller of volatility insurance.
Given investors’ well-documented aversion to risk, both theory and evidence suggest that those willing to accept downside risk should be rewarded well.
In addition, given the evidence on the high cost of downside protection, investors who find the risks too great to bear are better served either by reducing their exposure to, or eliminating, the responsible assets rather than seeking to buy downside protection.
Finally, investors willing to embrace the idea of selling downside risk protection should consider accessing the VRP in a diversified way.
This commentary originally appeared September 11 on ETF.com
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