Economists have long puzzled over the simultaneous demand from consumers for risk-reducing insurance and risk-increasing lottery tickets. Every year, people spend trillions of dollars on the two combined. These behaviors may seem unrelated, but they are actually symmetrical forms of risk transfer.

The insurance policy is a means of risk transfer in which a buyer pays to eliminate the possibility of an extreme, rare downside event—such as a premature death, destruction from an earthquake or hurricane or an equity market crash—while the lottery ticket is a means of risk transfer in which a buyer pays to create the possibility of an extreme, rare upside event.

The price of such a risk transfer decomposes into two parts: an expected payout; and a risk premium to compensate the seller for the uncertain nature of any payout, which may be sudden and dramatic. Financial markets are full of strategies resembling either insurance or lotteries.

**VRP Explained**

For example, in options markets, the premium to compensate the seller for the uncertain nature of the payout is called the variance (or volatility) risk premium (VRP). This risk premium is rational for both the buyer and the seller.

The buyer willingly pays it to create, or to eliminate, uncertainty. The seller charges for taking the risk. And the evidence is that, the more remote the risk, the higher the ratio of risk premium to expected payout.

The bottom line is that over a large sample size, there is an expected fair value set by the probabilities of outcomes, and option sellers charge a premium to that fair value to compensate the seller for providing a risk-transfer service.

The VRP refers to the fact that, over time, the option-implied volatility has tended to exceed the realized volatility of the same underlying asset. This has created a profit opportunity for volatility sellers—those willing to write volatility insurance options, collect the premiums and bear the risk that realized volatility will increase by more than implied volatility.

Investors are willing to pay a premium, because risky assets—such as stocks—tend to perform poorly when volatility increases. In other words, the market tends to crash down, not up. Thus, the VRP isn’t an anomaly we should expect to be arbitraged away. Because the risks of the VRP (the selling of options performs poorly) tend to show up in bad times (when risky assets are performing poorly), we should expect a significant premium.

Another way to think of this is that investors pay to hedge catastrophic outcomes—they want to transfer the risk of some terrible outcome, like their house burning down or the price of oil going to $200. Thus, they knowingly and willingly pay above fair value to eliminate that risk.

Therefore, the VRP should be considered a unique risk premium that investors with long investment horizons and stable finances can harvest, allowing them to take on cyclical risks that show up in bad times.

**Analyzing The VRP**

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 but mainly derivatives. Their data set consisted of nearly two decades of volatility marks gathered through a variety of options exchanges and investment dealers.

They write: “A strategy-based approach was required because (1) pure volatility returns are not universally available and (2) risks vary among instruments, across asset classes, and over time.” The authors’ results account for transaction costs, which have a material impact on performance.

Their 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% of the MSCI World Index); bonds (covering four 10-year interest rate swaps denominated in U.S. dollars, euros, sterling and yen, which make up approximately 95% of the J.P. Morgan GBI Global Index); currencies (covering nine major currencies, traded against the U.S. dollar, which 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, making 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 starting dates varying depending on data availability.

To create series that were comparable across assets as well as time, the authors scaled each of the 34 volatility return series to target an annualized volatility of 1% 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% 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, they combined the four asset class return composites on an equal-weighted basis into a single composite scaled to target 1% annualized risk, again using the methodology previously described. They called this series the GVCP.

**The Results**

Following is a summary of their findings:

- Negative (short) volatility premiums are widespread, statistically significant and economically meaningful. There was a consistently positive mean for the spread between implied and realized volatility 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 enhanced substantially long-term returns (increasing the combined Sharpe ratio by as much as 12% in the authors’ sample) but at the cost of increased short-term tail risk.
- All 34 means were positive. The annual mean return to the 11 stock components ranged from 2.8% to 4.5%, and the annual standard deviation ranged from 5.4% to 7.9%. For the four bond components, the annual mean return ranged from 1.8% to 4.0%, and the annual standard deviation ranged from 4.6% to 14.1%. For the nine currencies, the annual mean return ranged from 0.6% to 1.3%, with the annual standard deviation ranging from 2.1% to 4.5%. For the 10 commodities, the annual mean return ranged from 0.7% to 3.5%, with the annual standard deviation ranging from 3.4% to 13.4%.

With all 34 means being positive, and with 32 significant at the 1% level and two at the 10% 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 being more than double the magnitude of the most-positive observations.

**Patient Trading Critical**

It’s important to note that Fallon, Park and Yu found that “on average, that transaction costs reduce gross returns by 47%, a significant reduction.” Thus, to successfully implement the strategy, patient trading is critical, as 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 there is a 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% higher than the average Sharpe ratio of the composites (1.02 versus 0.78) and 94% higher than the average Sharpe ratio across assets (1.02 versus 0.53). However, they found no improvement in tail risk.

They concluded: “Tail risk events in our sample are more highly correlated than typical month-to-month returns.”

Finally, Fallon, Park and Yu concluded that what the GVCP offers is largely distinct from the exposures of standard explanatory factors (market beta, size and value). The authors write: “Therefore, it may offer unique and additive diversification benefits to traditional portfolios.” The findings Fallon, Park and Yu present in their study are consistent with previous research.

**Historical Evidence**

In the paper “Option Markets and Implied Volatility: Past Versus Present,” published in the November 2009 issue of the Journal of Financial Economics, Scott Mixon shows the results of his hand-collected data set from newspapers published between 1873 and 1875.

He calculated implied and subsequently realized volatility and found that 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, markets are 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.

**Similar Patterns**

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 like 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 Strategic Wealth, 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. The VRP has been well documented, and is thus best known in U.S. equities.

For example, the implied volatility of S&P 500 Index options has exceeded the 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, 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.

**Summary**

The VRP provides another unique source of risk and return that investors can access, one that has the potential to improve the efficiency of diversified portfolios.

Diversifying sources of risk across “factors” (or unique sources of returns) that have demonstrated persistent and pervasive premiums capturable after costs has been shown to be a superior way to improve performance versus the alternative of pursuing the holy grail of alpha, which is becoming a more and more elusive quest as the market becomes more efficient over time.

In terms of VRP strategy implementation, due to its high turnover, it’s important there be a focus on being a patient trader, providing liquidity as opposed to being a buyer of it.

*Larry Swedroe is the director of research for **The BAM Alliance**, a community of more than 140 independent registered investment advisors throughout the country.*