Because investors are, on average, risk averse, we should expect that there is a positive relation between expected returns and *expected* volatility—the greater the expected volatility, the greater the rate of return required. Conversely, we should expect to see a negative relationship between returns and *unexpected* volatility as investors increase the discount rate they use to value future expected earnings on risky assets.

We should also expect, during periods of heightened uncertainty, that investors, in a flight to safety, would be willing to accept lower required returns on safe assets.

The Sharpe ratio was developed to create a measure of risk-adjusted returns. It measures returns per unit of risk, with “risk” being defined as volatility. Importantly, the Sharpe ratio assumes returns are normally distributed, which is not always the case.

**Skewness**

While volatility is certainly a measure of risk, and a good one, it’s not the only one. There are other measures of risk that investors care about, including skewness and kurtosis.

Skewness measures the asymmetry of a distribution. In terms of the market, the historical pattern of returns doesn’t resemble a normal distribution, and so demonstrates skewness. Negative skewness occurs when the values to the left of (less than) the mean are fewer but farther from it than values to the right of (greater than) the mean.

For example, the return series of -30%, 5%, 10% and 15% has a mean of 0%. There is only one return less than zero, and three that are higher. The single negative return is much farther from zero than the positive ones, so the return series has negative skewness. Positive skewness, on the other hand, occurs when values to the right of (greater than) the mean are fewer but farther from it than values to the left of (less than) the mean.

Investors have a preference for assets with positive skewness. This is evidenced by an investor’s willingness to accept low, or even negative, expected returns when an asset exhibits positive skewness.

The classic example of positive skewness is lottery tickets—the expected return is -50% (the government only pays out about 50% of the sales proceeds), and the vast majority end up worthless, but investors hope to hit the big jackpot.

Some examples of assets that exhibit both positive skewness and poor returns are IPOs, “penny stocks,” stocks in bankruptcy and small-cap growth stocks with high investment and low profitability (such as dot-com stocks).

On the other hand, investors generally dislike assets with negative skewness. High-risk asset classes (such as stocks) typically exhibit negative skewness. Because they dislike them, such assets must provide a large risk premium. And historically, such assets have provided high returns as compensation for their risk.

**Kurtosis**

Kurtosis measures the degree to which exceptional values—those much larger or much smaller than the average—occur more frequently (high kurtosis) or less frequently (low kurtosis) than in a normal (bell-shaped) distribution. High kurtosis results in exceptional values that are called “fat tails.”

Fat tails indicate a higher percentage of very low and very high returns than would be expected in a normal distribution. Low kurtosis results in “thin tails” and a wide middle to the curve. In other words, more values are closer to the average than would be found in a normal distribution, and tails are thinner.

Summarizing, if an investment exhibits both negative skewness and high kurtosis, it has the potential for large losses. That investment should have a large risk premium in order to compensate investors for accepting risk, which they prefer to otherwise avoid.

Another type of risk that is unrelated to the distribution of returns is liquidity. Investments with high liquidity (low trading costs) and no restrictions (such as mutual funds, which have daily liquidity and very low, if any, trading costs) should have lower expected returns than investments with lower levels of liquidity. For example, the greater trading costs of less liquid small stocks helps explain their higher historical returns and provide a risk-based explanation for their higher expected returns. Investments with “gates,” which restrict liquidity, such as partnerships that invest in private equity, hedge funds and interval funds, should carry risk premiums as compensation—if they do not, you should not invest.

We’ll now look at three investments that exhibit negative skewness and high kurtosis.

**Reinsurance Risk**

The returns to reinsurance investments are not normally distributed—far from it. As an example, a reinsurance fund might have an expected return of 7%. In a very good year, with few to no losses incurred, the return might be 12%. However, in a bad year, such as 2017, the losses could easily reach double digits. And in an exceptionally bad year, the losses could be even larger.

Because the number of good years has far exceeded the number of really bad years, the Sharpe ratio has been exceptionally high. However, as noted earlier, the Sharpe ratio is not a good measure of risk when returns are not normally distributed.

Reinsurance returns are negatively skewed with a long, but thin left (bad) tail. In addition, because reinsurance requires investing in contracts that typically are at least one year in length, reinsurance has liquidity risk that should be compensated for. Once these additional issues are considered, the risk-adjusted returns to reinsurance would look more like the risk-adjusted returns to other risky assets (such as stocks and bonds). And that is exactly what we should expect from an efficient market.

Two examples of reinsurance funds investors could consider are Stone Ridge’s Reinsurance Risk Premium Interval Fund (SRRIX) and Pioneer’s ILS Interval Fund (XILSX). These are both interval funds with limited quarterly liquidity (minimum of 5% per quarter).

**Alternative (Marketplace) Lending Risk**

The distribution of returns for alternative (prime consumer, student and small business loans) lending is similar to that of reinsurance, exhibiting both features investors dislike—negative skewness and high kurtosis.

If we assume an expected return of 7%, a very good year would have returns perhaps 3-5 percentage points higher. However, a really bad year caused by high unemployment might see losses of 7% or even higher.

And, as is the case with reinsurance, because the number of good years is expected to be far greater than the number of bad years (the number of years with very high unemployment is relatively low), we expect equitylike returns with only about one-quarter of the volatility (about 5% versus about 20%).

As is also the case with reinsurance, alternative lending requires investing in loans that are typically from three to five years in maturity. Thus, like reinsurance, alternative lending has liquidity risk which should be compensated for. Once these additional issues are considered, the risk-adjusted returns to alternative lending look more like the risk-adjusted returns to other risky assets. Again, that is exactly what we should expect from an efficient market.

Two examples of alternative lending funds investors could consider are Stone Ridge’s Alternative Lending Risk Premium Fund (LENDX) and RiverNorth’s Marketplace Lending Corporation Fund (RMPLX). These are both interval funds with limited quarterly liquidity (minimum of 5% per quarter).

**Variance Risk Premium (VRP)**

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 (puts and calls), 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, markets tend to crash down, not up.

Thus, the VRP isn’t an anomaly we should expect to be arbitraged away. Because the VRP’s risks (specifically, the sale of options performs poorly) tend to show up in bad times (when risky assets perform 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 a terrible outcome, like their house burning down or the price of oil going to $200 per barrel.

Thus, they knowingly and willingly pay above fair value to eliminate that risk. As a result, the VRP should be considered a unique risk premium that investors with long investment horizons and stable finances can harvest because they have the ability to accept the cyclical risks that show up in bad times.

Because the VRP is just another form of selling insurance, it has the same distribution of return properties as reinsurance—negative skewness and excess kurtosis. And like all such investments, it should carry a large risk premium. And like the other two alternative investments we have discussed, investing in the VRP requires investing in longer contracts that are not very liquid.

Thus, the best way to invest in this asset class is in an interval fund, such as Stone Ridge’s All Asset Variance Risk Premium Fund (AVRPX). The fund has a targeted volatility of 10%, or about half that of equities, while providing, we believe, equitylike returns. However, you must also consider the potential for large losses as well as the loss of daily liquidity.

**Summary**

All three of the above alternatives provide investors with unique sources of risk and return that can improve the efficient frontier by providing diversification benefits. However, you should be sure to understand that all three investments exhibit negative skewness and high kurtosis while sacrificing the benefits of daily liquidity.

That’s the trade-off you need to consider: equitylike returns with low average correlation to both stocks and bonds in return for sacrificing daily liquidity and accepting the risk of occasional large losses. (Full disclosure: My firm, Buckingham Strategic Wealth, recommends Stone Ridge funds in constructing client portfolios.)

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