Assessing Risk: The Sharpe Ratio
By Jim Stevens (JimStevens@aol.com)
Burlington, VT (July 1, 1999) -- Risk is a term that we hear tossed around often in investment circles. Since risk isn't something that is easily quantified, it is often used to give subjective explanations (excuses?) for why one investment has performed differently than another.
How many times have you heard "But the risk-adjusted return was better" as a justification for low performance?
There are some elements of "risk" that will remain unquantifiable. No model can perfectly predict the future of stocks, and no investor can know exactly what their future financial situation will be or how they will react to changes in their lives or their investment performance.
Luckily, there are some factors that describe "risk" that we can measure. In 1966, William F. Sharpe introduced a formula for evaluating historical investments based on how well they performed compared to a benchmark investment, and how much volatility had to be endured to realize those returns. At The Sharpe Ratio website, you'll find all the deep academic details.
The Sharpe Ratio can be used to compare various investments' risk-adjusted performance. The higher the Sharpe ratio is, the greater an investment's return per unit of risk. The formula for calculating the Sharpe Ratio is to subtract a benchmark return (usually U.S. Treasury bills) from the investment's return for each year of the time period you are working with. Next you take the average of these yearly differences and divide the result by standard deviation of the differences. The higher the number, the better the risk-adjusted performance score.
As an example of the calculation, here are the returns for the Keystone 5 from 1986 through the end 1998:
Year Key 5 T-bill Difference 1986 22.0% 6.2% 15.8% 1987 8.1% 5.5% 2.6% 1988 8.5% 6.4% 2.1% 1989 59.2% 8.4% 50.8% 1990 (0.3)% 7.8% -8.1% 1991 71.8% 5.6% 66.2% 1992 12.4% 3.5% 8.9% 1993 36.3% 2.9% 33.4% 1994 9.0% 3.9% 5.1% 1995 43.8% 5.6% 38.2% 1996 38.2% 5.2% 33.0% 1997 56.6% 5.3% 51.3% 1998 45.3% 5.1% 40.2%
The average of the annual differences is 26.12%, and the standard deviation
of the differences is 23.17%. Divide the average difference by the standard
deviation of the differences and you get a Sharpe Ratio of 1.13. Over the
same time period, the Sharpe Ratio for the Standard & Poor's 500 Index
(dividends reinvested) is 0.994, and the Sharpe ratio for the Foolish Four is
By this particular measure, over the last twelve years, the Keystone 5 has had a better risk-adjusted return than the market itself -- and it has beaten the Foolish Four as well.
Go Key 5!