When evaluating investment managers, looking at annualized return numbers without examining risk is too simplistic and can lead to poor investment choices. One must always ask, “How much risk was taken to generate that return”?
Investing in an asset with wild price swings can produce great pleasure or unendurable pain. For example, although gold seems like a sure thing today, those who paid $800 an ounce in the early 1980s and sold in frustration at $200 an ounce decades later understand pain. While gold can adorn the human body wonderfully, it’s a very risky investment.
How do we measure risk? And how do we incorporate risk in evaluating investment managers?
Investment analysts most commonly use volatility (also known as variability) of returns in measuring risk. There are mathematical and behavioral reasons that make this a useful method.
As for the mathematics, losses count more than gains. Suppose in year one, your mutual fund gains 10 percent, while in year two, it falls 10 percent. The loss percentage applies to a larger base than the gain percentage. After two years, your account balance is down 1 percent overall. Change the annual gain and loss to 50 percent, and you’ll lose 25 percent in two years. Another way to look at it: One year of a 100 percent loss will negate any number of years of 100 percent gains.
From a behavioral standpoint, it’s often said that investors aren’t risk averse, they’re loss averse. No matter how often they repeat the mantra that they’re invested for the long term, few investors can stomach persistent major losses. They exit the market to lick their wounds, usually waiting for the market to fully recover before sticking a few toes back in the water.
The Sharpe ratio
In 1966, Nobel-laureate economist William Sharpe first proposed the measure of risk-adjusted investment returns that now bears his name. Three elements are used in the Sharpe ratio: a time series of returns from an investment; the variability or volatility of those returns expressed in terms of standard deviation; and a “risk-free” return rate. The third element is critical to understanding risk-adjusted returns.
Remember when banks offered reasonable interest rates to get you to lock up your money for an extended period? Suppose you were offered a 5 percent annual interest rate for a U.S. Government-insured, $100,000 five-year CD. How much risk would you be willing to tolerate to generate a 6 percent return from an alternate investment for five years? The alternate investment is really only providing you with 1 percent annually of “excess return,” since you could get 5 percent with no risk.
Here’s an example of how you can use the Sharpe ratio. We’ll look at two five-year periods that were good for stocks—1996-2000, and 2003-2007.
For 1996-2000, the stock market, as measured by the Vanguard S&P 500 index fund, gained an average of 18.2 percent, compounded annually. From 2003-2007, the comparable number was 12.7 percent. Superficially, the earlier period outperformed the later period by 5.5 percent annually, a very significant difference when compounded over many years.
To calculate Sharpe ratios for the two periods, we first adjust the returns to eliminate the effect of the prevailing “risk-free” return. The most commonly used “risk-free” rate is that of U.S. Treasury bills that mature in 13 weeks. During 1996-2000, Treasury bills provided an average return of 5.2 percent; from 2003-2007, their average rate of return was 3 percent. Our “excess” returns for the two periods are 13 percent versus 9.7 percent, a difference of 3.3 percent, or 2.2 percent smaller than the difference in raw returns.
Now let’s take volatility into account. Volatility during 1996-2000 was 16.2 percent, somewhat higher than the average of 15 percent over the past two decades. The mid-2000s, on the other hand, were a period of remarkably low market turmoil, with volatility of only 8.6 percent. Dividing the excess returns by these volatility numbers, we get a Sharpe ratio for 1996-2000 of 0.80, while that for 2003-2007 is 1.13. The mid-2000s produced significantly better risk-adjusted returns.
It’s more common to use the Sharpe ratio to compare two managers using similar strategies for the same period. An experienced analyst would find the manager whose Sharpe ratio was 1.13, a better choice than the one whose Sharpe ratio was 0.80 for the same investment strategy under the same market conditions.
Interpreting the Sharpe ratio
Notice that the Sharpe ratio has no units associated with it. To use it, you must compare apples to apples. First, the time period for the returns you’re comparing must be the same for all managers you’re examining. Second, the Sharpe ratio doesn’t have much meaning for dissimilar investments—comparing stocks to bonds, for example.
You’ll find Sharpe ratios for mutual funds in the popular Morningstar guide. Although Morningstar has its own methodology for evaluating risk-adjusted performance, you can come pretty close to its “star” ratings by examining the Sharpe ratios for various funds. Here are Sharpe ratios for the past three years for large-cap growth funds available through Schwab, grouped by Morningstar ratings:
| Morningstar rating | Number of funds | Average Sharpe ratio |
| 5 star | 66 | 0.42 |
| 4 star | 192 | 0.25 |
| 3 star | 314 | 0.16 |
| 2 star | 230 |
0.05 |
| 1 star | 98 | -0.07 |
The difference of 0.49 between the worst and best risk-adjusted returns is pretty typical of the worst to the best stock portfolio managers. For comparison, the Vanguard S&P 500 Index fund had a Sharpe ratio of 0.14 for the same period, slightly below the middle of this range. The Sharpe ratio is found in databases that evaluate investment managers. The wise investor uses this tool.
