All investments are a balancing act between risk and return. Higher returns usually come with higher risk. The Sharpe Ratio is a frequently used formula for determining which investments offer the most return for a given amount of risk.
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First of all, you must be emotionally and financially prepared to take on extra risk. That means paying off all high-interest debt (e.g., your credit cards) and only investing money in the market that you won't need for several years (what I refer to as Bucket C money). You should also know your own risk tolerance. Higher returns are just not worth it if you can't sleep at night.
Once you've resolved those issues, one big question remains. Given two or more strategies with different returns and risks, which one offers the most return for the amount of risk involved? One way to answer this question is to use a calculation known as the Sharpe Ratio.
The Sharpe Ratio is named after its creator, William Ratio, a noted finance professor and 1990 Nobel Prize winner in economics. (I guess you could say he's a pretty sharpe guy.) The calculation itself is fairly simple, but the theory behind the Sharpe Ratio can be complex. [Editor's Note: Yes, you're right, the Sharpe Ratio is named after William Sharpe. Since you were paying attention, the bad jokes for this article end here, we promise.]
The Sharpe Ratio is calculated by comparing the returns of an investment strategy (investing in an index fund, or one of our Workshop screens, or whatever) to a "benchmark" strategy or security. The normal "benchmark" used is a "risk-free" investment, such as U.S. Treasury bills.
Let's walk through an example and calculate the Sharpe Ratio for a five-stock RS-26 strategy, using annual holds, rebalanced every January. The "benchmark" we'll use is the one-year U.S. Treasury bill, also purchased in January.
Year RS-26 US T-Bill Difference
1986 53.01% 7.21% 45.802590
1987 13.11% 5.46% 7.649806
1988 -10.97% 6.52% -17.492966
1989 46.59% 8.37% 38.222400
1990 7.34% 7.38% -0.039098
1991 126.70% 6.25% 120.446022
1992 21.13% 3.95% 17.183628
1993 9.05% 3.35% 5.695066
1994 42.46% 3.39% 39.071610
1995 23.20% 6.59% 16.612884
1996 22.34% 4.82% 17.517976
1997 17.96% 5.30% 12.661228
1998 22.91% 4.98% 17.925472
1999 116.65% 4.31% 112.342810
Note: The returns for RS-26 come from Jamie Gritton's Backtest Engine, and the T-Bill information is from the Federal Reserve Economic Database (FRED).
Once you have your "differential returns," you need two numbers. First, you need the average of the differences. In our example above, the average is 30.97.
Next, you need to calculate the standard deviation of the differences. Standard deviation is a measure of the variation in your results. For example, if our differences were all between 25 and 30, the standard deviation would be very low. If the differences were spread out between -17 and 120, like the above table, the standard deviation would be much higher. If you're a math whiz, you can calculate the standard deviation by hand, but if you're like me, you'll just use a computer spreadsheet. According to my Excel spreadsheet, the standard deviation of the differences above is 39.75.
Now comes the easy part. To calculate the Sharpe Ratio, simply divide the average return (30.97) by the standard deviation (39.75). This gives a result of 0.779. So, our RS-26 portfolio above has a Sharpe Ratio of 0.779.
If you don't want to do all that work, the Sharpe Ratio is calculated for each of our strategies automatically at Jamie Gritton's backtest website. The ratio calculated above is slightly different from the ratio calculated by Jamie's backtested (0.771), probably due to minor differences in the "benchmark" rate.
We can also compute the Sharpe Ratio for the S&P 500. If we do the same calculations as above, we get a ratio of 1.054 for the S&P 500. This means that the S&P 500 had a higher "risk-adjusted return" than our RS-26 strategy.
That's fine, but what does this mean? The average annual return for our RS-26 strategy was 32%, while the S&P returned only 18%. If you had invested in the RS-26 strategy, you would have more money than if you'd invested in the S&P 500. You can't take $50 to the supermarket, buy $100 worth of groceries, and tell the cashier, "Well, if you risk-adjust this money, it's really a hundred dollars." In other words, you can't eat a risk-adjusted return, right?
Actually, you can eat a risk-adjusted return. We'll explain how next week. In the process, we'll show some of the practical applications of the Sharpe Ratio. By the time we're finished, you'll appreciate how this simple ratio helped William Sharpe win the Nobel Prize. We hope to see you then -- same Fool time, same Fool channel!
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