The Sharpe Ratio calculates return per unit of risk. It uses "volatility," which is easy to measure, as a proxy for the general concept of "risk." However, volatility appears larger when one looks at shorter time periods, and smaller when one looks at longer time periods. This can dramatically change the Sharpe Ratio calculation.
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The Sharpe Ratio compares the return on an investment to the risk of that investment. The higher the Sharpe Ratio, the more return per unit of risk. But how do we define "risk" in our investments, and is that definition correct?
As investors, we face several risks. The most common risk is that our investments will decline in value. Another risk is that our investments will not perform well enough to allow us to retire in comfort. Each investor has her own unique definition of "risk," depending on her goals.
The Sharpe Ratio defines "risk" as the volatility of returns. A strategy that is up dramatically one year and down the next is considered to have more risk than a strategy that returns a steady amount every year, even if they both provide the same "average" annual return. This is the way most academics and professionals in the financial field define risk.
This definition is a good one, but it isn't perfect. For example, imagine a strategy that has returned a steady 15% per year for the last three years. In year four, the strategy suddenly returns 100%. Would you be upset about the increased volatility of your strategy? I didn't think so.
However, one might argue that if your strategy could shoot up by that much in one year, then it's possible that it could also decline dramatically in one year. In other words, your superb returns in year four indicate that there might be more risk in your strategy than you thought. Volatility, which we can measure, acts as a proxy for that intangible factor we call "risk."
Below are the annual returns of three different investments since 1986. One is a five-stock RS-26 strategy, holding for 12 months and rebalanced every January. The second is the S&P 500 Index. The third is a "risk-free" investment of FDIC insured one-month certificates of deposit (CDs). This assumes that you would buy one-month CDs every month and hold to maturity. For reasons that will become apparent shortly, I'm using CDs instead of U.S. Treasury bills as the risk-free investment for this example.Year RS-26 S&P 1-month CDs
1986 49.57 18.66 6.61
1987 12.39 5.25 6.73
1988 -11.12 16.61 7.58
1989 46.71 31.69 9.11
1990 6.22 -3.10 8.15
1991 121.53 30.47 5.82
1992 19.99 7.62 3.64
1993 8.33 10.07 3.11
1994 42.84 1.32 4.37
1995 22.34 37.58 5.87
1996 26.78 22.96 5.35
1997 17.22 33.36 5.54
1998 28.03 28.58 5.48
1999 116.63 21.04 5.19
Avg. 36.25 18.72 5.90
Std Dev 38.76 12.89 1.66
Sharpe 0.7795 1.0048
(Note that RS-26 and S&P data is from Jamie Gritton's backtest engines, and the one-month CD data is from the Federal Reserve Economic Database. Jamie has recently updated his website, so these numbers might be slightly different from those reported earlier.)
As you can see, the S&P 500 has a considerably higher Sharpe Ratio than the RS-26 strategy.
That's fine, but this only looks at volatility of returns each year. As all you Workshop investors know, a lot of volatility is "hidden" when you only look at annual returns. My own RS-26 annual strategy was up 18% as of last Friday, but it has gone through a roller coaster ride this year, reaching a high of 71% and a low of about -2%! That can take a toll on anyone, regardless of risk tolerance.
There is nothing magical about looking at one-year time periods, other than convenience. Say we have two strategies. Each has returns of, say, 15% in year one, 12% in year two, and 17% in year three. Strategy A has returns of 1.17% per month in year one, 0.95% per month in year two, and 1.3% in year three. However, Strategy B has returns of +4% in January of year one, -6% in February, +8% in March, and so on. The annual returns might be the same, but the monthly returns are much more consistent for Strategy A than Strategy B. Would these two strategies have the same "risk"? Our annual Sharpe Ratio doesn't know or care.
What happens if we calculate the Sharpe Ratio by looking at one-month time periods? I calculated the Sharpe Ratios for the RS-26 strategy shown above, and the S&P 500 Index. (You can download an Excel spreadsheet with all of these calculations here.) When we look at monthly instead of annual data, the Sharpe Ratios decline to 0.2308 for RS-26 and 0.2318 for the S&P 500. Same strategies, same results, but much lower Sharpe Ratios.
Also, the huge advantage the S&P 500 had over our RS-26 strategy has vanished: The two strategies now appear to be about equal in terms of "risk-adjusted" returns. Why? Because the monthly returns show greater volatility (and different volatility) than annual returns. The Sharpe Ratio for any strategy will vary dramatically depending on the length of time used in the calculation!
So, what time period should we use? In the Workshop and throughout The Motley Fool, we constantly remind people to invest for the long term. We recommend that you only invest money in stocks that you won't need for at least five years. At the Workshop, you might trade stocks as often as once a month, but you should stick with the strategy for the long term (as Ann Coleman writes, "The strategy is the stock").
I went back to 1969 and divided the 31 years of data (from January 1969 through December 1999) into six periods, each one 62 months long, and calculated the Sharpe Ratios. Not surprisingly, our RS-26 strategy had a much higher Sharpe Ratio of 1.15. The longer the time period you look at, the less "volatile" things appear! This is the main reason why we continually insist that you only invest long-term ("Bucket C") money in the stock market.
So, what should we make of the Sharpe Ratio? It is a useful tool, but we should be careful in using it. Remember that volatility and risk are not the same, and even volatility can vary, depending on the time period used to measure it. As investors, we should consider both our own risk tolerance and the timeframe of our investments before we calculate Sharpe Ratios.
Hopefully, I haven't lost too many of you. Also, I would appreciate any feedback from those of you who have done considerable reading and research on the Sharpe Ratio.
Next week I'll finish off with my last few problems with the Sharpe Ratio (yes, we'll finally end a series that's taken as long as the Florida recounts). I hope to see you all then -- same Fool Time, same Fool channel.
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