You can use the Sharpe Ratio to compare different strategies to see which strategy offers the best return for a given amount of risk. The strategy with the highest Sharpe Ratio wins.
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We'll consider three investing strategies. One is a five-stock Relative Strength (26-week) strategy, rebalanced every January. This represents a risky investment, risk being defined as volatility that is measured by the standard deviation of the returns. The second is the market-matching S&P 500 (AMEX: SPY). This strategy has average returns and is as risky as the market as a whole. The third choice is one-year U.S. Treasury bills, commonly assumed to be the closest thing we have to a risk-free investment. The recent returns for each of these strategies are as follows:
Year RS-26 S&P 500 T-bill
1986 53.01% 18.82% 7.21%
1987 13.11% 5.40% 5.46%
1988 -10.97% 15.99% 6.52%
1989 46.59% 31.56% 8.37%
1990 7.34% -2.97% 7.38%
1991 126.70% 30.51% 6.25%
1992 21.13% 7.45% 3.95%
1993 9.05% 10.09% 3.35%
1994 42.46% 1.33% 3.39%
1995 23.20% 37.28% 6.59%
1996 22.34% 22.69% 4.82%
1997 17.96% 33.60% 5.30%
1998 22.91% 30.73% 4.98%
1999 116.65% 21.10% 4.31%
Avg. 36.53% 18.83% 5.56%
St. Dev. 39.73% 12.99% 1.55%
Sharpe .7792 1.0528
(Note: Workshop veterans may notice that the returns above are the regular, or "arithmetic" average, rather than the compound annual growth rate (CAGR) we normally quote. Sharpe ratio calculations use that average, not the CAGR, for reasons we will touch on later.)
This week, we will talk about Nervous Ned, a conservative investor who can't handle much volatility. Nervous Ned is a good Fool and only invests his Bucket C money in the market. But, even with the proper long-term attitude, Ned has problems sleeping if his investments drop by a significant amount.
Ned likes the concept of the RS-26 screen. It makes sense to him, it's exciting, and the returns are certainly attractive -- but, he doesn't like risk. He's willing to give up some potential returns (reluctantly) in exchange for lower volatility.
One traditional approach to mitigating volatility and risk is portfolio allocation. Ned puts some of his long-term savings into a "risk-free" investment, such as T-bills (he could also use bonds). The rest can go into the highly volatile RS-26. This will reduce Nervous Ned's return (assuming that the RS-26 continues to perform in the future as it has in the past), but he'll sleep better during times like last week's sell-off.
Another possibility would be for Ned to invest in an S&P 500 index fund. The index fund may be boring, but it has much lower volatility than the RS-26, and the returns are considerably higher than the ultimate snooze-inducing investment, T-bills. Which choice is better, the RS-26/T-bill blend, or the index fund?
To match the volatility of the S&P 500 using the blend technique, Ned would need to put about two-thirds of his money into U.S. T-bills (actually 67.4%) and about a third of his money in an RS-26 strategy (32.6%, to be precise). Had he done that back in 1986, here's how his returns would have looked:
Year Return
1986 22.14%
1987 7.95%
1988 0.82%
1989 20.83%
1990 7.37%
1991 45.50%
1992 9.55%
1993 5.21%
1994 16.12%
1995 12.00%
1996 10.53%
1997 9.43%
1998 10.82%
1999 40.92%
Avg. 15.66%
St. Dev. 12.99%
Sharpe .7792
This strategy is much less volatile than the RS-26, in fact its standard deviation is exactly the same as that of the S&P 500 in the first example (yes, we planned it that way). But, let's look again: Eeek! The returns are much lower than the S&P 500 (see above). That wasn't part of the plan.
By contrast, the far simpler strategy of just buying the S&P 500 offered an average return in the neighborhood of 18.83%, with a standard deviation of only 12.99%. Compared to the traditional risk-mitigating approach (the RS-26/T-bill blend) the S&P 500 offers a better return for the same amount of volatility.
That's what the Sharp Ratio tells us: Given two strategies with equal volatility (in this case, the RS-26/T-bill blend vs. the S&P 500), the one with the higher Sharpe Ratio will have the higher return, and vice versa. When two strategies have similar returns, the one with the higher Sharpe Ratio will have lower volatility. You can boil that down to: Higher Sharpe Ratio = Good.
Of course, when two strategies have equal returns (or standard deviations), you can compare the other numbers directly. But how often does that happen? This is the significance of the Sharpe Ratio. When you compare strategies, the one with the most bucks (return) for the bang (risk), or the least bang for the bucks, will have the higher Sharpe Ratio.
Ned may not like it, but the boring S&P 500 would most likely give him more bucks, and the same amount of sleep, as the RS-26/T-bill blend.
Next week, we will talk about Nervous Ned's thrill-seeking sister, Crazy Cathy. She's more like a typical Workshop investor -- volatility be damned, show me the returns! (Just kidding.) We'll see you then -- same Fool time, same Fool channel.
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