WARNING: This is NOT an April Fool's joke!
Investments will appear smaller in your Sharpe Ratio mirror if they trail badly

You will recall that last week's article on risk and volatility ended with the general conclusion that risk, as expressed in terms of volatility and standard deviation, is not a very useful indicator by itself, but begs to be placed in the context of returns. While we vaguely remember that we have to accept higher risks in order to achieve higher returns, we also know that the better investments are the ones at the high end of the reward-to-risk scale. For example, what would be the point of holding an extremely low risk investment that consistently loses money, or to take disproportionate risks for mediocre returns?

Luckily, a fellow named William Sharpe came to the rescue by inventing the most widely used direct measure of reward-to-risk, the Sharpe Ratio. Besides getting to name the ratio he also received the Nobel Prize for his work. We wonder which he values the most.

The simple definition of the Sharpe Ratio is a measure of performance calculated as the average return divided by the variance of those returns, or risk adjusted performance.

The formula for the Sharpe Ratio is:

S(x) = ( r_x - R_f ) / StdDev(x)

where:

x is some investment
r_x is the average annual rate of return of x
R_f is the best available "risk-free" rate of return (e.g. T-bills)
StdDev(x) is the standard deviation of r_x

If the formula sounds too complicated, there is only one thing to remember: the higher the Sharpe Ratio, the better. The number will go up with larger average annual returns and/or lower risk/volatility. Understanding that you have better things to do with your week-end than crunching the Sharpe Ratios, we decided to run the numbers for you. We included our three preferred indices
(Nasdaq 100, Russell 2000, S&P 500), our four strategies plus Buy and Hold for comparison. Note that we took the liberty to drop the R_f, the "risk-free" return, from the formula because it is too small to matter in our examples. We did the calculations for 5-year, 10-year, and 15-year periods ending in 2004 to make sure the results were not affected by a particular phase of the market cycle. The tables below summarize our findings with the Average Annual Returns, Standard Deviation, and Sharpe Ratio sections separated out.

	Average Annual Returns (%)
	Index	Long Only	Long Only with Margin	Long & Short	Long & Short with Margin	Buy & Hold
5-years	Nasdaq 100	23.09	48.13	66.43	164.35	-9.72
	Russell 2000	25.39	53.50	44.10	100.68	7.52
	S&P 500	12.04	25.12	27.55	60.03	-2.33
10-years	Nasdaq 100	44.18	84.43	69.00	151.29	24.70
	Russell 2000	24.42	48.75	37.91	81.75	11.53
	S&P 500	19.25	38.60	26.95	55.84	12.07
15-years	Nasdaq 100	37.41	71.19	56.92	122.35	21.50
	Russell 2000	22.92	45.01	35.17	74.13	11.18
	S&P 500	15.69	31.37	21.73	44.81	10.03

	Standard Deviations
	Index	Long Only	Long Only with Margin	Long & Short	Long & Short with Margin	Buy & Hold
5-years	Nasdaq 100	0.14	0.30	0.43	1.16	0.34
	Russell 2000	0.20	0.42	0.26	0.66	0.23
	S&P 500	0.13	0.27	0.14	0.33	0.18
10-years	Nasdaq 100	0.39	0.68	0.40	0.98	0.59
	Russell 2000	0.15	0.32	0.21	0.55	0.18
	S&P 500	0.14	0.28	0.11	0.25	0.24
15-years	Nasdaq 100	0.34	0.61	0.40	1.02	0.52
	Russell 2000	0.15	0.32	0.21	0.53	0.20
	S&P 500	0.13	0.26	0.15	0.33	0.21

	Sharpe Ratio
	Index	Long Only	Long Only with Margin	Long & Short	Long & Short with Margin	Buy & Hold
5-years	Nasdaq 100	1.64	1.60	1.55	1.42	-0.29
	Russell 2000	1.28	1.27	1.67	1.52	0.33
	S&P 500	0.96	0.94	1.96	1.83	-0.13
10-years	Nasdaq 100	1.13	1.24	1.73	1.55	0.42
	Russell 2000	1.68	1.50	1.79	1.48	0.63
	S&P 500	1.37	1.38	2.54	2.22	0.50
15-years	Nasdaq 100	1.10	1.17	1.41	1.20	0.41
	Russell 2000	1.57	1.43	1.70	1.40	0.57
	S&P 500	1.22	1.21	1.47	1.35	0.47

First, when observing the standard deviations we note that, as expected, the Long and Short with Margin strategy ranks first in risk (volatility) as it does in performance, but contrary to at least some expectations, the Long Only strategy is substantially less risky than Buy and Hold. Also noteworthy is that Long and Short is very comparable with Buy and Hold from a volatility stand point.

The revelation comes with the Sharpe Ratio numbers which, by factoring in average returns, totally debunk the myth about Buy and Hold being less risky than market timing, or trading techniques such as selling short or trading on margin. The numbers clearly reveal that in terms of reward-to-risk, our four Trend Timing strategies beat Buy and Hold across the board, by big margins. The numbers also confirm that in the majority of cases the Long and Short strategy offers the best Sharpe Ratio, or reward-to-risk ratio, which justifies its continued position as our mainstream strategy.

Warm wishes and until next week.

The TimingCube Staff