By Ann Coleman (TMF AnnC)

RESTON, VA (Jan. 31, 2000) -- We are buried again. The Super Bowl Snow Storm dumped almost another foot of snow and ice on top of the foot and a half of snow we already had. This is pretty unusual for Northern Virginia, but I don't mind too much. It gives me a chance to casually mention to my commuter friends how nice it is to work for a progressive, highly wired company that lets me telecommute no matter what the weather. I try to make such comments on the phone, physical proximity being a bit dangerous when they've just arrived home after three hours on the beltway.

So for lack of much else to do this past weekend, I've been contemplating risk. In investing, risk seems to be the most difficult factor to get a hold on. There are formulas and theories and risk management plans, but none seem to have been widely accepted like some of the simple fundamental investing principles have, such as the relationship between stock price and company earnings.

One measure of risk that we like and use in the Dow Dividend Spreadsheet (available in FoolMart now with 1999 returns included) is the Sharpe Ratio. The Sharpe Ratio won't tell you which mutual funds lose the least money in a recession or how much of your portfolio should be in bonds or even how to find a low-risk stock, but it does let you assess the relative riskiness of stocks or portfolios by relating return to volatility (as measured by the standard deviation). In effect it answers the question "Is it worth the risk?"

Last Friday we published the results of a study that looked at Holding the Foolish Four for Two Years. In that article I compared the average annual returns and the standard deviations for two-year portfolios starting in January, February, March, et. al., with their one-year counterparts. We knew from previous studies that returns for a Foolish Four portfolio tended to drop if you held all of the stocks for second year, but they don't drop dramatically, and we also knew that volatility decreased with longer holding periods.

Prior to this study I had assumed that holding each Foolish Four portfolio for two years might reduce returns slightly but would also reduce volatility (which would show up in a lower standard deviation). Such a scenario might be beneficial for investors who were more interested in consistency than in maximizing their returns.

But, we were in for a surprise. We found that decreased returns and lower volatility were true only for January portfolios, and even there, the drop in returns seemed to be rather higher than could be justified by the decreased volatility.

But is it really? How can we tell? There is always a trade-off between risk and return. You want low risk, your bank has some nice CDs they'll sell you. You want high return, your broker has some great little Internet IPOs coming up. How do you integrate these two factors and figure out where the line is?

That's where our Sharpe Ratio comes in. The Sharpe Ratio is what let me say on Friday "the standard one-year, January portfolio still looks like the best bet."

The Sharpe Ratio looks at both return and volatility in terms of "excess return," in other words, how much more did the strategy pay than you could have earned simply sticking your money in a super-safe Treasury bill? The excess return is then divided by the standard deviation of the excess return. The result will be a number that is higher when the return is higher and, because you are dividing, higher when the standard deviation is lower. Bingo! That's just what we are looking for.

So the higher the Sharpe Ratio, the "better" the strategy. Using the Sharpe Ratio to compare strategies, we can at last get a sense of when increased volatility is "worth it."

Let's look at the Sharpe Ratios for the returns I reported on Friday.

Sharpe Ratios

        One-Year   Two-Year
Month     Port       Port 
Jan.     0.7765     0.6424
Feb.     0.6442     0.5970
Mar.     0.6287     0.6475
Apr.     0.5515     0.5337
May      0.5393     0.4960
June     0.4758     0.4990
July     0.5734     0.5656
Aug.     0.4044     0.4966
Sept.    0.5446     0.5107
Oct.     0.5467     0.6093
Nov.     0.6516     0.7654
Dec.     0.6431     0.6824

For reference, the Sharpe Ratio for the S&P 500 is 0.4784, so what we are seeing in that mass of decimals are strategies that beat the S&P to greater or lesser degrees with only one exception (August, one-year hold).

We can also see that the highest ratio is for the good ol' January, one-year-hold portfolio. Two-year portfolios starting at the end of the year (November and December) also look good, and if someone wants to go with a two-year strategy, that might be a viable idea, although, as we saw on Friday, those end-of-the-year portfolios tended to have higher SDs so the motivation for going with them escapes me.

Which brings up another question that will have to stay a question for now. Just how significant are these differences? It should be obvious to anyone that a small difference between two standard deviations is not worth worrying about. And the difference between a strategy that has a Sharpe Ratio of 0.5446 and 0.5467 is simply due to random chance. The difference between a Sharpe Ratio of 0.77 and 0.57 is more significant.

One of these days I will dig out the old college textbooks and calculate just how significant the differences are. One more snow storm here in Northern Virginia and I might have nothing better to do.

Fool on and prosper!