How do we measure risk? In the financial industry, the generally accepted method is the standard deviation of returns. A low standard deviation indicates that expected returns vary little from average returns (suggesting less risk), while a high standard deviation suggests that expected returns vary greatly from average returns (implying more risk). The assumption is that stable past returns are less risky, yet many practitioners are uneasy with this concept.
MONEY MANAGEMENT
Measuring Risk
by Dick Stoken
There are two common ways to measure performance, the standard deviation of returns and the Sharpe ratio. This hedge fund manager introduces a third technique.
FACTORING IN LOSSES
Let's examine a risk measure that factors in the actual losses experienced by asset managers. Say that portfolio manager Dick Smith experienced two negative years of -2.7% and -7.9%, a combined loss totaling -10.6% over a 25-year period. By dividing this total loss by the number of years in our observation (25), we derive an average loss of -0.42% per year. This is the average loss that an investor would have experienced had he bought at the beginning of a negative period, sold at the end of that span, and stayed on the sidelines in the interim.
Let us also suppose that during that same 25-year period, the Standard & Poor's 500 was down a total of five years for a combined loss of -56.7%, averaging -2.27% a year. When viewed from this perspective, Smith's portfolio was clearly less risky than the S&P 500.
Naturally, these average losses should be compared with the average return for the period. If Smith's average return was, say, 19.8% as opposed to an S&P return of 14.9%, Smith outperforms the S&P, hands down. Divide his 19.8% return by his -0.42% average loss per year and we get an average return to loss (AR/L) ratio of 47.1. For every percentage point of risk, you receive a 47.1% return. Compare this with the S&P 500, which returned 14.9% with an average loss of (2.27%), yielding an AR/L ratio of 6.6.
Now take this concept one step further. Rather than using simple positive vs. negative returns, we compare the annual return to the 90-day Treasury bill return. Three-month T-bills are a riskless and brainless investment; no skill is necessary. Wait three months and you pocket the interest rate. Any return of less than what could be achieved by buying T-bills will be considered a loss. A return of 1.2% coming at a time when T-bills are earning 5% becomes a loss of -3.8%. Of course, an actual -2.5% return plummets to a loss of -7.5%, which is a -7.5% underperformance to T-bills. From now on, when we refer to loss, we mean underperformance to the T-bill rate.
Excerpted from an article originally published in the December 1998 issue of Technical Analysis of STOCKS & COMMODITIES magazine. All rights reserved. © Copyright 1998, Technical Analysis, Inc.
