Considerable mathematical analysis of investments and portfolio construction rests on the acceptance of standard deviation as a measure of investment risk. Once accepted, mean-variance analysis takes center stage to generate optimal portfolios and eventually arrive at an elegant presentation of the "Efficient Frontier" and a focus on the asset allocation issue.
But for many, the acceptance of standard deviation as a proxy for risk is not straight forward. They argue that risk is about losing money, about downturns in the market, and about running out of money - not about returns that are significantly higher and lower than average.
William Bernstein emphasizes the different ways of looking at risk in The Intelligent Asset Allocator.
Incidently, this is one of the first books (along with Random Walk Down Wall Street by Malkiel) that I recommend to people who indicate a serious interest in the subject of investing.
The very foundations of investment theory, of course, rests on the crucial trade-off between risk and return. In this light, consider the following table (1964 study by Paul Miller) presented on page 116 of The Intelligent Asset Allocator:
The interesting point of the table, however, is that it also shows additional measures of risk; and these measures are not as cooperative to the theory. The number of losing years and the number of years where the loss exceeds 10% are both less for the "riskier" low p/e stocks! With these measures, a higher return was achieved with less risk.
This points to one of the values of utilizing a total market index, in that it automatically gets an investor to hold stocks that are deemed unattractive, i.e. have low p/e ratios.
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