Question

1. In your opinion, what's the main reason finance textbooks use means and standard deviations to measure the return and risk in the stock market?
2. Are there any other (maybe more useful) measures of risk and return?

Answer 1

Most investors are familiar with standard deviation and how it can be used to measure risk. In its simplest terms, standard deviation is a measure of how spread out values are in a series of numbers/returns. In calculating the standard deviation, it gives investors a “standard” way of knowing what is normal, and what is outside the range of normality. A lower standard deviation is better, and it means returns are more likely to be in a narrower range, whereas a larger standard deviation means returns are more likely to be scattered. Thus this being a simple method to analyze the market.

When attempting to develop an optimally allocated portfolio of investments, using standard deviation as a definition of risk leads to unreliable conclusions when your objective is to avoid risk. Using standard deviation as a measure of risk assumes a symmetrical return distribution and assumes, absurdly, that unexpected gains are as risky as unexpected losses. Yet, an unexpected gain is not what an ordinary investor considers risk. Any practical investor will confirm that making an
unusually large return isn’t risky. Losing money is risky.

Standard Deviation assumes a normal distribution of historic returns. There are many examples in Finance where this is a poor or patently incorrect assumption. In fact, very few investments exhibit “normal” returns.
A more practical problem is that Standard Deviation equal weights positive variation (generally a good thing) with negative variation (generally a bad). Standard Deviation, however, remains the favorite of Finance professors and Options traders.

For most investors and traders however, two measures of risk may be more useful: Average True Range (ATR), and Drawdown.

When thinking about how much to invest, one must often consider ATR. ATR is the n-period moving average of the True Range for a given period. The True Range for any period is the greatest value of the following:

• The difference between the current high and the current low;
• The difference between the current high and the previous close; and
• The difference between the current low and the previous close.