When the data points are spread apart and the bell-shaped curve is flat, the standard deviation -- and the variation -- is great.
Standard deviation with regard to finance can be defined as "Statistical measure that shows the likelihood of an investment to yield above- or below-average returns over a period of time. For example, if hypothetical XYZ Fund has an average annual total return of 11% and a standard deviation of 6.00, which means XYZ Fund's performance is likely to vary from a low of 5% to a high of 17%. Calculated by the fund, standard deviation is only relative to the asset class being measured." (2)
The standard deviation of investment returns is widely accepted as the best, and perhaps only commonly used indicator of portfolio risk in the investment management business. However, its usefulness is actually quite limited. In fact, relying on it can often produce misleading and inaccurate
conclusions. Although standard deviation does provide some insight, and in many circumstances is in fact meaningful but there are a number of flaws associated with relying on the standard deviation of returns as a risk measure.
The bigger flaw with standard deviation is that it isn't intuitive. ...
Although standard deviation does provide some insight, and in many circumstances is in fact meaningful but there are a number of flaws associated with relying on the standard deviation of returns as a risk measure.
The bigger flaw with standard deviation is that it isn't intuitive. Sure, a standard deviation of seven is obviously higher than a standard deviation of five, But are those high or low figures Because a fund's standard deviation is not a relative measure-which means it's not compared with other funds or with a benchmark-it is not very useful to you without some context.
Another limitation to standard deviation lies with the underlying data. Most investors will recall normal distribution from their introduction to statistics course. This bell curve underlies all of the assumptions about standard deviation. If the underlying data is not normally distributed, then the standard deviation is likely to give misleading results. It's worth noting that a number of studies show that investment returns are not normally distributed.
There are some drawbacks to using standard deviation as a measure of risk, however. It interprets any difference from the average, above or below, as bad. This runs contrary to the way most investors feel about returns.
Few investors fret about their portfolios doubling; most only worry about the downside--their returns being below average.
There is another theory which is called Utility Theory. "This theory gives us a way to measure investor's preferences for wealth and the amount of risk they
are willing to undertake in the hope of attaining greater wealth. This makes it possible to develop a theory of portfolio optimization. Thus utility theory lies at the heart of modern portfolio theory." (3)