How is risk aversion measured in modern portfolio theory (MPT)?

According to modern portfolio theory (MPT), degrees of risk aversion are defined by the additional marginal return an investor needs to accept more risk. The required additional marginal return is calculated as the standard deviation of the return on investment (ROI), otherwise known as the square root of the variance.

The general level of risk aversion in the markets can be seen in two ways: by the risk premium assessed on assets above the risk-free level and by the actual pricing of risk-free assets, such as United States Treasury bonds. The stronger the demand for safe instruments, the larger the gap between the rate of return of risky versus non-risky instruments. Prices for Treasury bonds should also increase, pushing yields lower.

When MPT was introduced, its definition of risk, or the standard deviation from the mean, seemed unorthodox. Over time, standard deviation probably became the most-used gauge for investment risk.

Standard deviation shows how dramatically an asset's returns oscillate over a period of time. A trading range around the mean price can be created using the upswings and downswings as measured by standard deviation. Investors use this information to estimate possible returns for future portfolios.

Those who are more risk averse tend to want assets with lower standard deviations. A lower deviation from the mean suggests the asset's price experiences less volatility and there is a lower probability for major loss. Aggressive investors are comfortable with a higher standard deviation because it suggests higher returns are also possible.

The reason standard deviation is so widely accepted is it is always expressed in the same units and proportions as the underlying data. For example, the standard deviation of height is expressed in feet or inches, while the standard deviation for stock prices is quoted in terms of dollar price per share. Other risk metrics develop in accordance with MPT, including beta, R-squared and turnover rate.

Though historically rare, it is possible to have a mutual fund or investment portfolio with a low standard deviation and still lose money. Losing periods in the market tend to be steep and short-lived; low standard deviation assets tend to lose less in short time periods than others. However, since risk information is backward-looking, there is no guarantee future returns follow the same pattern.

A larger, trickier issue is standard deviation is relative in nature. Suppose an investor looks at two balanced mutual funds. One has a standard deviation of five units and the other a standard deviation of 10 units. Without other information, MPT cannot tell the investor if five is low, average or high. If five is low, 10 might be average. If five is high, 10 might be extremely high. Investors using standard deviation should take the time to find the appropriate context.

(For related reading, see "How Investment Risk Is Quantified.")