Financial theory tells us that investors should expect a positive relationship between risk and return: Those who assume greater levels of market risk are expected to earn higher returns, while lower risk portfolios should earn lower returns. However, investors should not expect to earn higher returns by accepting higher levels of risk from single stocks or a concentrated portfolio, because the markets do not compensate investors for risks that easily can be diversified away.
Key to determining an investment is a measurement to estimate the magnitude of the risk-return tradeoff that can differ across investments and investment managers. Performance measures may show that a high return is not attractive given the extraordinarily high level of risk that is needed to earn that return, while lower levels of return may be quite attractive if they come with minimal risk.
There are two major types of performance measures. First, there are ratios of return to risk. Return can be expressed in several ways in the numerator, and risk can be expressed in numerous ways in the denominator. The denominator of the ratio can be any risk measure, although the most popular performance measures employ the most widely used risk measures, such as volatility (standard deviation) or beta. The risk measure may be an observed estimate of risk or the investor’s belief regarding expected risk. These ratios include those developed by William Sharpe, Jack Treynor and Frank Sortino.
A second method to measure performance is to generate the risk-adjusted return of an asset and compare that return to a standard. The alpha measure, developed by Michael Jensen, compares the return on an investment to the expected return on an investment of similar risk.