where 
in essence this formula states that the expected return in excess of the risk free rate of return depends on the investment s beta or relative volatility compared to the broader market the expected return and standard deviation are two statistical measures that can be used to analyze a portfolio the expected return of a portfolio is the anticipated amount of returns that a portfolio may generate making it the mean average of the portfolio s possible return distribution the standard deviation of a portfolio on the other hand measures the amount that the returns deviate from its mean making it a proxy for the portfolio s risk the expected return is not absolute as it is a projection and not a realized return limitations of the expected returnto make investment decisions solely on expected return calculations can be quite na ve and dangerous before making any investment decisions one should always review the risk characteristics of investment opportunities to determine if the investments align with their portfolio goals for example assume two hypothetical investments exist their annual performance results for the last five years are both of these investments have expected returns of exactly 8 however when analyzing the risk of each as defined by the standard deviation investment a is approximately five times riskier than investment b that is investment a has a standard deviation of 11 26 and investment b has a standard deviation of 2 28 standard deviation is a common statistical metric used by analysts to measure an investment s historical volatility or risk in addition to expected returns investors should also consider the likelihood of that return after all one can find instances where certain lotteries offer a positive expected return despite the very low chances of realizing that return gauges the performance of an assetweighs different scenarios