The Difference Between the Expected Return and the Standard Deviation of a Portfolio

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, whereas the standard deviation of a portfolio measures the amount that the returns deviate from its mean.

Expected return measures the mean, or expected value, of the probability distribution of investment returns. The expected return of a portfolio is calculated by multiplying the weight of each asset by its expected return and adding the values for each investment.

For example, a portfolio has three investments with weights of 35% in asset A, 25% in asset B and 40% in asset C. The expected return of asset A is 6%, the expected return of asset B is 7%, and the expected return of asset C is 10%. Therefore, the expected return of the portfolio is 7.85% (35%*6% + 25%*7% + 40%*10%).

Conversely, the standard deviation of a portfolio measures how much the investment returns deviate from the mean of the probability distribution of investments. The standard deviation of a two-asset portfolio is calculated by squaring the weight of the first asset and multiplying it by the variance of the first asset added to the square of the weight of the second asset multiplied by the variance of the second asset. Then, add this value to 2 multiplied by the weight of the first asset and second asset multiplied by the covariance of the returns between the first and second asset. Finally, take the square root of that value, and the portfolio standard deviation is calculated.

For example, consider a two-asset portfolio with equal weights, variances of 6% and 5%, respectively, and a covariance of 40%. The standard deviation can be found by taking the square root of the variance. Therefore, the portfolio standard deviation is 16.6% (√(0.5²*0.06 + 0.5²*0.05 + 2*0.5*0.5*0.4*0.0224*0.0245)).