Expected Return vs. Standard Deviation: An Overview

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.

Key Takeaways

  • Expected return calculates the mean of an anticipated return based on the weighting of assets in a portfolio and their expected return.
  • Standard deviation takes into account the expected mean return, and calculates the deviation from it.
  • An investor uses an expected return to forecast, and standard deviation to discover what is performing well and what is not.

Expected Return

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%.

Asset Weight  Expected Return
A 35% 6%
B 25% 7%
C 40% 10%

Therefore, the expected return of the portfolio is

[(35% * 6%) + (25% * 7%) + (40% * 10%)] = 7.85%

This is commonly seen with hedge fund and mutual fund managers, whose performance on a particular stock isn't as important as their overall return for their portfolio.

Standard Deviation

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 as:

σP = √(wA2 * σA2 + wB2 * σB2 + 2 * wA * wB * σA * σB * ρAB)

Where:

  • σP = portfolio standard deviation
  • wA = weight of asset A in the portfolio
  • wB = weight of asset B in the portfolio
  • σA = standard deviation of asset A
  • σB = standard deviation of asset B; and
  • ρAB = correlation of asset A and asset B

Expected return is not absolute, as it is a projection and not a realized return.

For example, consider a two-asset portfolio with equal weights, standard deviations of 20% and 30%, respectively, and a correlation of 0.40. Therefore, the portfolio standard deviation is:

[√(0.5² * 0.22 + 0.5² * 0.32 + 2 * 0.5 * 0.5 * 0.2 * 0.3 * 0.4)] = 21.1%

Standard deviation is calculated to judge the realized performance of a portfolio manager. In a large fund with multiple managers with different styles of investing, a CEO or head portfolio manager might calculate the risk of continuing to employ a portfolio manager who deviates too far from the mean in a negative direction. This can go the other way as well, and a portfolio manager who outperforms their colleagues and the market can often expect a hefty bonus for their performance.