So far, we have focused on the risk and return of single investments held in isolation. Investors rarely place their entire wealth into a single asset or investment. Rather, they construct a portfolio or group of investments. Therefore we need to extend our analysis of risk and return to include portfolios.
The expected return of a portfolio is simply a weighted average of the expected returns of the securities constituting that portfolio. The weights are equal to the proportion of total funds invested in each security (the weights must sum to 100 percent). The general formula for the expected return of a portfolio, Rp, is as follows:
Rp = ∑ WjRj
where Wj is the proportion, or weight, of total funds invested in security j; Rj is the expected return for security j; and m is the total number of different securities in the portfolio.
The expected return and standard deviation of the probability distribution of possible returns for two securities are shown below.
|SECURITY A||SECURITY B|
|Expected return, Rj||14.0%||11.5%|
|Standard deviation, σj||10.7||1.5|
If equal amounts of money are invested in the two securities, the expected return of the portfolio is (0.5)14.0% + (0.5)11.5% = 12.75%.