If the investor holds only two assets in the portfolio, we can therefore be able to compute the portfolio's expected return (sometimes referred to as the portfolio mean). This will be a weighted average of the expected return of each asset held in isolation, and can be given by the following formula:
E(RP) = E(αXA + ßXB) ... (3.a)
Where (E(RP) is the expected portfolio return
α is the investment in asset A
ß is the investment in asset B
XA is the expected return of asset A
XB is the expected return of asset B
Formula 3.a can be simplified as follows:
E(RP) = αEXA + ßEXB ... (3.b)
Not also that α + ß = 1. This is because all the investor's wealth is invested in either asset A or asset B.
Consider two investments, A and B each having the following investment characteristics;
Investment Expected Return (%) Proportion
A 10 2/3
B 20 1/3
Compute the expected return of a portfolio of the two assets.
Using formula (3.b)
Note α = 2/3 ß = 1/3
EXA = 10 EXB = 20
E(RP) = 2 (10%) + 1 (20%)
Note that the expected return is a weighted average of the expected return of assets held in isolation.