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(R_P) = E(αX_A + ßX_B) ... (3.a)

Where (E(R_P) is the expected portfolio return

α is the investment in asset A

ß is the investment in asset B

X_A is the expected return of asset A

X_B is the expected return of asset B

 Formula 3.a can be simplified as follows:

 E(R_P) = αEX_A + ßEX_B ... (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.

 Illustration

Consider two investments, A and B each having the following investment characteristics;

 Investment Expected Return (%) Proportion

A 10 2/3

B 20 1/3

 REQUIRED:

Compute the expected return of a portfolio of the two assets.

 Solution

Using formula (3.b)

Note α = 2/3 ß = 1/3

EX_A = 10 EX_B = 20

 E(R_P) = 2 (10%) + 1 (20%)

3 3

 = 13.3%

 Note that the expected return is a weighted average of the expected return of assets held in isolation.