## PORTFOLIO EXPECTED RETURN

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.

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

EXA = 10 EXB = 20

E(RP) = 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.