Mr Patel has approached you for an advice on how best to invest his savings. You have proposed that he can invest all his savings in shares of Sanlam, or all his savings in Sasol. Alternatively, he could diversify his investment between these two (share companies). There are three possible states of the economy, boom, growth or recession, and the returns on Sanlam and Sasol depend on which state will occur.

State of Economy Probability of growth occurring Sanlam return (%) Sasol return (%)

Recession 0.3 40 10

Growth 0.4 30 15

Boom 0.3 -10 20

Required:

1 Calculate the expected return, variance and standard deviation for each share.

2 Calculate the expected return, variance and standard deviation for the following diversifying allocations of Mr Patel’s savings:

(i) 50% in Sanlam, 50% in Sasol.

(ii) 10% in Sanlam, 90% in Sasol.

3 Explain the relationship between risk reduction and the correlation between individual financial security returns.