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:
3.1 Calculate the expected return, variance and standard deviation for each share.
3.2 Calculate the expected return, variance and standard deviation for the following diversifying allocations of Mr Patelâs savings:
(i) 50% in Sanlam, 50% in Sasol.
(ii) 10% in Sanlam, 90% in Sasol.
3.3 Explain the relationship between risk reduction and the correlation between individual financial security returns
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:
3.1 Calculate the expected return, variance and standard deviation for each share.
3.2 Calculate the expected return, variance and standard deviation for the following diversifying allocations of Mr Patelâs savings:
(i) 50% in Sanlam, 50% in Sasol.
(ii) 10% in Sanlam, 90% in Sasol.
3.3 Explain the relationship between risk reduction and the correlation between individual financial security returns
Related questions
Mr Jackson has approached you for an advice on how best to invest his savings. You proposed that he can invest all his savings in shares of Facebook, or all his savings in Walmart. 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 Facebook and Walmart depend on which state will occur.
| State of economy | Probability of growth occuring | Facebook return (%) | Walmart return (%) |
| Boom | 0.3 | 40 | 10 |
| Growth | 0.4 | 30 | 15 |
| Recession | 0.3 | -10 | 20 |
1.1 Calculate the expected return, variance and standard deviation for each share (10 marks)
1.2 Calculate the expected return, variance and standard deviation for the following diversifyng allocation of Mr Jackson's savings:
(a) 50% in Facebook, 50% in Walmart (5 marks)
(b) 10% Facebook, 90% walmart (5 marks)
1.3 Explain the relationship between risk reduction and the correlation between individual financial security returns ( 5 Marks)
A project requires an immediate outflow of cash of $ 400 000 in return for the following probable cash flows:
| State of Economy | Probability | End of year 1 ($) | End of year 2 ($) |
| Recession | 0.3 | 100 000 | 150 000 |
| Growth | 0.5 | 300 000 | 350 000 |
| Boom | 0.2 | 500 000 | 550 000 |
Assume that the state of the economy will be the same in the second year as in the first. The required rate of return is 8%. There is no tax or inflation.
1.1 Calculate the expected NPV. (10 marks)
1.2 Calculate the standard deviation of NPV and the coefficient of variance of the NPV. Interpret these results taking into consideration the state of the economy (10 marks).
