Consider the following scenario analysis involving asset A and asset B:
Economic Condition
Probability
Return on X
Return on Y
Boom
0.1
30%
12%
Accelerated Growth
0.2
20%
10%
Normal Growth
0.4
15%
9%
Slowdown
0.2
10%
8%
Recession
0.1
-50%
-4%
a).Compute the expected returns and the standard deviation of returns for both assets. Then compute the correlation coefficient between the returns on the two assets.
b) Find the expected return and the standard deviation of the minimum variance portfolio of A and B, when short-selling is allowed.
Consider the following scenario analysis involving asset A and asset B:
| Economic Condition | Probability | Return on X | Return on Y |
| Boom | 0.1 | 30% | 12% |
| Accelerated Growth | 0.2 | 20% | 10% |
| Normal Growth | 0.4 | 15% | 9% |
| Slowdown | 0.2 | 10% | 8% |
| Recession | 0.1 | -50% | -4% |
a).Compute the expected returns and the standard deviation of returns for both assets. Then compute the correlation coefficient between the returns on the two assets.
b) Find the expected return and the standard deviation of the minimum variance portfolio of A and B, when short-selling is allowed.
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)
