An investor is uncertain about how much to invest in two risky assets. The first asset (equity) yields an expected return of 10% and has a standard deviation equal to 8%. The second asset (debt) yields an expected return of 5% and has a standard deviation of 7%. The correlation coefficient between the returns is 0.1.
a. Compute the expected return and standard deviation of the following portfolios:
|
|
Portfolio
|
Percentage in equity
|
Percentage in debt
|
|
|
1
|
90
|
10
|
|
|
2
|
50
|
50
|
|
|
3
|
10
|
90
|
|
Equity
|
Debt
|
|
|
|
|
|
R
|
0.1
|
0.05
|
|
|
|
|
|
SD
|
0.08
|
0.07
|
|
|
|
|
|
Var
|
0.0064
|
0.0049
|
|
|
|
|
|
|
|
|
|
|
|
|
Portfolio
|
% in equity
|
% in debt
|
Expected R
|
Var
|
SD
|
|
|
1
|
0.9
|
0.1
|
0.095
|
0.005
|
0.073
|
|
|
2
|
0.5
|
0.5
|
0.075
|
0.003
|
0.056
|
|
|
3
|
0.1
|
0.9
|
0.055
|
0.004
|
0.064
|
|
|
|
|
|
|
|
|
|
|
|
|
b. In the mean-standard deviation space, sketch the set of portfolios composed of debt and equity and identify portfolios 1, 2, and 3 on your graph.
c. Would a rational risk-averse investor ever choose portfolio 3? Would a rational risk-averse investor ever choose portfolio 1?