Question

Security Y is a risk-free security with an expected return of 5%. Security Z has an expected return of 10% with an associated standard deviation of 28%. Find the expected portfolio return and standard deviation for the following portfolios:

Weight of Y	Weight of Z
20%	80%
40%	60%
60%	40%
80%	20%

Does the slope of the expected portfolio return versus portfolio risk (measured as standard deviation) change? Answer this question by comparing the slope between the first two portfolios and the last two portfolios. Is the risk-return trade-off simply a straight line in this instance?

Answer 1

If risk-free security has weight (1-w) with return rf and risky security has weight w with return r, then expected portfolio return E(r) = rf + y x (r-rf) and Expected Standard Deviation = E(s) = y x S (where S is the standard deviation of the risky security as the standard deviation of a riskless security is zero).

Weight of Y	Weight of Z	Expected Return E(r) (%)	Expected Standard Deviation E(s) (%)
0.2	0.8	9	22.4
0.4	0.6	8	16.8
0.6	0.4	7	11.2
0.8	0.2	6	5.6

When the last two columns from the right-hand side are plotted against each other we get the following curve:

As is observable, the risk-return profile is depicted by a single straight line.