Consider two securities, the first having μ1 = 1 and σ1 = 0.1, and the second having μ2 = 0.8 and σ2 = 0.12. Suppose that they are negatively correlated, with ρ = −0.8.
a. If you could only invest in one security, which one would you choose, and why?
b. Suppose you invest 50% of your money in each of the two. What is your expected return and what is your risk?
c. If you invest 80% of your money in security 1 and 20% in security 2, what is your expected return and your risk?
d. Denote the expected return and its standard deviation as functions of π by μ(π) and σ(π). The pair (μ(π), σ(π)) trace out a curve in the plane as π varies from 0 to 1. Plot this curve.
e. Repeat b–d if the correlation is ρ = 0.1.
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