# In a world of one risk-free and one risky asset, an investor faces the following values: Expected return on risky portfolio E(r P ) = 0.

In a world of one risk-free and one risky asset, an investor faces the following values:

Expected return on risky portfolio E(rP) = 0.12

SD of risky portfolio                              σP   = 0.25

Risk-free rate                                           rf     = 0.05

In what follows the notation is such that:

y = fraction of the complete portfolio in the risky portfolio

E(rC) = return on the complete portfolio

σC= SD of the complete portfolio

a)      What does the complete portfolio look like for the investor who says, “I won’t

accept more than σC =10% (SD in my complete portfolio)?” In other words what is y(the percentage of risky asset), and what is 1-y (the percentage of the risk free asset) for this investor? Show your work.

b)    What is E(rC) for this investor? Show your work.

c)     What does the complete portfolio look like for the investor who says, “I want to

achieve a 15% expected return, at minimum risk of course.”

In other words, what is y and (1-y) for this investor? Show your work. (Hint: Don’t be discouraged if y>1 and thus (1-y) is negative. Remember an investor can borrow money at risk free rate)