Asset Allocation
Tonya has a choice between investing her funds in a risky portfolio or investing her funds in a money market mutual fund (the risk-free portfolio). The risky portfolio has an expected return of 12.75% [E(rp) = 0.1275] and a standard deviation of 21.5% [?p = 0.215]. The money market mutual fund has an expected return of 2.22% [rf = 0.0222].
(a) Suppose Tonya constructs an investment portfolio where 65% of her funds are invested in the risky portfolio and 35% of her funds are invested in the risk-free portfolio. Calculate the expected return E(rc) and standard deviation (c) of the overall portfolio.
(b) Calculate the Sharpe ratio of the risky portfolio. Calculate the Sharpe ratio of the overall portfolio. Round your final answers to two decimal places.
(c) Draw the capital allocation line (CAL) for Tonya’s portfolio. What is the slope of the CAL line? Show the position of Tonya’s overall portfolio (Found in Part (a) on the CAL (label this point, “A” on your graph).
(d) Suppose that Tonya wants to create an overall portfolio consisting of a mixture of the risky portfolio and the risk-free portfolio that has an expected return of 11% [E(rc) = 0.11]. What proportion of her funds (y) must Tonya invest in the risky portfolio in order to achieve the desired expected return of the overall portfolio? What would be the standard deviation of the overall portfolio?
(e) Suppose instead that Tonya wants to create an overall portfolio consisting of a mixture of the risky portfolio and the risk-free portfolio that has a standard deviation of 15% [?c = 0.15]. What proportion of her funds (y) must Tonya invest in the risky portfolio in order to achieve the desired standard deviation on the overall portfolio? What would be the expected return of the overall portfolio?