Question

Suppose you manage a risky fund (call it P) with an expected return of 18% and a standard deviation of 25%. The risky fund is comprised of three stocks in the following investment proportions: A = 20%; B = 30%; C = 50%. The risk-free rate is 2%.

Given the data above, the equation of the CAL is E(rC) = rF + σC (E(rP) - rF/σP) = E(rC) = 2 + σC ((18-2)/25) = E(rC) = 2 + .64σC

A client wishing to construct a portfolio with an expected return of 14% needs to invest 75% in the portfolio that is risky and 25% in the portfolio that is risk-free (part B)

The standard deviation of the portfolio with an expected return of 14% is 18.75%. (Part C)

E) Another client wishes to make an optimal allocation in risky portfolio P. What is his optimal allocation, y*? Note: Assume that his degree of risk aversion is 3.0. Please show your work.

F) Based on your answers to (b&c) and (e), which of the two clients is more risk averse? Explain.

Answer 1

Poertfolio return expected = 14% = weighted Average return of individual assests

E(rC) = rf + 0.75[E(rM) − rf] = 2 + [0.75 × (14 – 2)] = 11%

The standard deviation of the complete portfolio using the passive portfolio would be: σC = 0.75 × σM = 0.75 × 18.75% = 14.0625%

E)

To achieve a target mean of 14%, we first write the mean of the complete portfolio as a function of the proportion invested in fund (y): E(rC) = 2 + y(18 − 2) = 2 + 16y Our target is: E(rC) = 14%. Therefore, the proportion that must be invested in my fund is determined as follows: 14 = 2 + 16y ⇒

y = 75%

The standard deviation of this portfolio would be: σC = y × 18.75% = 0.75 × 18.75% = 14.0625%

The formula for the optimal proportion to invest in the passive portfolio is:

Y = E(rm)-Rf/(A*σm^2) = (18-2)/(3*18.75*18.75) = 1.51

F) Client B is risk averse since he expects higher return at same risk