Question

Consider the following information about a risky portfolio that you manage and a risk-free asset: E(r_P) = 12%, σ_P = 22%, r_f= 4%.

a. Your client wants to invest a proportion of her total investment budget in your risky fund to provide an expected rate of return on her overall or complete portfolio equal to 7%. What proportion should she invest in the risky portfolio, P, and what proportion in the risk-free asset? (Do not round intermediate calculations. Round your answer to 2 decimal place.)

Risky portfolio		%
Risk-free asset		%

b. What will be the standard deviation of the rate of return on her portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Standard deviation

%

c. Another client wants the highest return possible subject to the constraint that you limit his standard deviation to be no more than 12%. Which client is more risk averse?

first or second client

Answer 1

Given about a risky portfolio,

Expected return E(rP) = 12%

standard deviation σ_P = 22%

Risk free rate Rf = 4%

a). for a client with expected return of 7% on complete portfolio, let weight in risky portfolio be w

=> Weight in risk free asset = (1-w)

expected return on portfolio is weighted average return on its assets

=> E(P) = w*E(rP) + (1-w)*Rf

=> 7 = w*12 + (1-w)*4

=> w = 3/8 or 37.5%

So, proportion in risky portfolio = 37.5%

proportion in risk free asset = 1-0.375 = 0.625 or 62.50%

b). standard deviation on this portfolio is

σ = w*σP = 0.375*22 = 8.25%

c). for another client with standard deviation of 12%

weight of risky portfolio is

w = 12/22 = 54.55%

So, expected return on its portfolio is 0.5455*12 + 0.4545*4 = 8.36%

A risk averse client prefer to invest in lower risk portfolio and since 8.25% is less than 12% First client is more risk averse