This assignment contributes 5% of your overall module mark.

Your solutions  to  these problems  must  be  your own work.   You  risk  losing  all  credit for the assignment if this is not the case .  You must include your name, your student ID and the module  code  on your script.   You must also  complete  an academic integrity form and upload this with your solutions .

The deadline for this assignment is 4pm Friday 3 March 2023.  Scripts must be submitted via Minerva.  Late submissions are not accepted and will not be marked at all.

Once marking is  complete, it is your responsibility to  check for your mark on Minerva.   You must do this as soon as possible after marks are released.

1. An investor has utility function U given by one of the functions below. For each choice of the utility function, determine the type of investor.  If the investor is risk-averse, determine the type of ARA and the type of RRA.

(a) U(w) = w

(b) U(w) = w2 + 2w for w > 0

(c) U(w) = log(w + 1) for w > 0

(d) U(w) = −e −2w  for w > 0

2. Alice believes that her car would cost $12,500 to replace if it was stolen or damaged. Based on crime statistics for the area she lives in, she believes that the probability of her car being stolen or damaged is 0.15.

(a) Alice’s utility function is given by U(w) = ln(w) for w > 0 and she has $35,000

in the bank.  Calculate how much Alice would be prepared to pay (in a single payment) to insure her car against theft or damage.

(b) Repeat the calculation in part (a) but now assume that Alice has $500,000 in the

bank. Give a short explanation of your answer.

3. A market consists of two risky assets and no risk-free asset. Let R1  and R2  denote the return on each of the risky assets. Using market data the following have been estimated: E[R1] = 0.10, E[R2] = 0.15, σ1(2)  = Var(R1) = 0.12 , σ2(2)  = Var(R2) = 0.22  and ρ 1,2  = −  where ρ 1,2  denotes the correlation coefficient for R1  and R2 .

(a) Given that an investor is targeting a total expected return of µ  =  0.15 on a

portfolio, what is the minimum variance that can be achieved?

(b) Determine the global minimum variance portfolio and the expected return and

variance of return on this portfolio.

(c) Using your answers to parts (a) and (b) to make a rough sketch of the minimum- variance set in µ − σ 2  space.  You should indicate the efficient frontier and the global minimum variance portfolio.