1. Suppose you have a risky portfolio that has an expected return of 15% and a standard deviation of 22%. Return from risk free assets is 5%. You have three clients. Following is their capital allocation according to their choices

Clients	Proportion of investment in your risky portfolio	Proportion of investment in risk-free asset
Client A	70%	30%
Client B	50%	50%
Client C	30%	70%

a) Show expected returns and standard deviation of the rate of returns of portfolio consisting of risky and risk-free asset of each client. Show the calculation in detail. (5 points)

b) Now that you run a survey on clients risk averseness and find out the risk aversion (A) of client A is 2, client B is 3, and client C is 5. The utility function to measure each clients utility level is:

For each of the following weights in risk-free and risky portfolio, calculate each clients utility level.

Weight in risk-free asset	Weight in risky portfolio
0	1
0.2	0.8
0.4	0.6
0.6	0.4
0.8	0.2
1	0

Based on utility levels you calculated for each client, find out the optimal allocation in risky and risk-free assets for client A, client B, and client C. Note that a desired weight or allocation is what maximizes a clients utility level. (5 points)