Problem 1 

Consider the mean variance utility U for two risk averse investors, one with risk aversion (A) of 2 and the other with risk aversion of 5. Suppose that there are three mutually exclusive investment opportunities available: (i) a small-cap index with expected return of 12% and a standard deviation of 30%; (ii) a stock index with expected return of 8% and a standard deviation of 20%; (iii) risk free asset with return of 2%. There 

b) Suppose now that risk free asset is no longer offered and the risky investments are still mutually exclusive (you can't combine them). Assume no inflation. What would the more risk averse investor (with A=5) chose to do if she has $1000 in cash? How inflation might change her choice? (Hint: think about how stocks may respond to higher inflation, i.e. how the value of assets and project owned by companies may be affected by inflation and compare this to cash)

c) What must be the risk aversion of an investor who claims to be indifferent between a small cap index (i) and a stock index (ii)?

Problem 2
 
The Triad family of mutual funds allows investors to split their money between three portfolios managed by Triad.Portfolio C has an expected return of 10% and a standard deviation of return of 15%.  Portfolio B has an expected return of 19% and a standard deviation of return of 25%.  The correlation coefficient between returns on portfolio B and C is 0.2.  Portfolio A consists entirely of risk-free securities, and has a certain return of 4%. Your client is leaning towards investing her money entirely in portfolio C, since she is unwilling to take the higher risk associated with portfolio B, but wants a higher return than offered by portfolio A.

(A) As a Triad investment advisor, you suggest to her an alternative portfolio P (consisting of a combination of only A and B) that has the same expected return as portfolio C but a lower standard deviation.  If she has $200,000 to invest, how much should she invest in B and how much in A?  What is the standard deviation of return on her investment in this case? Sketch a mean standard deviation diagram you would use to explain why portfolio you suggest is better. 

(B) However, after your convincing presentation of alternative P, your client says that she is really comfortable with the level of risk in C. So, you suggest her, another portfolio P1 (consisting of a combination of only A and B) that has the same standard deviation as C, but higher expected return. If she has $200,000 to invest, how much should she invest in B and how much in A?  What is the expected return on her investment in this case? Sketch a mean standard deviation diagram you would use to explain why portfolio you suggest is better.