Your client holds 125% of her wealth in an index fund that tracks the S&P 500, which has expected return & risk of 11% & 21% respectively. The risk-free rate = 3.2%. What is the client's risk aversion?

 

2) As stated in Problem #1 above, the client holds 125% of her wealth in the S&P 500 index fund. Explain how that can be accomplished. What is the client's allocation to T-Bills?

 

3) A risky investment has a 15% expected return & 25% volatility. The risk-free rate is 4%. At what risk aversion coefficient (A) would the investor be indifferent between the risky investment and T-Bills?

 

4) Stocks have outperformed T-Bills by about 7% per year over the past 95+ years. Use utility theory to explain why an investor might want to investment in T-Bills.

 

5) You play a game that has the following payoffs:

35% probability of winning $1,000

35% probability of losing $1,500

30% probability of winning $550

Answer the following questions:

a) What is the expected value of playing the game?

b) Would a risk neutral person play this game? Why or why not?

c) What level of risk tolerance (e.g. risk seeking, risk averse, risk neutral) must a person have to play this game?

d) How much in dollars, would a risk-averse and a risk neutral person need to be paid to play the game. Explain.

e) Which party has a positive risk premium for this game - the game's sponsor or the game's player? Explain.

 

6) The market portfolio represented by the S&P 500 has a 12% expected return & 20% risk. The risk-free rate = 5% & the investor's risk aversion coefficient A = 2.5.