Question

Jack and Diane, grew up in the heartland, have now been married for 20 years and would like to invest some money. Assume the risk-free rate is 2% annually. They take a test that rates their individual risk preference. Jack is given a 5 and Diane a 2.(this is A in the equation 5.15 in the book which is E{Geometric average} =E{Arithmetic average} ½ var2

A. Using these risk preferences and the below investment choices find the risk-free equivalent for each of these investments for Jack and Diane.

Expected return       Standard Deviation

6%                                  10%

8%                                  20%

12%                                25%

B. Which investment can the couple agree on, that it is better than the risk free asset?

C. Using the stock that Jack and Diane have chosen in part B of question 1, find the optimal allocation between risky(y) and risk free(1-y) investments for each person, with no shorting. What is the optimal y for Jack?

Answer 1

A) This is risk aversion and utility and is calculated using following formula

where U is utility

Er= expected return

A= risk preference of indivisual

= standard deviation square

	jack(5)	Diane(2)
1	3.5%	5%
2	-2%	4%
3	-3.6%	5.75%

B) couple should investment A as its giving more return than risk free return and also both jack and diane can get more return and in other investment jack will not be able earn any return

c) optimal risk for jack is 50% based on his risk preference for jack portfolio return is calculated as

portfolio return=Y* risky asset return+ (1-y)* rrisk free asset return

y= 50%

so return is 4% for jack