a) Draw a decision tree for this scenario, making your consequence your cash in hand at the end of one year in thousands of dollars. b) Solve this decision tree using EMV. What is the optimal decision strategy? c) If we assume that an investor’s utility function is given by ?(?) = √? where x is in thousands of dollars, what is the optimal decision and what is its expected utility (round your utilities to 3 decimal places when calculating the utilities)? Based on the utility function, is the investor risk averse, risk seeking, or risk neutral? Does the optimal investment choice make sense given that risk attitude? d) If we assume that an investor’s utility function is given by ?(?) = ? 2 , again with x in thousands of dollars, what is the optimal decision and what is its expected utility? Based on the utility function, is the investor risk averse, risk seeking, or risk neutral? Does the optimal investment choice make sense given that risk attitude?
You are considering three investment options (and, of course, you could choose not to invest). You have
$50,000 to invest and for your consequence you will consider the cash (in thousands of dollars) that
remains one year after you make your investment. The investment amounts for each of the options and
the potential returns are as follows: Investment
Option
Investment
Outcome Probability Value of Investment after
one year
Large Cap Stock
Excellent 18% $53,000
Average 60% $52,000
Poor $45,500
Mid Cap Stock
Excellent 33% $56,000
Average 45% $50,000
Poor $44,500
Small Cap Stock
Excellent 40% $60,000
Average 25% $55,000
Poor $35,000
Assume that if you do not invest your money, you do not earn interest.
a) Draw a decision tree for this scenario, making your consequence your cash in hand at the end of
one year in thousands of dollars.
b) Solve this decision tree using EMV. What is the optimal decision strategy?
c) If we assume that an investor’s utility
of dollars, what is the optimal decision and what is its expected utility (round your utilities to 3
decimal places when calculating the utilities)? Based on the utility function, is the investor risk
averse, risk seeking, or risk neutral? Does the optimal investment choice make sense given that
risk attitude?
d) If we assume that an investor’s utility function is given by ?(?) = ?
2
, again with x in
thousands of dollars, what is the optimal decision and what is its expected utility? Based on
the utility function, is the investor risk averse, risk seeking, or risk neutral? Does the optimal
investment choice make sense given that risk attitude?
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