Question

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 Amount Probability 18% 60% Large Cap Stock $50,000 Investment Outcome Excellent Average Poor Excellent Average Poor Excellent Average Poor 33% 45% Value of Investment after one year $53,000 $52,000 $45,500 $56,000 $50,000 $44,500 $60,000 $55,000 $35,000 Mid Cap Stock $50,000 Small Cap Stock $50,000 40% 25% Assume that any

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 Investment Option Amount

Investment Outcome

Excellent Average Poor Excellent Average Poor Excellent Average Poor

Probability

18% 60%

33% 45%

40% 25%

Value of Investment after one year

$53,000 $52,000 $45,500 $56,000 $50,000 $44,500 $60,000 $55,000 $35,000

      

Large Cap Stock Mid Cap Stock Small Cap Stock

$50,000 $50,000 $50,000

                         

Assume that any money not invested does not earn interest.

1. 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.

2. b) Solve this decision tree using EMV. What is the optimal decision strategy?

3. c) If we assume that an investor’s utility function is given by ?(?) = √?, again with x in thousands of dollars, what is the optimal decision and what is its expected utility (round your utilities to 2 decimal places when calculating the utilities)? Based on the utility function, is the investor risk averse,riskseeking,orriskneutral? Doestheoptimalinvestmentchoicemakesensegiventhat risk attitude?

4. d) If we assume that an investor’s utility function is given by ?(?) = ?2, again with x in thousands ofdollars,whatistheoptimaldecisionandwhatisitsexpectedutility? Basedontheutility function,istheinvestorriskaverse,riskseeking,orriskneutral? Doestheoptimalinvestment choice make sense given that risk attitude?

Answer 1

Investment	Probability	Investment in one year	Probable value	Earnings
50000	18%	53000	9540
	60%	52000	31200
	22%	45500	10010
			50750	750
50000	33%	56000	18480
	45%	50000	22500
	22%	44500	9790
			50770	770
50000	40%	60000	24000
	25%	55000	13750
	35%	35000	12250
			50000	0
50000	Not to invest	50000	50000	0

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