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# Q2 Suppose that two Investments have the same three payoffs but the p

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Q2 Suppose that two Investments have the same three
payoffs but the probability associated with each payoff
differs, as illustrated in the table below: Ken has the utility
function U = 5 root I, (1) Find the expected value of
payoffs in Investment A and investment B. (2) Which
investment A or B is riskier. To answer this question,
calculate the standard deviation of each investment. (3) Is
Ken a risk lover, averse, or neutral? Explain why.
Solution
(1) The expected value of an uncertain event is the sum of
the possible payoffs multiplied by each payoff\'s chance of
occurring.
Expected payoff in investment A = 300(0.1) + 250(0.8) +
200(0.1) = \$250
Expected payoff in investment B = 300(0.3) + 250(0.4) +
200(0.3) = \$250
(2) To calculate standard deviation lets use the formula
S.D = summation [Pt (Rit - E(Ri))2]1/2
where Pt = Probability of outcome t
Rit = Return of assest i if outcome t occuurs
E(Ri) = Expected return for asset i.
S.D of investment A = [ 0.1(300-250) + 0.8(250-250) +
0.1(200-250) ]1/2 = 0

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Q2 Suppose that two Investments have the same three payoffs but the probability associated with each payoff differs, as illustrated in the table below: Ken has the utility function U = 5 root I, (1) Find the expected value of payoffs in Investment A and investment B. (2) Which investment A or B is riskier. To answer this question, calculate the standard deviation of each investment. (3) Is Ken a risk lover, averse, or neutral? Explain why. Solution (1) The expected value of an uncertain event is the sum of the possible payoffs multiplied by each payoff \'s chance of occurring. Expected payof ...
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