You are a risk-averse investor. Investment A has E(r) =12% and standard deviation = 18%.
Investment B has standard deviation = 24% and has end of year cash flows of either $84,000
or $144,000 with equal probability. At what price for Investment B would you be indifferent
between A and B? Hint: think about individual security selection statistic...not portfolio.
Investment A's return per unit of risk is 0.12/0.18 = 0.67. For the investor to be indifferent about A and B, B's return per unit of risk should also be 0.67. Therefore, the expected return on investment B is 0.24*0.67 = 16%.
Now, the expected dollar amount to be received after 1 year in investment B is 0.5*84,000 + 0.5*144,000 = $114,000. Therefore, given the expected return and the dollar amount expected to receive after 1 year, the current price is:
P(1+0.16) = 114,000
P = $98,275.86
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