SOLUTION: A portfolio's value increases by 18% during a financial boom and by 9% during normal times. It decreases by 12% during a recession. What is the expected return on this portfolio i

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Question 1132694: A portfolio's value increases by 18% during a financial boom and by 9% during normal times. It decreases by 12% during a recession. What is the expected return on this portfolio if each scenario is equally likely? (round to the nearest whole percent)
Answer by ikleyn(52781) About Me  (Show Source):
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Let the portfolio value will be x (dollars).


Then with the probability  1%2F3  we have  x*(1+0.18)  dollars  at a financial boom,

     with the probability  1%2F3  we have  x*(1+0.09)  dollars  at normal times,

and  with the probability  1%2F3  we have  x*(1-0.12)  dollars  at a recession.


Then the expected return is  %281%2F3%29%2A1.18x+%2B+%281%2F3%29%2A1.09x+%2B+%281%2F3%29%2A0.88x = %281%2F3%29.%281.18+%2B+1.09+%2B+0.88%29x = %281%2F3%29.3.15%2Ax = 1.05x.


ANSWER.  Expected return on this portfolio is  5%  at given conditions.