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Expected Returns and Standard Deviations for Two Stocks

Two Stocks, X and Y, have three states of nature based on the state of the economy:

State of Economy Probability Stock X Return Stock Y Return

Recession 0.10 -0.20 0.30

Normal 0.60 0.10 0.20

Boom 0.30 0.70 0.50

1. What are the expected returns and standard deviations for these two stocks?

2. Suppose you have $20,000 total. If you put $6,000 in X and the remainder in Y,

what will be the expected return and standard deviation on your portfolio be?

Solution Preview

1. What are the expected returns and standard deviations for these two stocks?

kX = 0.1 x (-20) + 0.6 x 10 + 0.3 x 70 = 25 %

kY = 30%

St. Dev X = [(20 - 25)2 + x 0.10 + (10 - 25)2 + x ...

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