If the economy booms, RTF, Inc., stock is expected to return 9 percent. If the economy goes into a recessionary period, then RTF is expected to only return 4 percent. The probability of a boom is 68 percent while the probability of a recession is 32 percent. What is the variance of the returns on RTF, Inc., stock

    Variance = 5.44

Explanation:

The variance of a portfolio is a measure of the deviation of the returns of the assets making up the portfolio. Using the standard deviation, the variance can be worked out.

Standard deviation is measure of the total risks of an investment. It measures the volatility in return of an investment as a result of both systematic and non-systematic risks.

Non-systematic risk includes risk that are unique to a company like poor management, legal suit against the company .

The variance would be determined as follows:

Variance = Sum of  P×(R- r )^2  

P- probality

R- return on each asset

r- Expected return on portfolio

r =( Wa*Ra) + (Wb*Rb)

Expected return (r) = (9% × 0.68 ) + (4% × 0.32) = 7.4 %

Outcome                 R          (R- r )^2             P×(R- r )^2  

Recession              9              2.56                1.74

Boom                     4             11.56                3.70

Total                                                            5.44

Variance = Sum of  P×(R- r )^2  

    Variance = 5.44

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