Question

In: Finance

Consider the following table: Stock Fund Bond Fund Scenario Probability Rate of Return Rate of Return...

Consider the following table:

Stock Fund Bond Fund
Scenario Probability Rate of Return Rate of Return
Severe recession 0.20 −18% −18%
Mild recession 0.25 −11.0% 20%
Normal growth 0.25 8% 5%
Boom 0.30 34% −6%


a. Calculate the values of mean return and variance for the stock fund. (Do not round intermediate calculations. Round "Mean return" value to 1 decimal place and "Variance" to 4 decimal places.)

Mean return ??? %
Variance ??? %-Squared


b. Calculate the value of the covariance between the stock and bond funds. (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 4 decimal places.)

Covariance ??? %-Squared

Solutions

Expert Solution

Square of Actual return less Expected return of particular stock is multiplied with Probability. Calculated amount is variance.

Probability is multiplied with actual return. Sum of all these is expected return.

Stock fund
State Probability Return (%) Return deviation from expected return Squared Return deviation from expected return * prob.
Severe recession 0.2 -18 -23.85 113.7645
Mild recession 0.25 -11 -16.85 70.98063
Normal 0.25 8 2.15 1.155625
Boom 0.3 34 28.15 237.7268
Mean(Expected) return = 5.85 423.6275
Bond fund
State Probability Return (%) Return deivation from expected return Squared Return deivation from expected return * prob.
Severe recession 0.2 -18 -18.85 71.0645
Mild recession 0.25 20 19.15 91.68063
Normal 0.25 5 4.15 4.305625
Boom 0.3 -6 -6.85 14.07675
Mean(Expected) return = 0.85 181.1275
Co-variance
Stock fund Bond fund Prob. Co-variance
Return deviation from expected return Return deviation from expected return
-23.85 -18.85 0.2 89.9145
-16.85 19.15 0.25 -80.6694
2.15 4.15 0.25 2.230625
28.15 -6.85 0.3 -57.8483
-46.3725
(a) Mean return of stock fund is 5.85% and variance is 181.1275%.
(b) Covariance between stock fund and bond fund is -46.3725%.

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