In: Finance
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
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. |
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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%. | |||||||