Question

Consider the following table: Scenario Severe recession Mild recession Normal growth Boom Probability 0.10 0.20 0.35 0.35 Stock Fund Rate of Return -18% -4.0% 23% 43% Bond Fund Rate of Return -8% 12% 10% 3% 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

Answer 1

Solution:

a. The mean of the stock fund is calculated using the formula

$Mean = \sum S.P$

Mean = 0.10*(-18%) + 0.20*(-4%) + 0.35*(23%) + 0.35*(43%)

Mean = 20.5%

The variance for the stock is calculated using the formula

$Variance = \sum P(S-Mean)^2$

Variance = 0.10*(-18 - 20.5)^2 + 0.20*(-4 - 20.5)^2 + 0.35*(23 - 20.5)^2 + 0.35*(43 - 20.5)^2

Variance = 447.6500 (%)-squared

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b. First, we calculate the mean of the bond fund

$Mean = \sum B.P$

Mean = 0.10*(-8%) + 0.20*(12%) + 0.35*(10%) + 0.35*(3%)

Mean = 6.15%

The covariance between stock and bond funds is calculated using the formula

$Cov (S, B) = \sum P(B - mean)(S - mean)$

$Cov (S, B)$ = 0.10 (-8 - 6.15) (-18 - 20.5) + 0.20 (12 - 6.15) (-4 -20.5) + 0.35 (10 - 6.15) (23 - 20.5) + 0.35 (3 - 6.15) (43 - 20.5)

$Cov (S, B)$ = 4.3750(%) - squared