# Consider the following table: Stock Fund Bond Fund Scenario Probability Rate of Return Rate of Return Severe recession 0.05 −26% −11% Mild recession 0.25 −6% 17% Normal growth 0.40 11% 10% Boom 0.30 16% −7% 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 2 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 2 decimal places.) Covariance %-Squared

Solution a) Calculation of Mean avail of a Stock Investment

 Scenario Probability Stock Return % Probability * Stock Return % Severe Recession 0.05 -26 -1.3 Mild Recession 0.25 -6 -1.5 Normal Growth 0.4 11 4.4 Boom 0.3 16 4.8 6.40

Calculation of Variance of Stock Investment

 Scenario Probability Stock Return % Probability * Stock Return % Stock Return – Mean Return (Stock Return – Mean Return) ^2 Stock Return – Mean Return ^2) * Probability Severe Recession 0.05 -26 -1.3 -7.70 59.29 2.9645 Mild Recession 0.25 -6 -1.5 -7.90 62.41 15.6025 Normal Growth 0.4 11 4.4 -2.00 4 1.6 Boom 0.3 16 4.8 -1.60 2.56 0.768 6.40 20.94

For Stock Investment

Mean Return = 6.40%

Variance = 20.94

Standard Deviation of Stock investment = Variance^(1/2)

= 20.94^(1/2)

= 4.57%

Solution b) Calculation of Standard Deviation of Bond Investment.

 Scenario Probability Bond Return % Probability * Bond Return % Bond Return – Mean Return (Bond Return – Mean Return) ^2 (Bond Return – Mean Return ^2) * Probability Severe Recession 0.05 -11 -0.55 -16.60 275.56 13.778 Mild Recession 0.25 17 4.25 11.40 129.96 32.49 Normal Growth 0.4 10 4 4.40 19.36 7.744 Boom 0.3 -7 -2.1 -12.60 158.76 47.628 5.6 101.64

Therefore, Standard Deviation of Bond Investment = Variance^(1/2)

= 101.64^(1/2)

= 10.08%

Covariance of Stock and Bond Investment =

∑Probability * (Stock Return – Mean Return of Stock) * (Bond Return – Mean Return of Bond)

 Scenario Probability Stock Return – Mean Return Bond Return – Mean Return Probability * (Stock Return – Mean Return) * (Bond Return – Mean Return) Severe Recession 0.05 -7.70 -16.60 6.39 Mild Recession 0.25 -7.90 11.40 -22.52 Normal Growth 0.4 -2.00 4.40 -3.52 Boom 0.3 -1.60 -12.60 6.05 -13.60

Covariance of Stock and Bond Investment = -13.60

Covariance is a value of the directional sympathy between the avail on span risky goods. A disclaiming covariance means avail provoke inversely.