Consider the following table: Stock Fund Bond Fund Scenario Probability Rate of
ID: 1175974 • Letter: C
Question
Consider the following table: Stock Fund Bond Fund Scenario Probability Rate of Return Rate of Return Severe recession 0.20 ?38% ?12% Mild recession 0.20 ?26% 7% Normal growth 0.35 8% 3% Boom 0.25 46% 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 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
Explanation / Answer
a) Mean return of stock fund = 0.20 x -38% + 0.20 x -26% + 0.35 x 8% + 0.25 x 46% = 1.5%
Variance for stock fund = (Returnsevere recession - Mean return)2 x Probsevere recession + (Returnmild recession - Mean return)2 x Probmild recession + (Returnnormal growth - Mean return)2 x Probnormal growth + (ReturnBoom - Mean return)2 x ProbBoom
or, Variance for stock fund = (-38% - 1.5%)2 x 0.20 + (-26% - 1.5%)2 x 0.20 + (8% - 1.5%)2 x 0.35 + (46% - 1.5%)2 x 0.25
or, Variance for stock fund = 973.15%2
b) Mean return for bond fund = 0.20 x -12% + 0.20 x 7% + 0.35 x 3% + 0.25 x 7% = 1.8%
Covariance = (Returnstock fundsevere recession - Mean Returnstock fund) x (Returnbond fundsevere recession - Mean Returnbond fund) x Probabilitysevere recession
+
(Returnstock fundmild recession - Mean Returnstock fund) x (Returnbond fundmild recession - Mean Returnbond fund) x Probabilitymild recession
+
(Returnstock fundnormal growth - Mean Returnstock fund) x (Returnbond fundnormal growth - Mean Returnbond fund) x Probabilitynormal growth
+
(Returnstock fundBoom - Mean Returnstock fund) x (Returnbond fundBoom - Mean Returnbond fund) x ProbabilityBoom
Long formula so I divided it like that to help you better understand.
Covariance = (-38% - 1.5%) x (-12% - 1.8%) x 0.20 + (-26% - 1.5%) x (7% - 1.8%) x 0.20 + (8% - 1.5%) x (3% - 1.8%) x 0.35 + (46% - 1.5%) x (7% - 1.8%) x 0.25
or, Covariance = 141.00%2