Consider the following table:
Stock Fund | Bond Fund | ||
Scenario | Probability | Rate of Return | Rate of Return |
Severe recession | 0.10 | −43% | −12% |
Mild recession | 0.20 | −17.0% | 12% |
Normal growth | 0.30 | 17% | 6% |
Boom | 0.40 | 31% | 4% |
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.)
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.)
Scenario | Probability | Stock Fund return |
Bond fund return |
Severe recession | 0.1 | -43% | -12% |
Mild recession | 0.2 | -17% | 12% |
Normal growth | 0.3 | 17% | 6% |
Boom | 0.4 | 31% | 4% |
Stock Fund
Expected return is calculated using the formula:
Expected return = E[R] = p1*R1 + p2*R2 + p3*R3 + p4*R4
Expected return of stock Fund = E[RS] = 0.1*(-43%) + 0.2*(-17%) + 0.3*17% + 0.4*31% = -4.3% + (-3.4%) + 5.10% + 12.4% = 9.80%
Expected return or mean return of stock Fund = 9.8%
Variance is calculated using the formula:
Variance = p1*(R1 - E[R])2 + p2*(R2 - E[R])2 + p3*(R3 - E[R])2 + p4*(R4 - E[R])2
Variance of the stock Fund = σS2 = 0.1*(-43%-9.8%)2 + 0.2*(-17% - 9.8%)2 + 0.3*(17% - 9.8%)2 + 0.4*(31% - 9.8%)2 = 0.0278784 + 0.0143648 + 0.0015552 + 0.0179776 = 0.061776
We need to calculate the variance in %-squared. So to convert it into %-squared we need to multilply it by 10000.
Variance of the stock fund in %-squared = 0.061776*10000 = 617.76
Answer part a
Mean Return (%) = 9.8
Variance (%-Squared) = 617.76
Part b
Expected return of the bond fund = E[RB] = 0.1*(-12%) + 0.2*12% + 0.3*6% + 0.4*4% = -1.2% + 2.4% + 1.8% + 1.6% = 4.6%
We have the following data:
p1 = 0.1, p2 = 0.2, p3 = 0.3, p4 = 0.4
R1,S = -43%, R2,S = -17%, R3,S = 17%, R4,S = 31%
R1,B = -12%, R2,B = 12%, R3,B = 6%, R4,B = 4%
Expected return of the stock Fund = E[RS] = 9.8%, Expected return of the bond Fund = E[RB] = 4.6%
Covariance between the stock fund and the bond fund is calculated using the formula:
Covariance between stock fund and bond fund = Cov(S,B) = p1*(R1,S - E[RS])*(R1,B - E[RB]) + p2*(R2,S - E[RS])*(R2,B - E[RB]) + p3*(R3,S - E[RS])*(R3,B - E[RB]) + p4*(R4,S - E[RS])*(R4,B - E[RB])
Cov(S,B) = 0.1*(-43% - 9.8%)*(-12% - 4.6%) + 0.2*(-17% - 9.8%)*(12% - 4.6%) + 0.3*(17% - 9.8%)*(6% - 4.6%) + 0.4*(31% - 9.8%)*(4% - 4.6%) = 0.0087648 + (-0.0039664) + 0.0003024 + (-0.0005088) = 0.004592
To convert the covariance to %-squared, we need to multiply it by 10000
Cov(S,B) in %-squared = 0.004592*10000 = 45.92
Answer b -> Covariance (%-Squared) = 45.92
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 0.10 −43% −12% Mild recession 0.20 −17.0% 12% Normal growth 0.30 17% 6% Boom 0.40 31% 4% 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.) b. Calculate the value of the covariance between the stock and bond funds....
Consider the following table: Stock Fund Bond Fund Rate of Return Scenario Severe recession Probability Rate of Return 0.10 -43% -12% Mild recession 0.20 -17% 17% 12% Normal growth 0.30 6% 31% Boom 0.40 4% a. Calculate the values of mean return and variance for the stock fund. (Do not round interr Round "Mean return" value to 1 decimal place and "Variance" to 4 decimal places.) 06 Mean return %-Squared Variance b. Calculate the value of the covariance between the...
Consider the following table: Bond Fund Rate of Return -138 Scenario Severe recession Mild recession Normal growth Boom Probability 0.10 0.20 0.40 0.30 Stock Fund Rate of Return -40% -20% 25% 30% 19% 12% -9% 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.) 11.01% Mean return Variance b.Calculate the value of the covariance between the stock and...
Consider the following table: Stock Fund Bond Fund Scenario Probability Rate of Return Rate of Return Severe recession 0.05 −30% −8% Mild recession 0.20 −15.0% 8% Normal growth 0.30 9% 4% Boom 0.45 38% 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.) b. Calculate the value of the covariance between the stock and bond funds....
Consider the following table: Scenario Severe recession Mild recession Normal growth Boom Stock Fund Probability Rate of Return 0.10 -35% 0.20 -15% 0.40 20% 0.30 25% Bond Fund Rate of Return -14% 20% 13% -10% 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 9.01% 434.00 b.Calculate the value of the covariance between the stock...
please show steps with answers Consider the following table: Bond Fund Rate of Return Scenario Severe recession Mild recession Normal growth Boom Stock Fund Probability Rate of Return 0.05 -308 0.25 SS-106 0.40 158 0.30 206 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.) 1% Mean return Variance b.Calculate the value of the covariance between the stock...
Consider the following table: Stock Fund Bond Fund Scenario Probability Rate of Return Rate of Return Severe recession 0.05 −38% −8% Mild recession 0.15 −10.0% 5% Normal growth 0.30 15% 6% Boom 0.50 25% −4% 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.) b. Calculate the value of the covariance between the stock and bond funds....
Consider the following table: Stock Fund Bond Fund Scenario Probability Rate of Return Rate of Return Severe recession 0.10 −39% −8% Mild recession 0.20 −19.0% 8% Normal growth 0.35 16% 5% Boom 0.35 30% −5% 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.) b. Calculate the value of the covariance between the stock and bond funds....
Consider the following table: Stock Pund Bond Pund Probability 0.10 0.20 Rate of Return -36 -16 21 Scenario Severe recession Mild recession Normal growth Rate of Return -98 154 8 -56 0.40 Boom 0.30 264 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 declmal places.) Mean return Variance b.Calculate the value of the covariance between the stock and bond...
Consider the following table: Stock Fund Bond Fund Scenario Probability Rate of Return Rate of Return Severe recession 0.08 −36% −23% Mild recession 0.34 −6% 1% Normal growth 0.45 16% 5% Boom 0.13 40% 5% a. Calculate the values of mean return and variance for the stock fund. (Do not round intermediate calculations. Round "Mean return" value to 2 decimal places and "Variance" to 4 decimal places.) Mean return % Variance b. Calculate the value of the covariance between...