Question

Return to question Consider the following table: Scenario Severe recession Mild recession Normal growth Boom points Probability 0.10 0.20 0.30 0.40 Stock Fund Rate of Return -46% -24.0% 8% 44% Bond Fund Rate of Return -20% 14% 5% 8 00:45:38 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.) Answer is complete but not entirely correct. Mean return 10.6 0.1008 % %- Squared 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 4 decimal places.) Answer is complete but not entirely correct. Covariance 0.0079 Squared

Answer 1

Scenario	Probability	Stock Fund return	Bond Fund return
Severe Recession	0.1	-46%	-20%
Mild Recession	0.2	-24%	14%
Normal growth	0.3	8%	5%
Boom	0.4	44%	5%

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*(-46%) + 0.2*(-24%) + 0.3*8% + 0.4*44% = -4.6% + (-4.8%) + 2.40% + 17.6% = 10.60%

Expected return or mean return of stock Fund = 10.6%

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*(-46%-10.6%)2 + 0.2*(-24% - 10.6%)2 + 0.3*(8% - 10.6%)2 + 0.4*(44% - 10.6%)2 = 0.0320356 + 0.0239432 + 0.0002028 + 0.0446224 = 0.100804

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 = 0.100804*10000 = 1008.04

Answer part a

Mean Return (%) = 10.6

Variance (%-Squared) = 1008.04

Part b

Expected return of the bond fund = E[RB] = 0.1*(-20%) + 0.2*14% + 0.3*5% + 0.4*5% = -2% + 2.8% + 1.5% + 2% = 4.3%

We have the following data:

p1 = 0.1, p2 = 0.2, p3 = 0.3, p4 = 0.4

R1,S = -46%, R2,S = -24%, R3,S = 8%, R4,S = 44%

R1,B = -20%, R2,B = 14%, R3,B = 5%, R4,B = 5%

Expected return of the stock Fund = E[RS] = 10.6%, Expected return of the bond Fund = E[RB] = 4.30%

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*(-46% - 10.6%)*(-20% - 4.3%) + 0.2*(-24% - 10.6%)*(14% - 4.3%) + 0.3*(8% - 10.6%)*(5% - 4.3%) + 0.4*(44% - 10.6%)*(5% - 4.3%) = 0.0137538 + (-0.0067124) + (-0.0000546) + 0.0009352 = 0.007922

To convert the covariance to %-squared, we need to multiply it by 10000

Cov(S,B) in %-squared = 0.007922*10000 = 79.22

Answer b -> Covariance (%-Squared) = 79.22