Question

Consider the following table: Scenario Severe recession Mild recession Normal growth Boom Stock Fund Probability Rate of Return 0.11 -34% 0.16 -12% 0.58 17% 0.15 49% Bond Fund Rate of Return -16% -4% 7 % 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 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

Answer 1

The detailed explanation is shown in the handwritten solution and the complete answers are provided in the other two excel sheet images. Do look at all the images.

Solution) Mean Return (R) of an investment is given by : • R = 2 (P; . R;) where, b, a probability of ith Scenario R; =) Return in ith scenario i= 1, 2, 3, 4 . Mean return of stock and, ēs = 0.11% (-34%) + 0-16 X(-12"%) + 0.58x(17%) + 0.15x(494) = 11.55% Mean Variance of an investment is given by : V = I (pi-V;) where, Vj = Variance in ith scenario i=1,2,3,4. & Vi= (Ri - Ř² where, R; = Returns in ith scenario R =) Mean return VE 011 (-34-f155) + 016x(+12–55)* +058 (17-11-59+0.45X(4-7-1563" or, J = 10.0545 N © Covaiance = { p. 64-7). 4;-7) ; = 11-55% J = -3.52 % where, x; & K: return & mean return for stock fund deviation & į ; return & mean return Find for bond find) stock Bond fund Probabilita stock 1 I Bond Product of Deviation | Deviation Deviation i) 0.11 -34% -16% -34-11-55% -16+3.52% E0.4555)x(-0.1248 5-04555 -0.1248 = 0.0568 0.16 -12% -4% -0.2355 -0.0048 10) 0:58 0.0011 17% 0.0545 0.4052 iv) 0.15 0.0057 49% 0 0.3745 0.0352 0-0132 Covariance = (0.11 X 0.088) + (0-16 x0.0011) +(0:52X0.0057) +(0:15 20:0132) sportheast -10.117

Mean Return and Variance Probability SCENARIO Severe Recession Mild Recession Normal Growth Boom 0.11 0.16 0.58 0.15 Stock Fund Squared Return Deviation -34% 0.2075 -12% 0.0555 17% 0.0030 49% 0.1403 Bond Fund Squared Return Deviation -16% 0.0156 -4% 0.0000 7% 0.0111 0% 0.0012 11.55% 0.0545 -3.52% 0.0034 Mean variance

Mean Return and Variance Probability Stock Fund Bond Fund SCENARIO Return Deviation Return Deviation Severe Recession Mild Recession Normal Growth Boom -16% 4% 0.11 0.16 0.58 0.15 0.15 -34% -12% 17% -0.4555 -0.2355 0.0545 0.3745 -0.1248 -0.0048 0.1052 Product of Deviations 0.0568 0.0011 0.0057 0.0132 7% 49% 0% 0.0352 Covariance 0.0117