Betty Muye has invested 75% of her fun The following probability distribution re

Question

Betty Muye has invested 75% of her fun The following probability distribution relates to the shares of the two companies. ds in shares of company X and 25% in shares of company Y, ate of economy Boom Steady growth Probability Return on company X shares (%) 24 12 0 Return on Company Y shares (%) 0.2 0.6 0.2 30 -5 Slump Required: i) Expected returns on the shares of companies X and Y. ii) Standard deviation of return on shares of companies X and Y. ii) Coefficient of Correlation between the returns on shares of companies X andY iv) Expected portfolio return. v) Portfolio risk.

Explanation / Answer

Question - 1

P = probabilities, X represents possible returns of X - shares and Y represents that of Y - shares.

Expected value = sum of the products of Prob and respective returns

Question - 2

Dx = X - E(x) and Dy = Y - E(y)

Standard deviation of X = Square root over [  SUM (P*Dx2)] = Square root [ 57.6 ] = 7.59

Standard deviation of Y = Square root over [ SUM P*Dy2 ) ] = Square root [ 226] = 15.03

Question - 3

Coefficient of correlation = Cov (X,Y) / SD(x) * SD(y) = 24 / (7.59 * 15.03) = 24 / 114.08 = 0.21

Note COV (X,Y) is computed as under ........

Question - 4

Expected portfolio return = E(X) * W(x) + E(Y) * W(y) ........ Here w = weight or portion invested.

= 12 * 0.75 + 18 * 0.25 = 13.5%

Question - 5

Portfolio risk or Standard deviation of portfolio

= Square root of [ V(X) * (Wx)2 + V(Y) * (Wy)2 + 2 * Wx * Wy * Rxy * SD(x) * SD(y) ]

Here V = Variance = SD2 and Rxy = correlation between X and Y

= Square root of [ 57.6 * (0.75)2 + 226 * (0.25)2 + 2 * (0.75) * (0.25) * (0.21) * (7.59) * ( 15.03) ]

= Square root of [ 32.4 + 14.125 + 8.984 ] = 7.45

State P X Y X*P Y*P Boom 0.2 24 5 4.8 1 Steady 0.6 12 30 7.2 18 Slump 0.2 0 -5 0 -1     Expected Returns   = E(x) = 12 E(y) = 18

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