The following table provides the share return forecasts and associated probabili

Question

The following table provides the share return forecasts and associated probabilities for Ally Ltd and Bell Ltd. Answer parts a. to c. using the information provided. Please provide worked solutions, including formulae used, progressive and final answers to the question.

Ally Ltd
Return (%) Probability (%)
15.5 30
12.0 30
9.5 40

Bell Ltd
Return (%) Probability (%)
20.3 20
10.5 50
7.0 30

a. Calculate the expected return on each share.

b. Calculate the variance and standard deviation for each share.

c. Suppose a portfolio comprised of 60% investment in Ally Ltd and 40% investment in Bell Ltd can be constructed. An analyst has estimated that the correlation coefficient of the two-asset portfolio is -0.50, calculate the return and standard deviation of this portfolio. Compare your answer with those reported in parts a. and b. and draw your conclusion.

Explanation / Answer

Expected Return = PiRi
Variance = Pi(Ri - Expected R)2

Ri is Rerutn in a scenario i
Pi = Probability of Ri

(a)

Ally Ltd expected return = (15.5*30%) + (12*30%) +(9.5*40%) = 4.65 + 3.6 + 3.8 = 12.05

Bell Ltd expected return = (20.3*20%) + (10.5*50%) +(7*30%) = 4.06 + 5.25 + 2.1 = 11.41

(b)

Variance of Ally Ltd = [(15.5-12.05)2*30%] + [(12-12.05)2*30%] +[(9.5-12.05)2*40%]
= 6.1725

Variance of Bell Ltd = [(20.3-11.41)2*20%] + [(10.5-11.41)2*50%] +[(7-11.41)2*30%]
= 22.0549

Standard Deviation of Ally Ltd = 1 = Variance = 6.1725 = 2.4845

Standard Deviation of Bell Ltd = 2 = Variance = 22.0549 = 4.6963

(c)

Return of portfolio = weighted return of stock = (12.05*60%) + (11.41*40%) = 11.794

weight of stock 1 = w1 = 60%
weight of stock 2 = w2 = 40%

Correlation coefficient of 1,2 = = -0.5

Standard deviation of portfolio = (w12*12 + w22*22 + 2w1w212)

=(0.62*2.48452 + 0.42*4.69632 + 2*(-0.5)*0.6*0.4*2.4845*4.6963)

=2.950714

=1.7177642

Return of the portfolio is between the returns of the individual stocks

Standard deviation is lower than both the stocks, making the portfolio less risky than individual stocks

Return/risk of portfolio = 11.794/1.7177642 = 6.8659 is higher than that of the individual stocks making the portfolio a better option than the individual stocks.

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