You must allocate your wealth between two securities. Security 1 offers an expec

Question

You must allocate your wealth between two securities. Security 1 offers an expected return of 10% and has a standard deviation of 30%. Security 2 offers an expected return of 15% and has a standard deviation of 50%. The correlation between the returns on these two securities is 0.25.

a. Calculate the expected return and standard deviation for each of the following portfolios, and plot them on a graph:

b. Based on your calculations in part (a), which portfolios are efficient and which are inefficient?

c. Suppose that a risk-free investment is available that offers a 4% return. If you must divide your wealth between the risk-free asset and one of the risky portfolios in the preceding table, which risky portfolio would you choose? Why?

d. Repeat your answer to part (c) assuming that the risk-free return is 8% rather than 4%. Can you provide an intuitive explanation for why the optimal risky portfolio changes?

% Security 1 % Security 2 E(R) Standard Deviation 100 0 80 20 60 40 40 60 20 80 0 100

Explanation / Answer

b) In case where correlation between two securities is less than 1 the efficient portfolios would be where there is diversification. In these cases portfolio 2,3,4 and 5 are efficient portfolio and 1 and 6 are inefficient portfolio.

Security 1 Security 2 Expected return 10 15 Standard deviation 30 50 Correlation 0.25 Portfolio Security 1 % Security 2 E(R) Standard Deviation A 100 0 10(1) + 15(0) = 10 30.00 B 80 20 10(0.80) + 15(0.20) = 11 28.21 C 60 40 10(0.60) + 15(0.40) = 12 30.07 D 40 60 10(0.40) + 15(0.60) = 13 34.99 E 20 80 10(0.20) + 15(0.80) = 14 41.90 F 0 100 10(0) + 15(1) = 15 50.00 Now let us calculate standard deviation Scenario 1 : Sec 1 - 100%, Sec 2 -0 Weights Sec 1 - 1, Sec 2- 0 Variance = ((1^2)(0.30^2)) + ((0^2)(50^2)) + (2*1*30*0*50*0.25) Variance = 0.09 Standard deviation = 0.09^0.5 0.3 30% Scenario 2 : Sec 1 - 80%, Sec 2 -20% Variance = ((0.80^2)(0.30^2)) + ((0.20^2)(0.50^2)) + (2*0.80*0.30*0.20*0.50*0.25) Variance = 0.0796 Standard deviation = 0.0796^0.5 0.282135 28.21% Scenario 3 : Sec 1 - 60%, Sec 2 -40% Variance = ((0.60^2)(0.30^2)) + ((0.40^2)(0.50^2)) + (2*0.60*0.30*0.40*0.50*0.25) Variance = 0.0904 Standard deviation = 0.0904^0.5 0.300666 30.07% Scenario 4 : Sec 1 - 40%, Sec 2 -60% Variance = ((0.40^2)(0.30^2)) + ((0.60^2)(0.50^2)) + (2*0.40*0.30*0.60*0.50*0.25) Variance = 0.1224 Standard deviation = 0.1224^0.5 0.349857114 34.99% Scenario 5 : Sec 1 - 20%, Sec 2 -80% Variance = ((0.20^2)(0.30^2)) + ((0.80^2)(0.50^2)) + (2*0.20*0.30*0.80*0.50*0.25) Variance = 0.1756 Standard deviation = 0.1756^0.5 41.9 Scenario 6 : Sec 1 - 0%, Sec 2 -100% Variance = ((0^2)(0.30^2)) + ((1^2)(0.50^2)) + (2*0*0.30*1*0.50*0.25) Variance = 0.25 Standard deviation = 0.25^0.5 0.5 50

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