Question

# You must allocate your wealth between two securities. Security 1 offers an expected return of 10%...

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:

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

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?

E(R) of a portfolio = w1R1 + w2R2 + ...+ wnRn

R1 = 10% , R1 = 15%

Standard Deviation of a Portfolio =

Cov12 = ?1?2Corr12 = 0.30 * 0.50 * 0.25 = 0.375

When w1 = 100% & w2 = 0%

E(R) of a portfolio = w1R1 + w2R2 + ...+ wnRn

= (1*0.1) + (0*0.15) = 10%

= ? (1)2(0.3)2 + (0)2(0.5)2 + 2(1)(0)(0.375)

= ? 0.09 + 0+ 0

= 30%

Likewise, doing the same method for all the options of portfolios :

 % Security 1 % Security 2 %E(R) %Standard Deviation 100 0 10 30 80 20 11 68.38 60 40 12 50.24 40 60 13 53.33 20 80 14 53.25 0 100 15 50

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