Question

(a) Suppose there are 2 assets A1 and Plan B. A1 has an expected return of 7.6% and a standard deviation of 20%. Plan B has an expected return of 12.4% and a standard deviation of 28%. Al is expected to trade at £180 in two years' time. What should its current market price be? (10 marks) The correlation between A1 and Plan B is 0. Suppose portfolio ANB has a weight of 50% in A1 and 50% in Plan B. What is the expected return and standard deviation of ANB? (b) (10 marks) (c) Now suppose a portfolio manager has a maximum standard deviation of 20%. Estimate the two sets of weights in A1 and Plan B which can generate this. What is the maximum expected return they could generate when forming portfolios from A1 and Plan B for a standard deviation of 20%. (15 marks) (d) Discuss the main advantages of using standard deviation to measure risk. (15 marks)

Answer 1

Current market price should be the present value of the expected value.

Expected return and portfolio variance can be calculated as follows:

A1 Plan B Assets Expected Return Standard Deviation 7.60%) 12.40% 28% Expected value of A1 after two £ 180.00 ears Period Rate of return of A1 10 2 Years 7.60% 12 13 14 15 16 17 Current market price should be the present value of the expected value 180 / (1+7.6096)2 155.47 Current market price Hence the Current market price IS £155.47 19 Portfolio return can be calculated as follows: 23 Expected portfolioreturn, r. -w,r; 2б 27 Where w and r are the weights and return of assets A 29 Weight and returns of the stocks of the portfolio1 is as follows: A1 Plan B 31 Expected Return Weights 7.60%) 50.00%) 12.40% 50.00% 32 Hence Portfolio return is calculated as follows: Portfolio expected return 50%*7.60%+50% * 12.40% 35 36 37 38 39 10.00%-SUMPRODUCT(D32:E32,D31:E31) Hence Portfolio return is 10.00%

41 42 43 Calculation of Standard Deviation of portfolio Portfolio variance is given by following formula Portfolio variance-w2A*σ"(%) + w2B"G2(Re) + 2"(%) *(we)"cov(A, B) where wA and we are weights of assets A and B, σΑ and Og are standard deviation of assets A and B Given the following data: A1 Plan B Expected Return Standard Deviation Weight Correlation(A1,B) Cov (A1,B) Portfolio Variance 7.60%) 20.00% 0.5 12.40% 28.00% 0.5 47 49 51 52 53 54 2.96%-D48"D47)^2+(E48*E47)^2+2*D48*E48"D50 Standard Deviation of Portfolio Sqrt(Var) 17.2096 SQRT(D52) 56 57 Hence Expected return of the portfolio Standard Deviation of Portfolio 10.00% 17.20% 59 61 62 63 Solver function of excel can be used to find the weights of the portfolio such that the return is maximum when standard deviation of the portfolio becomes equal to 20%. Plan B 7.60%) 20.00% 0.32 12.40% 28.00% 0.68 67 69 70 71 72 73 74 75 Expected Return Standard Deviation Weight Correlation(A1,B) Cov (A1,B) Portfolio Variance 0-D70 D68 E68 4.00%-D69"D68)^2+(E69*E68)^2+2*D69"E69"D71 Standard Deviation of Portfolio Sqrt(Var) 20.00% =SQRT(D73) Expected Return 10.84%-SUMPRODUCT(D69:E69,D67:E67) Hence, 81 A1 Plan B 83 84 85 Weight 0.32 0.68 Maximum return is 10.84% 87 Standard deviation is the best measure of variation. Advantage of standard deviation to measure risk is that combined standard deviation can be calculated for any number of assets in the portfolio. 89
Solver Setting

Solver Parameters Set Objective To: O Max OMin alue Of By Changing aiable Cells: SDS78 SDS69 Subject to the Constraints: SDS76 2096 Add Change Delete Reset All Load/Save Make Unconstrained Variables Non-Negative Selt a Solving Method: GRG Nonlinear Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve Close