Question

Jane is considering investing in three different stocks or creating three distinct two stock portfolios. Jane views herself as a rather conservative investor. She is able to obtain historical returns for the three securities for the years 2012 through 2018. The data are given in the following table. Year Stock A Stock B Stock C 10% 10% 13 12% 14 11 15 2012 2013 2014 2015 2016 2017 8 10 14 12 10 16 14 12 2018 15 15 10

Answer 1

Expected return on the portfolio = w(x)*E(x) + w(y)*E(y)

Standard deviation of portfolio =

(wxox)2 + (wyoy)2 + 2 * 0x *0x *W, * Wy* P1,2

where x and y are the securities

A B с D E F G H K 1 2 3 4 Expected return Standard deviation Portfolio AB Portfolio AC Portfolio BC 12.50% 12.07% 12.07% 1.47% 0.93% 1.41% 5 Year 2012 2013 2014 2015 2016 2017 2018 Stock A Stock B Stock C 10% 10% 12% 13% 11% 14% 15% 8% 10% 14% 12% 11% 16% 10% 14% 15% 9% 12% 15% 10% 6 7 9% 00 9 10 11 Average return 13.43% 11.57% 10.71% Standard deviation 1.99% 2.64% 1.80% 12 13 14 15 Correlation matrix А B 1 -0.213 С 16 A -0.519 17 B 1 -0.241 18 С 1 19

A B C D E F G H 1 2 Year Stock A Stock B Stock C 3 0.1 0.1 0.12 Portfolio AB Portfolio AC Expected return =0.5*C11+0.5*D11 =0.5*C11+0.5*E11 Standard deviation =((0.5*c12)^2+(0.5*D12)^2+2*0.5*0.5*c12*D12*D16)^0.5 =((0.5*c12)^2+(0.5*E12)^2 2012 2013 2014 4 0.14 5 0.13 0.15 0.14 0.11 0.08 0.12 0.1 6 2015 7 0.16 0.1 2016 2017 0.11 0.09 0.09 0.1 8 0.14 0.15 0.15 9 2018 0.12 10 11 Average return |=AVERAGE(C3:09) CAVERAGE(D3:09) Standard deviation =STDEV(C3:09) =STDEV(D3:09) =AVERAGE(E3:19) ESTDEV(E3:E9) 12 13 14 15 A 16 A 1 Correlation matrix B C =CORREL(C3:C9,D3:09) =CORREL(C3:C9,E3:E9) 1 =CORREL(D3:09, E3:E9) 1 17 B 18 C 19

F G H 1 2 3 Portfolio AB Portfolio AC Portfolio BC Expected return =0.5*C11+0.5*011 =0.5*C11+0.5*E11 =0.5*C11+0.5*E11 Standard deviation =((0.5*C12)^2+(0.5*D12)^2+2*0.5*0.5*C12*D12*D16)^0.5 =((0.5*(12)^2+(0.5*E12)^2+2*0.5*0.5*C12*E12*E16)^0.5 =((0.5*D12)^2+(0.5*E12)^2+2*0.5*0.5*D12*E12*E17)^0.5 4 5 6 7 8

e.

The expected return by the standard deviation ratio for Stock A = 13.43/1.99 = 6.75

The expected return by the standard deviation ratio for Portfolio AB = 12.50/1.47 = 8.50

Since, the ratio is higher for portfolio AB, the portfolio AB must be invested into.

f.

The expected return by the standard deviation ratio for Stock B= 11.57/2.64 = 0.595

The expected return by the standard deviation ratio for Portfolio BC= 12.07/1.41 = 8.560

Since, the ratio is higher for portfolio BC, the portfolio BC must be invested into.