Question

The expected return on stock W is 10% and its standard deviation is 15%. Expected return on stock V is 16% and its standard deviation is 24%. The correlation between returns of W and V is 20%.

a)     calculate expected return and standard deviation of a portfolio that invests 40% in W and 60% in V.

b)    determine the minimum variance combination of W and V and determine its expected return and standard deviation.

c)     If the risk-free rate is 4%, determine the tangency portfolio and derive the capital market line equation.

Answer 1

Expected return of stock W=E(R_W)=10% " " " " V=E(R_V)=16%

  Standard deviation of stock W=(SD_W)=15% " " " " V=(SD_V)=24% Standard deviation of portfolio return measuring portfolio risk=SD_p

correlation coefficient between stock W and V=r_{W V}=20%

Proportion of total portfolio value invested in stock W=X_W=40%   " "       " " "    " " " " V=X_V=60%

expected return on the portfolio=E(R_p)

E(R_p)=X_W*E(R_W)+X_V*E(R_V) =0.40*10+0.60*16 =13.6%

SD_p= (X_W²SD_W²+X_V²SD_V²+2.X_W.X_V.r_WV.SD_W.SD_V)^1/2

=(0.4²*15²+0.6²*24²+2*0.4*0.6*0.2*15*24)^1/2

=16.67%