Question

1.a. The correlation between A and B is -0.07. Calculate the expected return of the minimum variance portfolio. Express your answer as a decimal with four digits after the decimal point (e.g., 0.1234, not 12.34%).

Asset	Expected Return	Standard Deviation
A	0.07	0.32
B	0.17	0.42

1.b. The correlation between A and B is +1. Calculate the expected return of the minimum variance portfolio. Express your answer as a decimal with four digits after the decimal point (e.g., 0.1234, not 12.34%).

Asset	Expected Return	Standard Deviation
A	0.12	0.19
B	0.15	0.26

Answer 1

1a).

Given that,

Standard deviation of asset a Sa = 0.32

Standard deviation of asset b Sb = 0.42

Correlation between asset A and B, C = -0.07

So, weight of asset A in minimum variance portfolio is

Wa = (Sb² - Sa*Sb*C)/(Sa² + Sb² - 2*Sa*Sb*C) = (0.42^2 - 0.32*0.42*(-0.07))/(0.32^2 + 0.42^2 - 2*0.32*0.42*(-0.07))

=> Wa = 0.6243

So, Weight of asset B, Wb = 1-Wa = 1-0.6243 = 0.3757

So, expected return on this portfolio is

E(r) = Wa*Ra + Wb*Rb = 0.6243*0.07 + 0.3757*0.17 = 0.1076

1b).

Given that,

Standard deviation of asset a Sa = 0.19

Standard deviation of asset b Sb = 0.26

Correlation between asset A and B, C = 1

When correlation is 1, lowest standard deviation that can be reached is the lowest of the two asset when all on the portfolio is invested in that asset

So, Weight of asset A Wa = 1

So, Weight of asset B, Wb = 1-Wa = 1-1 = 0

So, expected return on this portfolio is

E(r) = Wa*Ra + Wb*Rb = 1*0.12 + 0*0.15 = 0.12