Question

Stock A’s expected return and standard deviation are E[rA] = 6% and σA= 12%, while stock B’s expected return and standard deviation are E[rB] = 10% and σB= 20%.
(a) Using Excel to compute the expected return and standard deviation of the return on a portfolio with weights wA=0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1, for the following alternative values of correlation between A and B: ρAB=0.6 and ρAB= -0.4. Under the two different correlations, plot the expected return—standard deviation pairs on a graph (with the standard deviations on the horizontal axis, and the expected returns on the vertical axis).
(b) How would you construct a portfolio p with expected return of 8% using Stock A and Stock B? What is the standard deviation of the portfolio? (Assume ρAB = 0.4)
(c) How would you construct a portfolio q with standard deviation of 15% using Stock A and Stock B? What is the expected return of the portfolio? (Assume ρAB = 0.4)
(d) If you want to have the minimum variance for your portfolio z, what will be your portfolio weights? In this case, what are the expected return and variance of your portfolio? (Assume ρAB = 0.4)

Answer 1

(a)

(b)

Expected Return = 0.08

Let Weight of A = x

Let Weight of B = 1-x

Expected Returns = Weight of A * Return of A + Weight of B * Return of B

0.08 = x * 0.06 + ( 1 - x ) * 0.10

0.08 = 0.06x + 0.10 - 0.10x

x = 0.5

So, Weight of A and B are 50% and 50% respectively.

Variance of Portfolio = Weight(A)² * StDev(A)² + Weight(B)² * StDev(B)² + 2 * Weight(A) * Weight(B) * Standard Deviation of A * Standard Deviation of B * Correlation

= 0.5² * 0.12² + 0.5² * 0.20² + 2 * 0.5 * 0.5 * 0.12 * 0.20 * 0.4

= 1.84%

Standard Deviation = Sqrt of Variance

SquareRoot of 1.84% is 13.56%

(c)

	Stock A	Stock B
Expected Returns	6%	10%
Standard Deviation	12%	20%
Weights	36%	64%	100%
Portfolio:-
Expected Return	8.54%
Standard Deviation	0.15
Correlation	0.4

Using Excel Solver, We got Expected return is 8.54%

(d)

Using Excel Solver:-

Weight of A is 86.36%

Weight of B is 13.64%

Portfolio Return is 6.55%

Portfolio Standard Deviation is 11.72%