Question

Please show all work using formulas, not a financial calculator.

2. You currently own a portfolio of two stocks. JH Chemical has an expected return of 11% with a standard deviation of 15% while AAC Agriculture has an expected return of 15% with a standard deviation of 20%. The correlation coefficient between these two stocks is 0.30. a. (10 points) If you invest $14,000 in JH and $6,000 in AAC, what is the expected return and standard deviation of the portfolio? Was risk reduced relative to the individual risk of each security? Why? b. (10 points) What are the weights of each stock for the minimum variance portfolio?

Answer 1

Total investment = 14000 + 6000 = 20000

Let w_j and w_a be the weightage of investments in JH Chemicals and AAC Agriculture respectively.

Hence, w_j = 0.7, and w_a = 0.3

Let E(r) be the expected return of the portfolio.

Hence, we have;

$E(r)=w_j\times E(j)+w_a\times E(a)=0.7\times 11+0.3\times 15=0.122$

Hence, expected return of the portfolio is 12.2%

Let σ_r be the standard deviation of the portfolio, and let σ_j and σ_w are the standard deviation of JH chemicals and AAC Agriculture.

Hence, we have;

${\sigma_{r}}^{2}=w_j^{2} \times {\sigma_{j}}^{2}+w_a^{2} \times {\sigma_{a}}^{2}+2\times w_j \times w_a \times Cov(J,A)$

Where, Cov(J,A) is nothing but the Co-variance of JH chemical and AAC Agriculture stock. If ρ_ja is correlation coefficient, then Cov(J,A) is defined as;

Cov(J,A) = ρ_ja * σ_j * σ_w

$\therefore {\sigma_{r}}^{2}=0.7^{2} \times 0.15^{2}+0.3^{2} \times 0.2^{2}+2\times 0.7 \times 0.3 \times 0.3 \times 0.15 \times 0.20 =0.018405$

$\therefore {\sigma_{r}}=\sqrt{0.018405}=0.1356$

Hence, standard deviation of the portfolio is reduced to 13.56%.