Homework Answers
Answer to part A)
Expected return of a portfolio is the weighted average of the expected return of te individual stocks in the portfolio
| STOCK | Expected Return(A) | Weight(B) | Weighted Return(A*B) |
| A | 10% | 0.5 | 5.00% |
| B | 5% | 0.5 | 2.50% |
| Portifolio Expected Return | 7.50% | ||
| (sum of weighted Return) |
Standard deviation or volatility of portfolio is calculated by the following formula
[Wa^2*S(a)^2 + Wb^2 *S(b)^2 + 2* Wa* Wb* S(a)* S(b) * Co] ^ 1/2
where Wa = weight of stock A = 0.5
Wb = weight of stock B = 0.5 ( note - ^ sign implies power)
S(a) = Expected return of stock A = 12%= 0.12
S(b) = Expected return of stock B = 8% = 0.08
Co = correlation coeffecient = 0.4
=( 0.5^2 * 0.12^2 + 0.5^2 * 0.08^2 + 2* 0.5*0.5*0.12*0.08) ^ 1/2
solving we get 10%
hence the volatility of the portfolio is 10%
Answer to part B)
Minimum Variance Portfolio Weight
weight of stock B = [S(a)^2 - S(a)*S(b)*Co] divided by S(a)^2 + S(b)^2 -2*S(a)*S(b)*Co
solving our above question
we get weight of stock B = (0.12^2 - 0.12*0.08*0.4) / 0.12^2 + 0.08^2 - 2 * 0.12*0.08*0.4
=80.49%
therefore weight of stock A = 19.51%
Expected return of the portfolio is
0.8049*5 + 0.1951*10 = 5.96%
volatility can be calculated by the same formula as explanied in part 1
volatility =[ (0.12)2 (0.1951)2 + (0.8049)2 (0.08)2 + 2 (.8049) (.1951) (0.12) (0.08) (0.4) ] ^ 1/2
=7.69%
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