答案和详解如下： Q6. Adding a stock to a portfolio will reduce the risk of the portfolio if the correlation coefficient is less than which of the following?
A) 0.00. B) +0.50. C) +1.00. Correct answer is C) Adding any stock that is not perfectly correlated with the portfolio (+1) will reduce the risk of the portfolio. Q7. An investor has a two-stock portfolio (Stocks A and B) with the following characteristics: - σA = 55%
- σB = 85%
- CovarianceA,B = 0.9
- WA = 70%
- WB = 30%
The variance of the portfolio is closest to: A) 0.59 B) 0.39 C) 0.54 Correct answer is A) The formula for the variance of a 2-stock portfolio is: s2 = [WA2σA2 + WB2σB2 + 2WAWBσAσBrA,B] Since σAσBrA,B = CovA,B, then s2 = [(0.72 × 0.552) + (0.32 × 0.852) + (2 × 0.7 × 0.3 × 0.9)] = [0.14822 + 0.06502 + 0.378] = 0.59124, or approximately 0.59.
Q8. An investor’s portfolio currently consists of 100% of stocks that have a mean return of 16.5% and an expected variance of 0.0324. The investor plans to diversify slightly by replacing 20% of her portfolio with U.S. Treasury bills that earn 4.75%. Assuming the investor diversifies, what are the expected return and expected standard deviation of the portfolio? ERPortfolio
σPortfolio
A) 14.15% 2.59% B) 10.63% 2.59% C) 14.15% 14.40% Correct answer is C) Since Treasury bills (T-bills) are considered risk-free, we know that the standard deviation of this asset and the correlation between T-bills and the other stocks is 0. Thus, we can calculate the portfolio expected return and standard deviation. Step 1: Calculate the expected return
Expected ReturnPortfolio = (wT-bills × ERT-bills) + (wStocks × ERStocks)
= (0.20) × (0.0475) + (1.00-0.20) × (0.165) = 0.1415, or 14.15%. Step 2: Calculate the expected standard deviation
When combining a risk-free asset and a risky asset (or portfolio or risky assets), the equation for the standard deviation, σ1,2 = [(w12)(σ12) + (w22)(σ22) + 2w1w2 σ1 σ2ρ1,2]1/2, reduces to: σ1,2 = [(wStocks)(σStocks)] = 0.80 × 0.03241/2 = 0.14400, or 14.40%. (Remember to convert variance to standard deviation). Q9. What is the variance of a two-stock portfolio if 15% is invested in stock A (variance of 0.0071) and 85% in stock B (variance of 0.0008) and the correlation coefficient between the stocks is –0.04? A) 0.0020. B) 0.0026. C) 0.0007. Correct answer is C) The variance of the portfolio is found by: [W12 σ12 + W22 σ22 + 2W1W2σ1σ2r1,2], or [(0.15)2(0.0071) + (0.85)2(0.0008) + (2)(0.15)(0.85)(0.0843)(0.0283)(–0.04)] = 0.0007. Q10. Which of the following equations is least accurate? A) Real Risk-Free Rate = [(1 + nominal risk-free rate) / (1 + expected inflation)] − 1. B) Standard Deviation2-Stock Portfolio = [(w12 × σ12) + (w22 × σ22) + (2 × w1 × w2 σ1σ2 × ρ1,2)]. C) Required Returnnominal = [(1 + Risk Free Ratereal) × (1 + Expected Inflation) × (1 + Risk Premium)] − 1. Correct answer is B) This is the equation for the variance of a 2-stock portfolio. The standard deviation is the square root of the variance. The other equations are correct. | 
发表于 2009-1-22 10:30
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