Problem 3 Scenario Analysis (33 points) Use the following scenario analysis for
ID: 2813413 • Letter: P
Question
Problem 3 Scenario Analysis (33 points)
Use the following scenario analysis for stocks X and Y to answer the questions. Round to the nearest 1/100 of 1% (i.e., 15.07%).
Bear
Normal
Bull
Market
Market
Market
Probability
35.00%
55.00%
10.00%
Stock X
-20.00%
11.00%
28.00%
Stock Y
-17.00%
16.00%
49.00%
3.a) What are the expected rates of return for stocks X and Y (9 points)?
3.b) What are the standard deviations for of returns for stocks X and Y (8 points)?
3.c) If the risk–free rate of return is 2.50%, what are the Sharpe Ratios for stocks X and Y (8 points)? (Please assume that the standard deviations of the excess returns are the same as the standard deviations of returns calculated in part b.)
3.d) Assume you have a $200,000 portfolio and you invest $75,000 in stock X and the remainder in stock Y. What is the expected return for this portfolio (8 points)?
Bear
Normal
Bull
Market
Market
Market
Probability
35.00%
55.00%
10.00%
Stock X
-20.00%
11.00%
28.00%
Stock Y
-17.00%
16.00%
49.00%
Explanation / Answer
3a Calculation of expected rate of returns: Stock X P R ER=P*R Market Condition Probability Return Probability *Return Bear 0.35 -0.2 -0.07 Normal 0.55 0.11 0.0605 Bull 0.1 0.28 0.028 SUM 0.0185 Epected Return of Stock X 0.0185 Epected Return of Stock X (in percentage) 1.85% Stock Y P R ER=P*R Market Condition Probability Return Probability *Return Bear 0.35 -0.17 -0.0595 Normal 0.55 0.16 0.088 Bull 0.1 0.49 0.049 SUM 0.0775 Epected Return of Stock y 0.0775 Epected Return of Stock Y(in percentage) 7.75% 3b Standard Deviation of Returns Stock X P R D=R-0.0185 (D^2) P*(D^2) Market Condition Probability Return Deviation from mean Deviation Square Deviation Square*Probability Bear 0.35 -0.2 -0.2185 0.047742 0.016709788 Normal 0.55 0.11 0.0915 0.008372 0.004604738 Bull 0.1 0.28 0.2615 0.068382 0.006838225 SUM 0.02815275 Variance of StockX 0.02815275 Standard Deviation =Squre root of Variance= 0.1678 Standard Deviation(in percentage) 16.78% Stock Y P R D=R-0.0775 (D^2) P*(D^2) Market Condition Probability Return Deviation from mean Deviation Square Deviation Square*Probability Bear 0.35 -0.17 -0.2475 0.061256 0.021439688 Normal 0.55 0.16 0.0825 0.006806 0.003743438 Bull 0.1 0.49 0.4125 0.170156 0.017015625 SUM 0.04219875 Variance of StockY 0.04219875 Standard Deviation =Squre root of Variance= 0.2054 Standard Deviation(in percentage) 20.54% 3c Sharp Ratio: Risk Free Return 0.025 Sharp ratio =(Expected return-Risk Free Return)/Standard Deviation Sharp Ratio of X=(0.0185-0.025)/0.1678 -0.0387366 Sharp Ratio of Y=(0.0775-0.025)/0.2054 0.25559883 3d Expected Portfolio return A Total Investment $200,000 B Investment in Stock X $75,000 C=A-B Investment in Stock Y $125,000 Wx=B/A Weight of Stock X in the portfolio 0.375 Wy=C/A Weight of Stock Y in the portfolio 0.625 Rx Expected Return of Stock X 0.0185 Ry Expected Return of Stock Y 0.0775 Rp=(Wx*Rx)+(Wy*Ry) Expected Return of the portfolio 0.055375 Expected Return of the portfolio(in percentage) 5.54%
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.