Please show work to understand how to compute and distinguish between the differ
ID: 2811828 • Letter: P
Question
Please show work to understand how to compute and distinguish between the different sections
Use the following scenario analysis for stocks X and Y to answer the questions. Round to the nearest 1/ 100 of 1% (ie., 15.07%). Normal Bull eaf Market Market Market Probability 15.00% 50.00% 35.00% Stock X -10.00% 11 .00% 25.00% Stock Y -24.00% 9.00% 40.00% 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)? 3c) 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)?Explanation / Answer
a)
Expected return of stock X = 0.15*(-0.1) + 0.5*(0.11) + 0.35*(0.25)
Expected return of stock X = -0.015 + 0.055 + 0.0875
Expected return of stock X = 0.1275 or 12.75%
Expected return of stock Y = 0.15*(-0.24) + 0.5*(0.09) + 0.35*(0.4)
Expected return of stock Y = -0.036 + 0.045 + 0.14
Expected return of stock Y = 0.149 or 14.9%
b)
Standard deviation of stock X = [0.15( -0.1 - 0.1275)2 + 0.5(0.11 - 0.1275)2 + 0.35(0.25 - 0.1275)2]1/2
Standard deviation of stock X = [ 0.007763 + 0.000153 + 0.005252 ]1/2
Standard deviation of stock X = 0.1148 or 11.48%
Standard deviation of stock Y = [0.15( -0.24 - 0.149 )2 + 0.5(0.09 - 0.149 )2 + 0.35(0.4 - 0.149 )2]1/2
Standard deviation of stock Y = [ 0.022698 + 0.001741 + 0.02205 ]1/2
Standard deviation of stock Y = 0.2156 or 21.56%
c)
Share ratio of X = ( expected retrun - risk free rate) / standard deviation
Share ratio of X = ( 0.1275 - 0.025) / 0.1148
Share ratio of X = 0.8929
Share ratio of Y = ( expected retrun - risk free rate) / standard deviation
Share ratio of Y = ( 0.149 - 0.025) / 0.2156
Share ratio of Y = 0.5751
d)
Expected return of portfolio = ( 75,000 / 200,000)*0.1275 + ( 125,000 / 200,000)*0.149
Expected return of portfolio = 0.047813 + 0.093125
Expected return of portfolio = 0.1409 or 14.09%