Question

Consider the following information: Probability of State of Economy State of Rate of Return If State Occurs Stock C Stock A Stock B Economy Boom 17 358 128 458 338 Good 43 .108 178 Poor 018 .028 -062 -098 Bust 07 258 118 Your portfolio is invested 29 percent each in A and C and 42 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) 11.24 % Expected return What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.) n/r Variance What is the standard deviation of this portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) n/r % Standard deviation

Answer 1

deviation^2x probability state of economy rate of return if state occurs Stock A Stock B Stock C Boom 0.358 0.458 0.338 Good 0.128 0.108 0.178 0.018 0.028 -0.062 Bust -0.118 -0.258 -0.098 weighted return (weight x return) Stock A Stock B Stock C 10.382% 19.236% 9.802% 3.712% 4.536% 5.162% 0.522% 1.176% -1.798% -3.422% -10.836% -2.842% weighted sum probability (sum of weighted return) 39.420% 0.17 13.410% 0.43 -0.100% 0.33 -17.100% 0.07 Expected return of portfolio deviation expected return (weighted return- deviation^2 expected return) 6.70% 28.182% 7.942420% 5.77% 2.172% 0.047189% -0.03% -11.338% 1.285434% -1.20% -28.338% 8.030252% 11.24% Variance Standard deviation = variance10.5 0.013502115 0.00020291 0.00424193 0.00562118 Poor Weight 29.00% 42.00% 29.00% 0.02357 15.35% Answers: Expected return = 11.24% Variance = 0.02357 Standard deviation = 15.35%