Consider the following information: Rate of Return If State Occurs State of Prob
ID: 2719010 • Letter: C
Question
Consider the following information: Rate of Return If State Occurs State of Probability of Economy State of Economy Stock A Stock B Recession .20 .08 .15 Normal .50 .11 .14 Boom .30 .16 .31 Calculate the expected return for each stock. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return Stock A % Stock B % Calculate the standard deviation for each stock. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Standard deviation Stock A % Stock B %
Explanation / Answer
State of probability Stock A Stock B Economy p return rA rA*p rA-ERA (rA-ERA)^2 return rB rB*p rB-ERB (rB-ERB)^2 Recession 0.2 0.08 0.016 -0.039 0.001521 -0.15 -0.03 -0.283 0.080089 Normal 0.5 0.11 0.055 -0.009 0.000081 0.14 0.07 0.007 0.000049 Boom 0.3 0.16 0.048 0.041 0.001681 0.31 0.093 0.177 0.031329 Expected return 0.119 0.133 Expected return on stock A = Sum of (probability of state of economy * return for state of economy) = 0.2 * 0.08 + 0.50 * 0.11 + 0.3 * 0.16 = 0.016+0.055+0.048 = 0.119 or 11.90% Expected return on stock B = Sum of (probability of state of economy * return for state of economy) = 0.2 * -0.15 + 0.5*0.14+0.3*0.31 = -0.03+0.07+0.093 = 0.133 or 13.30% Variance of Stock A = Sum of [ probability * (return - expected return)^2] = 0.20*0.001521+0.50*0.000081+0.3*0.001681 = 0.0003042 + 0.0000405 + 0.0005043 = 0.000849 Variance of stock B = Sum of [probability * (return - expected return)^2] = 0.20 * 0.080089 + 0.50 * 0.000049 + 0.30 * 0.031329 = 0.0160178 + 0.0000245 + 0.0093987 = 0.025441 Standard deviation of Stock A = Square root of (variance) = (0.000849)^0.5 = 0.029138 or 2.91% (rounded off) Standard deviation of Stock B = Square root of (Variance) = (0.025441)^0.5 = 0.159502 or 15.95% (rounded off)
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