Question

Returns and standard deviation- Consider the following information:

State of economy Probability of state of economy Rate of return if state occurs

Stock A Stock B Stock C

Boom .75 .07 .01 .27

Bust .25 .12 .19 -.05

a. What is the expected return on an equally weighted portfolio of these 3 stocks?

b. What is the variance of a portfolio invested 20% in each in A and B and 60% in C?

Answer 1

weighted return (weight x return) state of econom rate of return if state occurs weighted sum probability expected return Stock A StockBStock C Stock A Stock B Stock C (sum of weighted return 2.3339 0.3339 9.00096 4.0009 6.3339 -1.667% 875% 2.17% 10.92% Boom 0.07 0.01 0.19 0.27 11.667% 0.75 Bust 0.12 -0.05 8.667% 0.25 Weight 33.33% 33.33% 33.33% Answer: 10.92% [If equally weighted ]

weighted return (weightx return) deviation state of economy rate of return if state occurs weighted sum obability expected return (weighted return- deviation2 deviation 2x probability expected return StockA StckB Stock C Stock A Stock BStockC(sum of weighted return) Boom Bust 0.27 0.05 1.400% 2.400%) 0.200% 3.800% 16.200% -3.000% 17.800% 3.200% 13.35% 0.30% 14.15% 3.65096 10.950% 0.133225% 1.199025% 0.07 0.01 0.75 0.000999188 0.12 0.19 0.25 0.00299 75б Weight 20.00% 20.00% 60.00% Variance 0.00400 Standard deviation variance0.5 6.32% Answer: Variance 0.00400weighted not equally ]