8.12 The following are the rates of return (in percent) on assets A and B: Rate of Return (7) State of the Economy Asset A Asset B 1 -10 10 2 20 17 3 -2 0 4 4 8 5 12 19 a Calculate the return on a portfolio in State 4 of the economy if =% and 9=%. How would your answer change if the investment weights were wa="/2 and 10='/? b. Calculate the portfolio's mean rate of return and variance if ="/2 and w="/2. Assume each state of the economy has a probability of Vs of occurring. c. Now assume that the probability of State 1 of the economy is 6/10 and the probability of each of the other four states is 1/10. Calculate the portfolio's mean rate of return and variance for weights 24=1/2. 8.12 The following are the rates of return (in percent) on assets A and B: Rate of Return (7) State of the Economy Asset A Asset B 1 -10 10 2 20 17 3 -2 0 4 4 8 5 12 19 a Calculate the return on a portfolio in State 4 of the economy if =% and 9=%. How would your answer change if the investment weights were wa="/2 and 10='/? b. Calculate the portfolio's mean rate of return and variance if ="/2 and w="/2. Assume each state of the economy has a probability of Vs of occurring. c. Now assume that the probability of State 1 of the economy is 6/10 and the probability of each of the other four states is 1/10. Calculate the portfolio's mean rate of return and variance for weights 24=1/2