Question

Stock market tends to move with business cycles. In booms, analysts tend to have less disagreement than in recessions, because the economic uncertainty is higher in bad times. Answer the following two questions based on the following analyst forecasts about the stock market.

a. Suppose in booms, 16 (out of 20) analysts believe the stock market will increase by 30%, 3 analysts believe the market will go up by 10%, and only 1 believes the market will go down by 10%. What is the mean and standard deviation of the expected returns in booms?

b. Suppose in recessions, 5 (out of 20) analysts believe the stock market will increase by 30%, 5 analysts believe the market will go up by 10%, and 10 believe the market will go down by 10%. What is the mean and standard deviation of the expected returns in recessions?

Answer 1

2 a)In boom No of analysts that believe Weights Returns 0.8 30% 3 0.15 10% 1 0.05 -10% 20 1 Mean 1.25% Standard deviation 25.89% 13 b)In recession No of analysts that believe Weights Returns 5 0.25 30% 5 0.25 10% 10 0.5 -10% - 20 1 Mean 0.25% Standard deviation 14.83%

B No of analysts that believe a)In boom 16 Weights =B2/$B$5 =B3/$B$5 =B4/$B$5 =SUM(C2:04) Returns 0.3 0.1 -0.1 3 =SUM(B2:34) Mean =SUMPRODUCT(C2:C4,D2:04)/B5 Standard deviation =SQRT((C2*(D2-D7)^2)+(C3*(D3-D7)^2)+(C4*(D4-D7^2))/B5) No of analysts that believe b)In recession Weights =B13/$B$5 =B14/$B$5 =B15/$B$5 =SUM(C13:C15) Returns 0.3 0.1 -0.1 5 10 =SUM(B13:B15) Mean =SUMPRODUCT(C13:C15,D13:D15)/B16 Standard deviation =SQRT((C13*(D13-D18)^2)+(C14*(D14-D18)^2)+(C15*(D15-D18^2))/B16)

The whole solution and formulae are given for reference