4. Suppose we have 2 risky stocks: X and Y. Stock X can only have a return of 8% or 3% while Stock Y can only have a return of -5% or 9%. We randomly collected 215 simultaneous observations on X and Y and constructed the following 2 x 2 table: Total obs. X = 8% X= 3% Total obs. Y = -5% 25 43 68 Y = 9% 19 128 147 171 215 For example, in 25 of the 215 total observations, we observed that X = 8% and Y = -5% at the same time, etc. (a) Calculate the mean returns for stocks X and Y, respectively. (b) Calculate the variances of returns for stocks X and Y, respectively. (c) Calculate the covariance of returns between stocks X and Y. (d) Assume that the risk-free rate is 2% and short-selling is allowed, find the tangency portfolio weights for stocks X and Y. (e) Calculate the mean return and risk for your portfolio in part (d). 4. Suppose we have 2 risky stocks: X and Y. Stock X can only have a return of 8% or 3% while Stock Y can only have a return of -5% or 9%. We randomly collected 215 simultaneous observations on X and Y and constructed the following 2 x 2 table: Total obs. X = 8% X= 3% Total obs. Y = -5% 25 43 68 Y = 9% 19 128 147 171 215 For example, in 25 of the 215 total observations, we observed that X = 8% and Y = -5% at the same time, etc. (a) Calculate the mean returns for stocks X and Y, respectively. (b) Calculate the variances of returns for stocks X and Y, respectively. (c) Calculate the covariance of returns between stocks X and Y. (d) Assume that the risk-free rate is 2% and short-selling is allowed, find the tangency portfolio weights for stocks X and Y. (e) Calculate the mean return and risk for your portfolio in part (d)