A small stock that you are following has an alpha = 8% and a standard deviation of its regression residuals of 24.50%. The Sharpe ratio of the market index portfolio M is 0.45. According to the TreynorBlack Model,

a. by how much could this active investor improve his/her Sharpe ratio relative to investing only in the passive market index portfolio M? Please calculate the difference between the Sharpe Ratio for the optimal TreynorBlack portfolio and the market index portfolio M. Note that the Sharpe Ratio is usually expressed as a decimal.

b. what is the small active stocks information ratio? Please calculate the information ratio as a decimal not a percentage.