A small stock that you are following has an alpha $=8\%$ and a standard deviation of its regression residuals of $24\mathrm{.}50\%.$ The Sharpe ratio of the market index portfolio M is $0\mathrm{.}45.$ According to the Treynor$$Black Model, by how much could this active investor improve his$/$her Sharpe ratio relative to investing only in the passive market index portfolio M$?$ Please calculate the difference between the Sharpe Ratio for the optimal Treynor$$Black portfolio and the market index portfolio M$.$ Note that the Sharpe Ratio is usually expressed as a decimal. Enter your answer rounded to two decimal places. For example, if your answer is $12\mathrm{.}345$ then enter as $12\mathrm{.}35$ in the answer box.