Suppose you have two stocks X and Y$.$ Stock X has expected return of $15\%$ and

standard deviation of $25\%,$ while stock Y has expected return of $8\%$ and standard

deviation of $10\%.$ Correlation coefficient between the two stocks is $0\mathrm{.}4$ and the risk$-$free rate is $6\%.$

$1.$ what are the weights of the two stocks in the optimal risky portfolio?

$2.$ what are the expected return, standard deviation and reward$-$to$-$variability

ratio of the above optimal risky portfolio?

$3.$ what would be the standard deviation of the portfolio with expected return of

$8\mathrm{.}5\%?$

$4.$ assuming no risk$-$free rate, what would be the standard deviation of the

portfolio with expected return of $8\mathrm{.}5\%?$

Notice that without the risk$-$free rate, the portfolio with expected return of $8\mathrm{.}5\%$

would have by $\_\_\_\_\_\_$ percentage points $\_\_\_\_\_\_\_$ standard deviation than

portfolio with the same expected return when the risk$-$free rate is available.