Q$3.$ Portfolio Risk$-$Returns $(20$ points$)$ i$.$ stock has mean of $10\%$ and stdev of $20\%$; ii bond has mean of $8\%$ and stdev of $16\%$; iii. Risk free rate for cash lending and borrowing is at $4\%.$ a$.$ What is the mean and stdev of a portfolio of that is $60\%$ in stock and $40\%$ in bond if correlation between stock and bond is $+0\mathrm{.}4(4$ points$)?$ b$.$ What is the mean and stdev of a portfolio of that is $60\%$ in stock and $40\%$ in bond if correlation between stock and bond is $-0\mathrm{.}4(4$ points$)?$ c$.$ How much can you leverage up a portfolio in case $($b$)$ to match the stdev of case$($a$)?$ What is the mean return after leverage? $(4$points$)$

d$.$ What is the mean and stdev of a fully invested yet unleveraged portfolio in stock and bond, that assign weights based on inverse of STDEV risk $($assume case $($b$)$ negative correlation$)(4$ points$)?$