Problem $11.$ For $1871-2022,$ consider the stock and bond annual inflation$-$adjusted returns: $S$ and $B.$ They have

standard deviations $16\mathrm{.}8\%$ and $5\mathrm{.}9\%,$ with correlation is $18\mathrm{.}5\%.$ Consider the portfolio of $95\%$ bonds and $5\%$

stocks. This portfolio has returns $Q=0\mathrm{.}95B+0\mathrm{.}05S.$ Find the standard deviation of $Q.($This is less than the

standard deviation of $B.$ We see that a risk$-$averse investor who wants ONLY to minimize variance still needs to

include a bit of stocks in the portfolio. This is counterintuitive, since stocks are riskier than bonds. However,

these assets are only weakly correlated.$)$