The data below corresponds to the historical performance of the Canadian bond market

and Canadian stock market.

Let $(w)$ and ${}^2(w)$ denote the mean and variance of my portfolio, assuming I invest

$100w\%$ of my wealth in the bond market $($I am not allowed to take short positions$).$

$($a$)$ Sketch $(w)$ and ${}^2(w).$

$($b$)$ Determine the volatility of the portfolio whose expected return is $6\%.$

$($c$)$ Plot the points $((w),(w))$ for $w=0,w=w^{**}$ and $w=1,$ where $w^{**}$ is the variance$-$

minimizing allocation to the bond market.

$($d$)$ Use your points from $($c$)$ to construct a rough sketch of the set of feasible risk$-$return

pairs $($i$.$e$.$ the parametric curve $\{((w),(w))$:$0w1\}).$

The data below corresponds to the historical performance of short$-$term and long$-$term

Canadian bonds.

$($a$)$ Which asset $(1$ or $2)$ corresponds to short$-$term bonds? Briefly explain your answer.

$($b$)$ What is the variance$-$minimizing allocation to short$-$term bonds?

$($c$)$ Why doesn't the minimum$-$variance portfolio hold any long$-$term bonds?

$($d$)$ Sketch $(w)$ and ${}^2(w).$

$($e$)$ Plot the points $((w),(w))$ for $w=0$ and $w=1.$

$($f$)$ Use your points from $($e$)$ to construct a rough sketch of the set of feasible risk$-$return

pairs $($i$.$e$.$ the parametric curve $\{((w),(w))$:$0w1\}.$