$6.$ Suppose you have $\backslash (\backslash$$ $100\backslash )$ million to invest in the three US treasuries in the previous problem. Your investment horizon is six months. You can form a bullet portfolio of the intermediate treasury B$,$ or you can form a barbell portfolio of treasury A and C$.$ a$)$ If you decide to have a barbell portfolio, what percentages should you allocate to A and C$,$ such that the modified duration of the barbell portfolio is the same as the bullet portfolio? b$)$ What is the convexity of the barbell portfolio you formed in part a$)?$ c$)$ After six months, you need to liquidate your portfolio. What would be your coupon payments of the barbell portfolio? Bullet portfolio? d$)$ If$,$ after six months, the yield curve remains unchanged, which portfolio would give you a higher holding period return and why? e$)$ If$,$ after six months, the yield curve has a parallel increase of $\backslash (0\mathrm{.}5\backslash \%\backslash )$ across all maturity, which portfolio would give you a higher holding period return and why? f$)$ If$,$ after six months, the yield curve flattens to the following: YTM of $5-$year T$-$note is $\backslash (7\mathrm{.}56\backslash \%\backslash ),$ YTM of $\backslash (10-\backslash )$ Year T$-$note is $\backslash (7\mathrm{.}80\backslash \%\backslash )$ and YTM of $20-$year Tbond is $\backslash (8\mathrm{.}10\backslash \%\backslash ).$ Which portfolio would give you a higher holding period return? g$)$ If$,$ after six months, the yield curve steepens to the following: YTM of $5-$year T$-$note is $\backslash (7\mathrm{.}26\backslash \%\backslash ),$ YTM of $10-$year T$-$note is $\backslash (7\mathrm{.}80\backslash \%\backslash )$ and YTM of $20$ T$-$bond is $\backslash (8\mathrm{.}5\backslash \%\backslash ).$ Which strategy would give you a higher holding period return?