The following four bonds are available to you:

Bond A B C D

Price $99,100,102,105$Coupon $2\mathrm{.}5\%,4\%,6\mathrm{.}5\%,7\%$Modified Duration $0\mathrm{.}9$ years, $4\mathrm{.}6$ years, $4\mathrm{.}5$ years, $9\mathrm{.}9$ years

Dollar Duration $0\mathrm{.}89,4\mathrm{.}6,4\mathrm{.}59,10\mathrm{.}39$

Maturity $1\mathrm{.}1$years, $5\mathrm{.}4$ years, $5\mathrm{.}1$ years, $14\mathrm{.}5$ years $$Price Value of a Basis Point $0\mathrm{.}0089,0\mathrm{.}046,0\mathrm{.}0459,0\mathrm{.}1039$

a$)$ The yield curve is upward sloping. The short$-$term interest rates are expected to decrease while the long$-$term rates are expected to increase. You are allowed to short$-$sell. Which bond trading strategy would you apply to best exploit the shift in the yield curve described in this scenario? Illustrate how you would apply that strategy using what you believe are two most suitable bonds from the table above if you had $2$ M to invest. Explain your rationale and workings.

b$)$ Are any bonds from the table suitable for a coupon spread trade? Explain.

c$)$ Use any three bonds from the table suitable for the construction of $50/50$ duration butterfly trade. Construct this butterfly trade for a $1$M par value of the bond you decide to sell and

explain the assumptions used.

d$)$Interpret a beta coefficient of $0\mathrm{.}78$ in a regression$-$based butterfly trade and explain the purpose $$it serves.

e$)$Assume a negative butterfly shift in the upward sloping yield curve. What type of bond portfolio would be most beneficial to hold: bullet or barbell? Explain, illustrating this yield curve shift.