You manage a portfolio consisting of the following bonds:

Bond

Face Value Price Coupon Rate Time till Maturity

A $$20$ million $1024\mathrm{.}00\%2$ yrs

B $$50$ million $98\mathrm{.}252\mathrm{.}00\%8$ years

C $$45$ million $103\mathrm{.}54\mathrm{.}00\%5$ years

D $$35$ million $101\mathrm{.}53\mathrm{.}50\%7$ years

E $$45$ million $96\mathrm{.}32\mathrm{.}50\%14$ years

Bond

YTM Market Value Duration Modified Duration

A

B

C

D

E

Portfolio xxxxxxxxxxxxxxxxx

a$.$ Calculate the Yield to Maturity for each bond

b$.$ Calculate the Market Value for each bond $($and the portfolio$)$

c$.$ Calculate the duration and modified duration of each bone $($and the portfolio$)$

d$.$ Calculate the convexity measure for Bond A

e$.$ Based solely on your answer to the modified duration of your portfolio you calculated above, what do you expect to be the percentage change in the market value of your portfolio if interest rates go up by $2$ basis points for all maturities?

f$.$ What will be the new market value of your portfolio based on your answer above?

g$.$ If bonds D and E are assets and bonds A$,$ B$,$ and C are liabilities, what is the market value of your assets and liabilities?

h$.$ What is now the duration of your assets and the duration of your liabilities $($based on $($g$))?$

i$.$ What is your duration gap $($also based on $($g$))?$