a$.$ Firm XYZ is required to make a $$10$M payment in $2$ years and another $$10$M payment in $4$

years. The yield curve is flat at $10\%$ with semi$-$annual compounding. Firm XYZ wants to form

a portfolio using a $1-$year floating rate note $($FRN$)$ and a $5-$year U$.$S$.$ strip to fund the

payments.

Required:

i$.$ What is the present value of the liabilities?

ii$.$ What is the $($modified$)$ duration of the liabilities? iii. What are the $($modified$)$ durations of the assets?

iv$.$ How much of each bond must the portfolio contain for it to still be able to fund the

payments after a small shift in the yield curve?

b$.$ The current yield curve for default$-$free zero$-$coupon bonds are as follows:

Maturity $($Years$)$ YTM $(\%)$

$15\%$

$26\%$

$37\%$

$48\%$

Required:

i$.$ What are the implied $1-$year forward rates?

ii$.$ Assume that the pure expectations hypothesis of the term structure is correct and that

the face value of all bonds is $$1,000.$ If market expectations are accurate, what will be

the pure yield curve next year?