FIXED INCOME FUNDAMENTALS

winter-spring 2019

Problem Set VIII

Corporates

IThe 5-year Treasury note yields 3%, the 10-year yields 3.75%.

A 5-year note from ABC company with a 4% semi-annual coupon trades at "120 over."What is its price?

IIA ten-year bond from company ABC has a 5% semi-annual coupon and is priced art par.What is its spread?

What is the percentage change in ABC's price if the 10-yr Treasury yield increases by 1% (with the spreadunchanged)?

What is the percentage change in its price if its spread increases by 1% (with the Treasury yield unchanged)?

IIIAssume the 5-year T-note in question I is semi-annual and at par.What is the hedge ratio of that note forthe 5-yr ABC note?

You sell short that number of T-notes to hedge one 5-yr ABC you own.Then the Treasury yield rises by 1%.What is your net gain or loss?

What if, instead, the ABC spread widens by 1%?What does this tell you about what a "Treasury hedge" does and what it cannot do?

IVAssume the probability of default for ABC is 10%.What does that imply about the 5-yr ABC note's recovery value (face value 100) in I?

VConsider a 1-year Treasury note (a full year, so no day-counts necessary, and annual compounding).The market discounts its single cash flow of 100 at 4%.What is the ROR if held for the full year?

Now consider a 1-year corporate note (same assumptions).The market believes there is a 10% probability of the company defaulting before maturity and, if it does so, a recovery rate of 65%.Investors discount the note's expected cash flow at 5%.What is its price?(Hint: use the probabilities of default and no default to calculate the weighted average cash flow and discount that.)

What is the ROR if held for the full year and the company does not default?

What is the ROR if held for the full year and the company defaults (use the recovery value)?

Why will the ROR never equal the original yield (discount rate), unlike the Treasury?!!