Risk Management puzzles, solved step by step

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  1. 031A floating rate note pays a coupon that resets every three months to the market rate, and it matures in 7 years. Roughly what is its interest rate duration?Duration and ratesWarm upTreasury and ALM

    Try it first

    Pick the duration before you reason it out.

    Show the worked solution

    About 0.25 years at most, and on average about an eighth of a year. Every coupon after the next one resets to the market rate, so a change in rates today is passed straight into future coupons and leaves their value unchanged. Only the next coupon is fixed, so the note behaves like a three-month bill: modified duration of about 0.25 just after a reset, falling towards zero before the next one.

    Why does maturity not drive a floater's rate risk?

    Think of renting a flat with the rent reset to the market every quarter. If rents jump tomorrow, your lease is not a bargain or a burden for more than a few months, because the next reset catches up. A bond loses value when rates rise only because its cash flows are fixed below the new market rate; a floater's cash flows are not fixed beyond the next reset. At each reset date the note is worth par again, provided the issuer's credit has not changed, so for rate purposes it is a claim to par plus one known coupon, three months away.

    Only the next coupon is locked in; everything after it resetsprincipalnext coupon: fixed today27 more coupons, each reset to the market rate0y1y2y3y4y5y6y7yrate risk ends here, at the next resetModified durationFloater, just after reset0.25 yearsFloater, quarter averageabout 0.12 years7-year fixed 8% bond5.32 yearsA 1 point rate rise costs the floater about 0.25 per 100 and the fixed bond about 5.32
    A 7-year quarterly floater has only its next coupon fixed, so its rate duration is about 0.25 years just after a reset, while a 7-year fixed 8% bond has a modified duration of about 5.32 years and loses about twenty times as much for a one point rise in rates.

    How do you check the number quickly?

    Right after a reset, the note is worth the present value of par plus one coupon, received in a quarter. That is a single cash flow a quarter away, so Macaulay duration is 0.25 years and modified duration is 0.25 divided by 1.02, about 0.25. A day before the next reset it is almost zero. Compare a 7-year fixed bond paying 8% quarterly at par: its modified duration is 5.32, so a one point rate rise costs it about 5.3 per 100 against about 0.25 for the floater.

    Now say where the 7 years still matter. The coupon is the market rate plus a fixed quoted marginThe fixed spread over the reference rate that a floating rate note pays, set at issue and unchanged for the life of the note.. If the issuer's credit worsens and investors demand a wider spread, that fixed margin is too low for all 28 remaining quarters, so the note's spread duration is close to a fixed bond's, several years. A treasury desk that files floaters under no rate risk and forgets spread risk has the right answer to the wrong question.

    Where candidates lose it

    The instinct is to answer 7 years because the note matures in 7 years, or about 5 because that is what a 7-year bond usually carries. Both confuse maturity with the length of time cash flows are fixed.

    The overcorrection is saying zero. Until the next reset one coupon is locked, and the credit spread is locked for the whole life. Give the rate answer, then name spread duration unprompted.

    What the interviewer asks next

    • What is the floater's spread duration, roughly, and why?
    • An inverse floater pays 16% minus the market rate. What is its duration?
    • How would you hedge a fixed-rate loan book funded with floating-rate deposits?