Debt Capital Markets puzzles, solved step by step

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  1. 063Which carries more interest rate risk: a 10-year floating rate note that resets every quarter, bought just after a reset, or a 2-year bond with a fixed 7% annual coupon yielding 7%? Estimate each one's duration.Duration and convexityWarm upFixed income asset management

    Try it first

    Which has the longer interest rate duration?

    Show the worked solution

    The 2-year fixed bond carries far more rate risk: a duration of about 1.9 years against about 0.25 for the floater. The floater's coupon resets to the market every quarter, so a rate move can only hurt it until the next reset, three months away. The fixed bond is locked at 7% for two years, and its Macaulay duration is 1.93 years. A 1 point rise in rates costs the floater about 0.25 points and the fixed bond about 1.78.

    Why is a 10-year floater so short on rate risk?

    Think of two landlords. One has let a flat for two years at a fixed rent; the other has a ten-year lease whose rent is reset to the market every three months. If market rents jump, the first is stuck for two years and the second catches up within a quarter. A floater's coupon resets to the market rate on every reset date, so its value can only drift from par for the few months until the next reset, whatever its final maturity. Just after a reset, that is about a quarter of a year.

    Rate risk lasts only as long as the coupon is locked10-year floater, just resetabout 0.25 years2-year fixed bond, 7% coupon1.93 yearsHow long each coupon is locked, both drawn on the same time scaleFloater: matures in 10 years10 yrsFixed: matures in 2 years2 yrslocked 3 months, then resetslocked for the whole 2 yearsA 1 point rise costs the floater about 0.25 and the fixed bond about 1.78 per Rs 100
    The 10-year floater's coupon is locked for only three months, a rate duration of about 0.25 years, while the 2-year fixed bond's coupon is locked for both years, a duration of 1.93 years, so the shorter bond carries about 8 times the rate risk.
    The relationship
    Dfix=1×71.07+2×1071.072100=1.93DFRN≈0.25D_{fix} = \frac{1 \times \tfrac{7}{1.07} + 2 \times \tfrac{107}{1.07^{2}}}{100} = 1.93 \qquad D_{FRN} \approx 0.25
    D_fixMacaulay duration of the fixed bond, its value-weighted average time to the cash flows
    7, 107the fixed bond's two annual cash flows per Rs 100
    D_FRNthe floater's rate duration, about the time to its next reset
    What it says in wordsA fixed bond's duration runs to its cash flows; a floater's runs only to its next reset.

    What does each lose if rates rise one point?

    Reprice both at a rate 1 point higher: the fixed bond falls from 100 to 98.22, a loss of 1.78, while the floater loses only 0.25, because it earns the old coupon for one quarter and then resets. The fixed bond carries about 8 times the rate risk of a note five times its length. This is why a bank funding itself with three-month deposits is comfortable holding floaters: the asset and the liability reprice together.

    Keep the other risk in view. The floater's short rate duration says nothing about credit: its spread duration runs to maturity, about 7 years here, so a widening in the issuer's spread hits it far harder than it hits the 2-year bond. Name both numbers if the interviewer pushes, because the claim that floaters are low risk is only half true. The limit: this assumes a flat 7% curve and an issuer whose credit does not change.

    Where candidates lose it

    The trap is equating maturity with rate risk. A 10-year floater sounds riskier than a 2-year bond, but its coupon catches up with the market every quarter, so a rate move can hurt it for a few months at most.

    The second loss is stopping there and calling the floater safe. It has almost no rate duration but a long spread duration; say both, or the follow-up on credit will catch you.

    What the interviewer asks next

    • Halfway between two resets, what is the floater's rate duration?
    • A bank funds itself with 3-month deposits. Which of the two bonds matches its funding better, and why?
    • Roughly what is the spread duration of the 10-year floater, and what does a 50 basis point widening cost it?