Mutual Fund Mastery puzzles, solved step by step

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  1. 096The RBI cuts the repo rate by 25 basis points and bond yields fall by the same amount. Roughly how much does a gilt fund with a modified duration of 8 gain, and a liquid fund with a modified duration of 0.1?Bond maths and durationWarm upFixed income desksIndian AMCs

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    Roughly how much does the gilt fund's NAV rise?

    Show the worked solution

    About 2.0% for the gilt fund and about 0.025% for the liquid fund. A bond fund's NAV moves by roughly minus its modified duration times the change in yield. With yields down 0.25 points, 8 x 0.25% is 2.0% and 0.1 x 0.25% is 0.025%, about 0.03%. The same rate move hits the gilt fund 80 times harder, which is the whole difference between the two products.

    Why does a fall in yields raise bond prices?

    Suppose you own a bond paying 7% and new bonds now pay only 6.75%. Anyone wanting 7% must buy yours, so they pay more for it, and they keep paying more until its yield matches the market's. Bond prices and yields move in opposite directions, and modified duration tells you by how much: roughly the percentage price change for each percentage point move in yield. A fund holding bonds with an average modified duration of 8 rises about 8% for a full point fall in yields, and about 2% for a quarter point.

    The same 0.25% fall in yields, three different NAV movesGilt fundmodified duration 8+2.00%Rs 20,000 on Rs 10 lakhShort duration fundmodified duration 2+0.50%Rs 5,000 on Rs 10 lakhLiquid fundmodified duration 0.1+0.025%Rs 250 on Rs 10 lakhNAV change is about minus duration x change in yield: 8 x 0.25% = 2.0%, 0.1 x 0.25% = 0.025%
    A 0.25 point fall in yields lifts a gilt fund with modified duration 8 by about 2.0%, a short duration fund with duration 2 by 0.5%, and a liquid fund with duration 0.1 by only 0.025%, because the price change scales with duration.
    The relationship
    ΔPP≈−Dmod×Δy=−8×(−0.25%)=+2.0%\frac{\Delta P}{P} \approx -D_{mod} \times \Delta y = -8 \times (-0.25\%) = +2.0\%
    \Delta P / Pthe percentage change in the fund's NAV
    D_{mod}modified duration, 8 for the gilt fund
    \Delta ythe change in yield, minus 0.25 points
    What it says in wordsMultiply the yield change by the duration and flip the sign to get the approximate price change.

    What does this approximation leave out?

    Two things, one small and one large. The small one is convexity: the price-yield curve bends, so for a fall in yields the gain is a little more than duration says. With an assumed convexity of 80, it adds only about 0.025% for a quarter-point move. The large one is the assumption that bond yields fall by exactly the cut: the repo rate is an overnight rate, and longer yields move on expectations, so if the market had already priced in the cut, long yields may barely move on the day. Gilt funds often gain before a widely expected cut and do little when it arrives.

    In rupees, on Rs 10 lakh the gilt fund gains about Rs 20,000 and the liquid fund about Rs 250. That symmetry is the point to make to a client: the gilt fund that gains Rs 20,000 on a quarter-point fall loses about the same if yields rise a quarter point instead. Duration is the dial for how much rate risk the investor is buying, in either direction.

    Where candidates lose it

    The common slip is answering 0.25%, the size of the cut, as if bond prices moved one for one with rates. They move by the yield change times the duration, so a duration-8 fund moves eight times the yield change.

    The quieter loss is ignoring which yields moved. The question assumes all yields fall by the full 25 basis points; say that this is an assumption and that long yields often move ahead of the actual cut.

    What the interviewer asks next

    • Yields rise 0.5 points instead. What happens to each fund?
    • Why might a gilt fund fall on the day the RBI cuts rates?
    • Which of the three funds would you expect to have the largest convexity, and why?