Mutual Fund Mastery puzzles, solved step by step

Puzzles
100
Traced to a firm
29
Topics
13
Hard
30
Topic
All topicsCompounding and time value9Statistics, correlation and diversification8Bond maths and duration10Performance measurement and returns8Costs and fee drag8Valuation riddles11Logic and numeracy brainteasers6Estimation and market sizing7Probability and expected value8NAV, units and fund mechanics7Risk, volatility and drawdown8Behavioural traps6Withdrawals and after-tax arithmetic4
Level
AnyWarm upCoreHard
Source
AnyReported at a firmStandard
Showing 1–2 of 2 · filtered from 100Clear filters
  1. 075A bond with a 7% annual coupon trades at 104. Is its yield to maturity above or below 7%, and what is its current yield?Bond maths and durationWarm upVanguardMalvern · 2023

    Try it first

    Which ordering is right for this bond?

    Show the worked solution

    The yield to maturity is below 7%, and the current yield is 6.73%. Current yield is the coupon over the price: 7 / 104 = 6.73%. The yield to maturity is lower still, because you pay 104 and get back only 100, so the Rs 4 premium is a loss spread over the bond's life. For an assumed five years left, the yield to maturity is about 6.05%.

    Why must the yield be below the coupon when the price is above 100?

    Pay Rs 104 for a gift voucher worth Rs 100 that also pays Rs 7 of cashback a year. The cashback is generous, but you have overpaid for the voucher by Rs 4. A bond priced above par returns less than its coupon, because the buyer pays more than the Rs 100 that comes back at maturity, and that premium is lost along the way. The coupon of 7% is set on the face value of 100 and never changes. The current yieldThe yearly coupon divided by the bond price today. It ignores any gain or loss as the price moves to face value at maturity. divides the same Rs 7 by what you actually pay: 7 / 104 = 6.73%.

    Above par, the yields sit below the coupon0%1%2%3%4%5%6%7%7.00%Coupon rate7 / 100 face6.73%Current yield7 / 104 price6.05%Yield to maturityadds the Rs 4 lossPrice pulls to parpar 100104 todayyr 0yr 1yr 2yr 3yr 4yr 5Rs 4 premium lost by maturity
    A 7% coupon bond bought at 104 has a current yield of 6.73% and, with five years left, a yield to maturity of 6.05%, because its price pulls down to 100 by maturity and the Rs 4 premium is lost.

    How far below 7% is the yield to maturity?

    That depends on how long the bond has to run, which the question does not say, so name an assumption. With five years left, the Rs 4 premium is lost at roughly Rs 0.80 a year. A quick estimate takes the coupon less that yearly loss, Rs 6.20, over the average of the purchase and redemption prices, 102: about 6.08%. The exact yield to maturityThe single discount rate that makes all remaining coupons and the final repayment worth exactly the price paid today. is 6.05%. The longer the bond, the thinner the yearly slice of the premium and the closer the yield to maturity sits to the current yield.

    The relationship
    104=∑t=157(1+y)t+100(1+y)5  ⇒  y≈6.05%104 = \sum_{t=1}^{5} \frac{7}{(1+y)^t} + \frac{100}{(1+y)^5} \;\Rightarrow\; y \approx 6.05\%
    104the price paid
    7the yearly coupon per 100 of face
    100the repayment at maturity
    ythe yield to maturity
    What it says in wordsThe yield to maturity counts the coupons and the loss of the premium, so it ends below both the coupon and the current yield.

    For a debt fund this ordering is everyday arithmetic: when rates fall, older high-coupon bonds trade above par, and the fund's quoted portfolio yield sits below the coupons it receives. The limit of yield to maturity: it assumes the bond is held to maturity, never defaults and that coupons are reinvested at the same yield, none of which is guaranteed. A bond callable before maturity at par makes the premium an even bigger risk.

    Where candidates lose it

    The trap is quoting 7% as the yield because that is the coupon. The coupon is fixed on the face value; the yield depends on the price you pay, and above par it is lower.

    The second miss is stopping at the current yield. Name the order, coupon above current yield above yield to maturity, and give the reason for the last step: the premium is lost by maturity.

    What the interviewer asks next

    • The same bond trades at 96. Put the coupon, current yield and yield to maturity in order.
    • With 20 years left instead of 5, is the yield to maturity closer to or further from the current yield?
    • Why do debt funds holding many premium bonds report a portfolio yield below their average coupon?

    Asked at Vanguard, Investments, Malvern, 2023 (Wall Street Oasis): Questions asked ranged from resume stuff, global macro/current news stuff, and simple bond math since I expressed interest in FICC.

  2. 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

    Try it first

    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?