Mutual Fund Mastery puzzles, solved step by step

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  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.