Bond Yield (Coupon)

Yield on a coupon bond

A coupon bond pays interest on a schedule, either semiannual or annual, and hands back the face value when it matures. The easiest number to compute is the current yield: current yield = annual coupon / current price. Say a bond has a R$ 1,000 face value and pays a 14% annual coupon, so R$ 140 a year. If it trades at R$ 950, the current yield comes to 14.74%. The catch is that this only looks at the cash income. It tells you nothing about whether you'll end up with more or less than you paid once the bond matures.

The fuller picture comes from yield to maturity (YTM), which is the internal rate of return that makes the present value of all the future cash flows (coupons plus principal) equal the price you pay today. Because it reaches all the way to maturity, it folds in the capital gain or loss. Buy a bond at a discount, below par, and its YTM sits above the current yield; buy it at a premium, above par, and the YTM comes out lower. Take a Tesouro Prefixado 2030 paying 14% per year with semiannual coupons. At par its YTM equals the coupon, 14%. At 95% of par the YTM climbs above 15%.

Practical applications

If you invest in coupon-paying fixed income, this is bread and butter: Tesouro Prefixado with semiannual coupons, IPCA+ with coupons, Brazilian corporate debentures, and international bonds such as Treasuries and corporate bonds. YTM lets you put papers side by side even when their prices, coupons and maturities differ. It also sits at the heart of portfolio management, since portfolio duration is a weighted average of each paper's duration and that duration depends on the YTM. Pension funds and insurers lean on YTM both to mark to market and to project the return on their actuarial liabilities.

FAQ

What is the difference between YTM and gross yield on Tesouro Direto? There isn't one, really. YTM is the rate that, applied to the purchase price, reproduces every future flow, and the gross rate the Tesouro Direto site shows you is exactly that YTM at the moment you buy.

Does YTM consider income tax? No, it is a gross rate. To land on the net yield, run Brazil's regressive table, which ranges from 22.5% down to 15% depending on how long you hold, against both the interest and the capital gain.

What happens to YTM if the Selic rate rises? Pre-fixed bond prices drop, which pushes up the YTM on papers offered in the secondary market. Whoever holds the bond eats a mark-to-market loss, while the next buyer walks away with a higher yield.