What is YTM, Really?

Coupon rate tells you what the issuer pays on face value. YTM tells you what you actually earn at the price you pay today. They are the same number only when you buy at par. This article explains the difference, the math behind YTM, its built-in assumptions, and where those assumptions cause your actual return to diverge from the stated yield.

Why coupon rate alone is not enough

Consider a bond with a 7% coupon on ₹100 face value. If you buy it at ₹100, you earn 7% per year — straightforward. But bond prices move in the secondary market. If you buy the same bond at ₹95, you still receive ₹7 per year in coupon, but you also receive ₹100 at maturity. You paid ₹95 and get back ₹100 — there is a ₹5 capital gain embedded in the purchase. Your actual annualised return is higher than 7%.

Conversely, if you pay ₹105 for the same bond, you paid a premium. You still receive ₹7 per year, but at maturity you only get back ₹100 — a ₹5 capital loss. Your actual return is below 7%.

YTM is the single number that captures all of this: coupon payments, face value at maturity, and the difference between the price you paid and par.

The YTM equation

YTM is defined as the discount rate r that makes the present value of all future cashflows equal to the bond’s current dirty price (clean price plus accrued interest).

For a bond paying annual coupons, with n periods remaining:

Dirty Price = C/(1+r) + C/(1+r)² + ... + C/(1+r)ⁿ + FV/(1+r)ⁿ

Where C is the coupon payment per period and FV is the face value. There is no closed-form algebraic solution for r — it must be solved numerically, which is what the YTM calculator does (using the Brent method under the hood).

For a concrete example: a 7% annual coupon bond with ₹100 face value, 5 years to maturity, trading at ₹95.00. YTM solves to approximately 8.15% — higher than the 7% coupon because you bought at a discount.

Clean price vs. dirty price

Bonds are quoted in the market at their clean price — the price excluding accrued interest. But you pay the dirty price, which adds the interest that has built up since the last coupon payment date.

If the bond above paid its last coupon three months ago (half of a six-month coupon period), you owe the seller 3 months of accrued interest: ₹7 × 0.5 (semi-annual rate) × (3/6) = ₹1.75. You pay ₹95 + ₹1.75 = ₹96.75 as the dirty price, and YTM is calculated on the dirty price basis.

The day-count convention determines exactly how accrued interest is calculated. Indian G-Secs use the 30/360 convention per FIMMDA standards; most corporate bonds use Actual/365. The difference is small but material for precise YTM calculations, which is why the calculator asks you to specify it.

The three assumptions baked into YTM

YTM is theoretically correct under three assumptions that are never fully met in practice:

1. You hold to maturity. If you sell before maturity, your actual return depends on the price you receive. If rates have risen since you bought, the price will be lower — you take a capital loss that erodes your return below YTM. If rates fell, you gain. YTM only equals your actual return if you hold every day until redemption.

2. All coupons are reinvested at the same YTM. This is the reinvestment assumption, and it is the most commonly violated. When you receive a coupon payment, you either spend it or reinvest it somewhere. If the rate available for reinvestment is lower than YTM, your compounded return falls short of YTM. This matters more for longer-dated bonds (more coupon payments to reinvest) and for high-coupon bonds (larger coupons to reinvest).

3. The issuer pays every coupon and the full face value on schedule. YTM assumes zero credit risk. A bond rated A+ has a lower probability of default than one rated BB, but neither is zero. The YTM on a lower-rated bond is higher partly because the market is pricing in a credit risk premium — the extra yield compensates for expected losses. If the issuer defaults, your actual return is not YTM.

Related yield measures

Current yield is simply Annual coupon / Clean price. On a ₹95 bond with ₹7 coupon: 7/95 = 7.37%. It ignores the pull-to-par effect (the capital gain or loss from discount or premium) and is only useful as a quick approximation of cash income relative to price.

Yield to call (YTC) applies to callable bonds — bonds where the issuer has the right to repay early at a specified call price and call date. If a bond is trading above par and the issuer can call it in two years at ₹102, the relevant yield for pricing is the yield to the call date, not to final maturity. Always check whether a bond is callable before using plain YTM.

Yield to worst (YTW) is the lowest of YTM, all yield-to-call calculations across each call date, and yield to put. It is the minimum yield you can expect if the issuer exercises every option in their favour. For callable or puttable bonds, YTW is a more conservative and often more relevant figure than YTM.

Duration: how YTM connects to price risk

Duration is a measure of how sensitive a bond’s price is to changes in yield. The higher the duration, the more the price moves for a given yield change.

Macaulay duration is the weighted average time (in years) until you receive the bond’s cashflows. A 10-year zero-coupon bond has a Macaulay duration of 10 years. A 10-year 7% coupon bond has a Macaulay duration of about 7.5 years, because some of the return comes in earlier as coupon payments.

Modified duration is Macaulay duration divided by (1 + YTM/frequency). It directly approximates the percentage price change for a 1% (100 bps) change in yield: if modified duration is 6, a 1% yield rise causes approximately a 6% price fall.

DV01 (dollar value of 1 basis point, or rupee value in Indian context) is the rupee price change for a 1 basis point (0.01%) yield change. On a ₹100 face value bond with modified duration 6 trading at ₹95: DV01 = 95 × 6 × 0.0001 = ₹0.057. For a ₹10 lakh position, a 1 bps yield move costs or earns ₹5,700. This is what traders use to size and hedge positions.

The practical takeaway: if you believe rates are more likely to rise than fall, prefer shorter-duration bonds. If you think rates will fall, longer-duration bonds benefit more from the price appreciation.

Post-tax yield: what you actually keep

YTM is a pre-tax number. The after-tax return depends on your tax bracket and on how the bond’s gains are taxed.

Coupon income from corporate bonds and NCDs is taxed as income at your slab rate (currently up to 30% plus surcharge for individuals in the highest bracket). Capital gains from selling a listed bond before maturity are treated as short-term gains (held <12 months) or long-term gains (held ≥12 months). G-Sec capital gains may have different treatment; verify with a chartered accountant.

A rough post-tax yield for coupon income: Post-tax yield = YTM × (1 − tax rate). At a 30% slab, a 9% YTM bond has a post-tax coupon yield of about 6.3%. The YTM calculator applies this adjustment and shows both pre-tax and post-tax figures.

Related reading: XIRR vs YTM: why your bond return doesn't match the quoted yield · YTM calculator →

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