Yield to Maturity
Also written YTM · Yield to Maturity (YTM) · Redemption yield · Yield to maturity (YTM)
The single discount rate at which a bond's future coupons and redemption amount add up to exactly its market price today — the return you actually earn if you hold it to maturity.
In plain language
A bond promises you a fixed set of payments: some coupons, then your money back. You do not have to pay face value to get them — in the secondary market you pay whatever the bond happens to cost that day.
So the real question is not "what is the coupon?" but "what return do I earn on the price I am actually paying?" That is Yield to Maturity.
YTM is the one interest rate which, used to discount every future rupee the bond will pay, gives back exactly today's market price. Nothing more mysterious than that. It is the bond market's equivalent of the effective rate on a fixed deposit, and when a dealer quotes "7.18 per cent" for a government security, YTM is what is being quoted.
How it works
The workbook builds it in four steps: list the coupon payments, add the redemption amount at maturity, discount each of those inflows at the market yield, and add them up. That gives the price from a known yield.
YTM runs the same machine backwards. The price is the number you can see on the screen; the yield is the unknown. There is no algebra that isolates it — you have to try a rate, see whether the resulting price is too high or too low, and close in. A spreadsheet does this in a millisecond; in the exam you either interpolate between two trial rates or use the approximation formula below.
The consequence to carry away is the one Chapter 2 hammers: price and yield move in opposite directions. Raise the discount rate and every future rupee is worth less today, so the price falls. A 10 per cent bond discounted at 8 per cent is worth Rs 107.98; discount the identical cash flows at 12 per cent and it is worth well under par.
The formula
YTM is the rate y that solves:
Price = C/(1+y)^1 + C/(1+y)^2 + ... + (C + Face value)/(1+y)^n
where C is the coupon in rupees and n the years to maturity. Solved by trial and error.
The examinable shortcut, good to within a few basis points:
Approximate YTM = [ C + (Face value − Price) ÷ n ]
÷ [ (Face value + Price) ÷ 2 ]
A worked example
A corporate bond: face value Rs 100, coupon 9 per cent paid annually, 3 years left to maturity, trading at Rs 95.
You receive Rs 9, Rs 9, and Rs 109. Find the rate that prices those at Rs 95.
Try 11 per cent:
| Year | Cash flow (Rs) | Factor 1/(1.11)^n | PV (Rs) |
|---|---|---|---|
| 1 | 9 | 0.9009 | 8.11 |
| 2 | 9 | 0.8116 | 7.30 |
| 3 | 109 | 0.7312 | 79.70 |
| Total | 95.11 |
Rs 95.11 is a shade above Rs 95, so the true yield is a shade above 11 per cent.
Try 12 per cent: 8.04 + 7.17 + 77.58 = Rs 92.79. Now we have overshot.
Interpolating between the two: (95.11 − 95.00) ÷ (95.11 − 92.79) = 0.05, so YTM ≈ 11.05 per cent. Check it: discounting at 11.05 per cent gives 8.10 + 7.30 + 79.59 = Rs 95.00. Exact.
The approximation formula gets you close without the table: [9 + (100 − 95) ÷ 3] ÷ [(100 + 95) ÷ 2] = 10.67 ÷ 97.5 = 10.94 per cent.
Now line the three measures up, because the ordering is itself an exam answer:
| Measure | Value |
|---|---|
| Coupon rate | 9.00% |
| Current yield (9 ÷ 95) | 9.47% |
| Yield to Maturity | 11.05% |
The bond is bought at a discount to face value, so YTM > current yield > coupon. Buy the same bond at a premium — say Rs 104 — and the order reverses exactly.
Why NISM asks about it
Chapter 2 (Securities: Types, Features and Concepts of Asset Allocation and Investing) introduces bond valuation, then "Yield and Price", "Current Yield" and "Yield to Maturity (YTM)" in sequence, and notes that yield quotations in the debt market usually refer to YTM. Chapter 2's own sample questions test the inverse relationship directly — "interest rates in the market have increased subsequently, this bond is likely to quote..." with "at a price below face value" as the answer. Expect the conceptual inverse-relationship item for certain, the coupon-versus-yield ordering very often, and occasionally a short discounting table to total.
Common exam traps
- Coupon is not yield. The coupon is fixed in rupees the day the bond is issued and never changes. The yield changes every time the price changes. The workbook is explicit that the coupon "merely helps in computing the cash flows".
- Bought below face value → yield above coupon. Bought above face value → yield below coupon. Candidates reverse this under time pressure. Sanity-check it: paying less for the same cash flows must mean earning more.
- YTM assumes you hold to maturity and that every coupon is reinvested at the YTM itself. Sell early, or reinvest coupons in a savings account, and your realised return will not be the YTM.
- YTM is not a promise for a corporate bond. It is the return if the issuer pays. That is why corporate bonds yield more than government bonds of the same maturity — the gap is the credit spread, and it widens in a recession.
- Current yield and YTM are different questions. Current yield ignores the capital gain or loss you book at redemption; YTM includes it. They only coincide when the bond trades exactly at par.
Where this is taught
- Series IV · Chapter 1: Introduction to Interest Rate, Interest Rate Instruments and Fixed Income Marketsintroduced here
- Series XXI-B · Chapter 4: Investing in Fixed Income Securitiesintroduced here
- Series II-A · Chapter 3: Characteristics of Debt Securitiesintroduced here
- Series II-B · Chapter 3: Characteristics of Debt Securitiesintroduced here
- Series XIX-A · Chapter 6: Risk and Return - Investor and Fund Perspectiveintroduced here
- Series XV · Chapter 3: Terminology in Equity and Debt Marketsintroduced here
- Series X-B · Chapter 10: Taxation of Debt Productsintroduced here
- Series V-D · Chapter 18: Introduction to Interest Rate, Interest Rate Instruments and Fixed Income Marketsintroduced here
- Series XIX-C · Chapter 9: Fee Structure and Fund Performanceintroduced here
- Series XXI-A · Chapter 4: Investing in Fixed Income Securitiesintroduced here
- Series XIX-D · Chapter 7: Fund Performance and Benchmarking of AIFsintroduced here
- Series X-A · Chapter 9: Investing in Fixed Income Securitiesintroduced here
- Series XII · Chapter 2: Securities: Types, Features and Concepts of Asset Allocation and Investingintroduced here
Related terms
- Current yieldA bond's annual coupon in rupees divided by its current market price — the cash income the bond throws off this year, ignoring any gain or loss at redemption.
- Face valueThe denomination a company's capital is divided into and carried in its books — fixed, printed on the certificate, and the base on which dividend percentages and stock splits are computed.
- Zero coupon bondA bond that pays no coupons: it is issued below face value and repays the face value at maturity, so its duration equals its maturity.
- Credit spreadThe extra yield a non-government borrower must pay over a government security of the same tenor — the market price of credit risk, quoted as an add-on over the risk-free rate.
- Coupon rateThe rate of interest a bond pays, applied to its face value and never to its market price — which is why the coupon tells you the cash flow but not the return.
- Volume Weighted Average YieldThe average yield of a debt security's trades, weighted by traded volume. Category III AIFs value T-bills and G-Secs on the VWAY of the last hour's trades, and other debt on the whole day's trades.
- Bond Equivalent YieldThe annualised simple-interest return on a money market instrument, computed on price and a 365-day year, so instruments of different maturities can be compared on one basis.
- Price Value of a Basis PointThe rupee change in a bond's price for a one basis point change in its yield — the unit in which a fixed income desk actually measures and hedges interest rate risk.
- ConvexityThe curvature of the price-yield relationship — the correction duration misses, because duration is a straight line and the true relationship bends.
- Effective interest rateThe rate actually earned over a year once compounding within the year is counted — always at or above the quoted nominal rate, and equal to it only when interest is paid once a year.
- Spot rateThe true return on money invested today for one stated term with no interim cash flow — read straight off a zero-coupon instrument, and the only rate a cash flow should be discounted at.
- Term structure of interest ratesInterest rate plotted against term — one curve per credit quality, with the risk-free curve as the base and every other borrower quoted as a spread over it.
- Real interest rateThe nominal rate adjusted for inflation — what the lender actually gains in purchasing power, and a number that turns negative whenever inflation runs above the coupon.
- Pull to parThe movement of a bond's price toward its face value as maturity approaches — premium bonds drift down to par, discount bonds drift up to par, and at maturity every bond is worth face value.
- Coupon effectThe fact that two bonds with the same issuer and maturity but different coupons show different yields to maturity even when both are priced correctly off the same zero curve — why YTM cannot judge mispricing.
- Yield to CallThe annualised return on a callable bond if the issuer redeems it at the first call date for the call price — YTM with the call price and call date substituted.
- Roll downAn active fixed income strategy that profits from the passage of time: on an upward-sloping yield curve a bond's remaining maturity shortens, its yield falls, and its price rises.
- Interest rate riskThe risk that an investor in a debt instrument loses return because rates rise — existing instruments carrying the old, lower coupon fall in value until their yield matches the new market rate.
- Term PremiumThe extra return investors demand for lending long rather than short, because a longer horizon means more uncertainty about future cash flows than money market paper of one year or less.
- Redemption valueWhat the issuer pays at maturity other than the coupon. Above face value the bond is redeemed at a premium, below it at a discount, and equal to it at par.
- Modified DurationMacaulay's duration divided by (1 + yield) — the percentage by which a bond's price moves for a one percentage point change in interest rates, and so the standard measure of interest rate risk.
- Holding period returnThe total of coupons, income earned on reinvesting them and any capital gain, expressed as a percentage of the purchase price — a crude return for the period actually held, with no compounding in it.
- Reinvestment riskThe risk that the coupons or other intermediate cash flows from an investment have to be put back to work at a lower rate than the original investment earned, pulling the total return below the promised yield.
- Equity Linked DebentureA debt instrument whose interest is tied to the return on an equity index or basket — the issuer parks most of the principal in bonds to protect capital and spends the rest on options to buy the equity upside.
- Call riskThe risk that a bond is called — redeemed by the issuer before maturity. Most prevalent when interest rates fall, and it usually goes hand in hand with reinvestment risk.
- Realised YieldThe annualised, compounding return earned on a bond sold before maturity, factoring in coupons, the interest earned reinvesting them, and the sale price — sharper than holding period return.
- Credit ratingAn opinion on how likely a borrower is to service an instrument on time, reduced to a symbol by a SEBI-registered rating agency — and reviewed continuously, not fixed for the life of the bond.
- Floating rate bondA bond whose coupon is not fixed but reset at intervals against a benchmark rate plus a stated mark-up — so the interest paid moves with market rates over the life of the bond.
- Macaulay durationThe weighted average time, in years, to receive a bond's cash flows, each weighted by the present value of that cash flow — the bond's effective payback period.
- Clean priceThe quoted price of a coupon bond, excluding interest accrued since the last coupon date. Bonds trade at the clean price and settle at the dirty price, which adds accrued interest.
- Market Linked DebentureA debenture whose return is linked to an underlying index or security rather than being a fixed coupon; since Section 50AA its gains are short-term capital gains taxed at slab, whatever the holding period.
- Present Value Annuity FactorThe number that converts a level stream of equal payments for n periods into its present value at rate r: PVA(n, r) = (1 − (1 + r)^−n) / r. Used with the PV factor to value bonds.
- Fixed Maturity PlanA close-ended debt scheme whose portfolio maturity is aligned to the scheme's own maturity date, so the investor who stays to the end has a reasonably visible outcome — though never a guaranteed one.
- Required Rate of ReturnThe minimum return an investor expects before committing money: the nominal risk-free rate plus a risk premium. It is not a guaranteed, forecast or realised return.
- Fixed income securityA debt instrument under which the issuer promises a fixed coupon at regular intervals and repayment of the face value at maturity — government bonds, corporate bonds, debentures and T-bills.
- Day count conventionThe rule for counting days in a holding period to calculate accrued interest. Indian bonds use 30/360; the Indian money market, including T-bills, uses actual/365.
- Intrinsic value of a bondThe sum of the present values of all a bond's future cash flows, discounted at the investor's required rate of return. Buy if it exceeds the market price; sell if it is below.
- Discount bondA bond whose market price sits below its par value because the prevailing market interest rate is higher than its coupon — a market-price condition of an ordinary bond, not a distinct bond type.
- Premium bondA bond whose market price sits above its par value because the prevailing market interest rate is lower than its coupon — the mirror image of a discount bond.
- Government SecurityA tradeable debt instrument issued by the Central Government or a State Government — treated as free of default risk, and the benchmark against which other rupee interest rates are priced.
- Dirty priceThe clean price of a bond plus the interest accrued since the last coupon date — what a buyer settling between coupon dates actually pays the seller.
- Effective yieldThe annual rate that would leave an investor with the same amount after one year as the quoted nominal rate does once its more frequent interest payments are taken into account.
- Convertible bondA bond carrying an embedded option that lets the holder exchange it for a specified number of the issuer's equity shares — a plain bond plus an equity conversion right.
- Inverted yield curveA yield curve on which short-term interest rates are higher than long-term rates — the reverse of the normal upward slope, read as a signal that the economy may go into recession.
- Non-competitive biddingBidding in RBI's government securities auctions without quoting a price or yield — the bidder is allotted at the weighted average price or yield that emerges from the competitive bids.
- Callable bondA bond that the issuer may redeem before its original maturity date — typically exercised when interest rates fall, leaving the investor to reinvest at lower rates.
- Puttable bondA bond that gives the investor the right to seek redemption from the issuer before maturity — useful when interest rates have risen and better-paying bonds are available.
- Masala bondA bond issued outside India by an Indian company but denominated in Indian rupees, so the foreign investor — not the Indian issuer — bears the risk of the rupee falling.