Zero coupon bond
Also written ZCB · Zero coupon bond (ZCB)
A bond that pays no coupons: it is issued below face value and repays the face value at maturity, so its duration equals its maturity.
In plain language
Most bonds pay interest every six months or every year and return the principal at the end. A zero coupon bond skips the interest entirely. You pay less than the face value today and receive the full face value on the maturity date. The difference is your return.
Because there is only one cash flow, two things follow:
- There are no coupons to reinvest, so there is no reinvestment risk.
- The whole value sits at the far end of the bond's life, so its Macaulay duration equals its remaining maturity — and its price is the most sensitive to interest-rate changes of any bond of the same maturity.
The workbook's everyday comparison: a simple bank fixed deposit that pays everything at maturity behaves like a zero coupon bond — except that an FD is not tradable.
How it works
Price is simply the present value of the face value:
The workbook's number: at an interest rate of 10% for a 10-year horizon, a zero coupon bond with a face value of ₹10,00,000 costs ₹3,85,543.30 today.
That single cash flow is why the zero is the textbook tool for immunization. Buying a zero whose maturity matches a liability locks the future value with no interest-rate risk or reinvestment risk. The workbook calls a zero with matching maturity "theoretically the best portfolio to immunize against interest rate risk".
On price volatility (Chapter 4): bonds with lower coupons show larger percentage price changes for a given change in rates, and among bonds of the same maturity a zero coupon bond experiences the largest percentage price change.
The workbook adds a market note: long-tenure zeros carry higher risk for the issuer and are now seen rarely.
The formula
Price of a zero coupon bond = Face value ÷ (1 + r)^n
Macaulay duration = n (remaining maturity)
A worked example
Illustrative figures. A school trust knows it must pay ₹25 lakh for a new building in exactly 5 years. Five-year yields are 8%.
Price today = 25,00,000 ÷ (1.08)^5 = 25,00,000 ÷ 1.4693 = ₹17,01,458
The trust invests ₹17,01,458 and, barring default, receives exactly ₹25 lakh on the date it needs it — whatever happens to interest rates in between. There are no coupons, so there is nothing to reinvest at an unknown future rate.
The risk moves to price, not to the final amount. If yields jump to 9% the day after purchase:
New price = 25,00,000 ÷ (1.09)^5 = ₹16,24,828 → a fall of about 4.5%
If the trust holds to maturity, that mark-to-market loss never becomes real. If it were forced to sell early, it would. A 5-year coupon bond at the same yield would have fallen less, because part of its value comes back earlier as coupons.
Why NISM asks about it
Chapter 4 (Investing in Fixed Income Securities) defines zero coupon bonds, notes that only a zero has duration equal to maturity, and ranks it as the most price-sensitive for a given maturity. Chapter 19 (Fixed Income Portfolio Management Strategies) uses the ₹10 lakh / 10% / 10-year zero as the benchmark cost of a perfectly immunized position and compares a bond portfolio against it.
Common exam traps
- No coupons means no reinvestment risk — but a zero still carries price (interest-rate) risk if sold before maturity, and more of it than a coupon bond of the same maturity.
- Duration = maturity only for a zero. For every coupon-paying bond, Macaulay duration is less than maturity.
- Issued at a discount, redeemed at face value. It does not "pay interest at maturity" as a separate cash flow; the return is the discount.
- A bank FD resembles a zero but is not tradable — the workbook's own qualification.
- For immunization, match the zero's maturity to the liability date; for a portfolio of coupon bonds, match duration instead.
Where this is taught
- Series XII · Chapter 2: Securities: Types, Features and Concepts of Asset Allocation and Investingintroduced here
- Series XXI-B · Chapter 4: Investing in Fixed Income Securitiesintroduced here
- Series IV · Chapter 1: Introduction to Interest Rate, Interest Rate Instruments and Fixed Income Marketsintroduced here
- Series II-A · Chapter 3: Characteristics of Debt Securitiesintroduced here
- Series II-B · Chapter 3: Characteristics of Debt Securitiesintroduced here
- Series XVII · Chapter 2: Financial Markets & Investment Productsintroduced here
- Series XXI-A · Chapter 4: Investing in Fixed Income Securitiesintroduced here
- Series XXI-B · Chapter 19: Fixed Income Portfolio Management Strategies
Related terms
- 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.
- 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.
- Yield to MaturityThe 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.
- 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.
- ImmunizationStructuring a bond portfolio so its value at a target date is protected from interest-rate changes — by matching the portfolio's duration to the liability's timing.
- 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.
- Risk-free rateThe rate on a sovereign borrowing in its own currency, where credit risk is absent because the government can print the money — the benchmark every other valuation is measured against.
- 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.
- 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.
- Constant Proportion Portfolio InsuranceA rebalancing strategy that keeps a multiple of the cushion — portfolio value minus a protected floor — in risky assets, and the rest in risk-free assets.
- Positive convexityThe favourable asymmetry of an option-free bond: when yields fall its price rises more than duration predicts, and when yields rise it falls less — so buying convexity is an active fixed income strategy.
- 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.
- Deep Discount BondA zero-coupon bond of very long tenure, issued at a steep discount to its face value and redeemed at par. IDBI issued such bonds; the Kisan Vikas Patra is another example.
- Inverse floaterA bond whose coupon moves opposite to its reference benchmark — it pays more as market rates fall and less as they rise, the reverse of an ordinary floating-rate bond.
- 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.
- 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.
- Amortising bondsBonds in which the borrower repays principal over the life of the bond along with interest, rather than all at maturity — so the stated maturity is only the date of the last instalment.
- STRIPSZero coupon bonds created by breaking a Government Security into its individual cash flows, so each coupon and the principal repayment trade separately as independent securities.
- 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.