Zero-coupon bond

Indian Economy glossary

Also called: Deep discount bond · Topic: Financial Markets, Instruments, Insurance and Pensions · NCERT: Beyond NCERT

Meaning

A zero-coupon bond is a bond that pays no interest during its life. It is sold at a discount (below face value) and repaid at full face value (the amount printed on the bond) at maturity. The gap between the two prices is the investor's whole return.

  • Formula: Price = F / (1 + r)ⁿ, where F is face value, r is the market interest rate and n is years to maturity.
  • Return to investor = Face value − Issue price.
  • It matters because India's Treasury Bills (T-bills) are zero-coupon [1]. It is also the purest way to see why bond prices and interest rates move in opposite directions.

Explanation

How it works

  • An ordinary bond pays a coupon (a fixed yearly interest payment, shown as a % of face value). A zero-coupon bond has a coupon rate of 0%.
  • So the investor gets only one payment, the face value at the end.
  • To earn anything, the investor must buy it for less than face value today.
  • Worked example (T-bill):
  • A 91-day T-bill with face value Rs 100 is issued at Rs 98.20 [1].
  • At maturity the investor gets Rs 100 and earns Rs 1.80 [1].

  • Annualised yield ≈ (1.80 / 98.20) × (365 / 91) ≈ 7.35% (illustration).

  • General yield formula for a discount instrument:

  • Yield ≈ [(F − P) / P] × (365 / days to maturity)

  • Deep discount bond is another name. It is used when the maturity is long. The price is then far below face value, because the money is discounted over many years.

Price, yield and the "discount"

  • Present value (PV) (what a future rupee is worth today) decides the price. There is only one cash flow, so PV = F / (1 + r)ⁿ.
  • Yield to maturity (YTM) = the single discount rate that makes the PV of future cash flows equal to today's price. It is the bond's internal rate of return (the yearly return you earn if you hold the bond to maturity) [1].
  • A zero-coupon bond always trades below face value. So its YTM is always above its coupon rate (which is zero) [1].
  • Current yield (annual coupon ÷ market price × 100) is zero for a zero-coupon bond. Current yield ignores capital gains at maturity [1]. For this bond the whole return is a capital gain (a gain from a rise in the asset's price).

What makes its price rise or fall

  • Market interest rate up → price down, and the other way round.
  • The face value is fixed in rupees.
  • A higher rate discounts that future rupee more heavily.

  • So PV falls, and the price falls.

  • Longer maturity → bigger price swings. This is interest-rate risk. Take two zero-coupon bonds of face value Rs 100, with the rate moving from 5% to 6% (illustration):

Bond Price at 5% Price at 6% Fall
1-year 100/1.05 = Rs 95.24 100/1.06 = Rs 94.34 about 0.9%
10-year 100/1.05¹⁰ = Rs 61.39 100/1.06¹⁰ = Rs 55.84 about 9%
  • Why zero-coupon bonds are the most sensitive:
  • A coupon bond gives back some money early through its coupons.
  • A zero-coupon bond gives back everything only at the end.

  • So a long zero-coupon bond gains the most when rates fall and loses the most when rates rise.

  • No reinvestment risk: there are no coupons to reinvest at uncertain future rates. If you hold it to maturity, the return you locked in at purchase is exactly the return you get.

In India

  • T-bills are zero-coupon. They are short-term Government securities (G-secs) (tradable papers that record the government's debt). They are issued at a discount in 91-day, 182-day and 364-day tenors [1].
  • Zero-coupon dated bond: the Government issued a zero-coupon dated (long-term) bond in 1996 and has not issued one since [1]. Normal dated securities pay a coupon every half-year and mature in 5 to 40 years [1].
  • STRIPS (Separate Trading of Registered Interest and Principal of Securities):
  • They split an existing G-sec's cash flows into separate coupon and principal pieces. Each piece trades on its own as a zero-coupon bond [1].
  • They are made from existing G-secs, not issued fresh [1].

  • Sovereign zero-coupon pieces like these help build a market-based zero-coupon yield curve (a graph of the yields on zero-coupon bonds of different maturities) [1].

  • Banks and mark-to-market (MTM) (valuing a bond at today's market price, not the price paid):

  • Under the RBI (Classification, Valuation and Operation of Investment Portfolio of Commercial Banks) Directions, 2023, in force from 1 April 2024, HTM securities are carried at amortised cost (the purchase price, moved step by step towards face value) [2].
  • For a zero-coupon bond, amortised cost rises slowly from the discount price towards face value.
  • AFS gains and losses go to an AFS-Reserve. FVTPL changes go straight to the P&L (profit and loss account) [2].

Don't confuse with

  • Coupon bond sold "at a discount": an ordinary coupon bond can trade below face value when the market rate goes above its coupon rate. It still pays coupons. A zero-coupon bond is designed to pay no coupon, so it is always issued at a discount.
  • Dated securities: these are long-term G-secs that pay a coupon every half-year [1]. T-bills are short-term and pay no coupon. Trap: T-bills do not pay a coupon [1].
  • STRIPS: these are zero-coupon too, but they are made by splitting existing G-secs, not issued fresh [1]. A 364-day T-bill, by contrast, is issued fresh as a zero-coupon paper.
  • Floating Rate Bond (FRB): its coupon is reset at fixed intervals, so its price swings much less [1]. A long zero-coupon bond has no coupon, so its price swings the most when rates change.

Prelims Hooks

  • A zero-coupon (deep discount) bond pays no periodic interest. It is issued at a discount and repaid at face value. Return = Face value − Issue price.
  • T-bills are zero-coupon, in 91/182/364-day tenors. Example: a 91-day T-bill issued at Rs 98.20 gives a return of Rs 1.80 on face value Rs 100 [1].
  • The Government issued a zero-coupon dated bond in 1996 and none since [1].
  • STRIPS turn existing G-secs into zero-coupon pieces and help build a zero-coupon yield curve [1].
  • Price is below face value, so YTM > coupon rate [1]. The current yield of a zero-coupon bond is zero, because current yield ignores capital gains [1].
  • For the same change in rates, a longer zero-coupon bond's price falls more. From 5% to 6%, a 10-year bond falls about 9% and a 1-year bond about 0.9% (illustration).

Mains Points

  • Government borrowing and cash flow:
  • T-bills let the government borrow short-term without paying any interest in cash along the way. The cost is built into the discount [1].

  • Long zero-coupon bonds push the whole repayment to a single date. This eases today's budget but creates a large one-time repayment later. This may be one reason India has not issued a zero-coupon dated bond since 1996 [1].

  • Deeper bond markets:

  • STRIPS create sovereign zero-coupon pieces. They help build a market-based zero-coupon yield curve [1].
  • That curve gives a clean benchmark for pricing corporate bonds and long-term loans.

  • Insurers and pension funds must make fixed payments decades ahead. They can match these with long zero-coupon pieces, which carry no reinvestment risk.

  • Interest-rate risk and bank stability:

  • Long zero-coupon bonds lose the most value when rates rise.
  • Silicon Valley Bank (March 2023) held long bonds bought when rates were low. When rates rose, it faced large unrealised losses and then a deposit run.
  • RBI's 2023 framework keeps HTM out of MTM and sends AFS losses to a reserve [2]. So supervisors must still track how much long-duration paper banks hold, not just credit risk.

Related concepts

Read more

Sources

  1. 1Government Securities Market in India – A Primer (RBI FAQ)rbi.org.in · tier 1
  2. 2RBI (Classification, Valuation and Operation of Investment Portfolio of Commercial Banks) Directions, 2023rbi.org.in · tier 1