1. What you will learn
By the end of this lesson you will be able to lay out a bond's contractual cash flows, distinguish the coupon rate from the current yield and from the yield to maturity and say what question each answers, explain why price and yield move in opposite directions, price a short bond from a given yield, and separate a clean price from a dirty one. This is education about bond arithmetic and is not advice about any bond, fund or issuer.
2. The idea explained
A bond is a contract to pay defined amounts on defined dates. Its value is the present value of those amounts, discounted at a rate that reflects the time until each payment and the risk that it will not arrive in full.
Three different rates get called yield and confusing them causes most beginners' errors. The coupon rate is fixed in the contract and tells you the rupee coupon relative to the face value. The current yield is the annual coupon divided by the current market price. The yield to maturity is the single discount rate that makes the present value of all remaining contractual cash flows equal to the market price, and it is the only one of the three that answers the question of what a buyer holding to maturity would earn if every payment arrived on time and coupons could be reinvested at that same rate.
The inverse relationship between price and yield is not a market convention; it is arithmetic. The contractual cash flows are fixed. If you pay less for a fixed set of payments, the return you earn on your outlay must be higher. If you pay more, it must be lower.
Three things move the discount rate. The general level of interest rates is one. Credit risk, the possibility that the issuer does not pay, is the second. Liquidity is the third: a bond that is hard to sell without moving its price must offer more to compensate.
Finally, embedded options change the whole picture. A callable bond may be redeemed early by the issuer, which caps the price upside precisely when rates fall.
Quoting conventions are the last piece. A clean price excludes interest accrued since the last coupon date; a dirty price includes it. A buyer pays the dirty price, because the seller is entitled to the interest earned during their holding period. The exact accrual is computed on the day-count convention in the bond's own terms.
3. The market, the regulator and the rulebook
India's debt market has two regulators with distinct roles. The Reserve Bank of India is the authority for government securities, money markets and the banking system,. The Securities and Exchange Board of India, the statutory securities regulator constituted by an Act of Parliament, regulates listed corporate debt securities, their issuance and disclosure, debenture trustees, credit rating agencies and the exchanges.
Read the source documents. For a specific bond, the offer document or information memorandum carries the coupon, the dates, the day-count convention, any call or put, the security and the covenants. For government securities, the Reserve Bank publishes auction notifications and results. For yields, the exchanges and the Reserve Bank publish data. Never quote a current yield level, a tax treatment or a threshold from memory; describe how the figure is arrived at and cite where the live one is published.
Worked example
4. Worked example
All figures are invented. Start with the simplest possible bond: a one-year instrument with no coupon that repays one thousand rupees and can be bought today for nine hundred and fifty.
Its one-year yield is one thousand divided by nine hundred and fifty, less one, which is about five point two six per cent. That is the whole return, since there is no coupon.
Now suppose the price rises to nine hundred and eighty. The yield becomes one thousand divided by nine hundred and eighty, less one, which is about two point zero four per cent. The promised payment did not change; only the price a buyer must pay to receive it did, so the return fell. That is the inverse relationship in its purest form.
Now a coupon bond. Take a two-year bond with a face value of one thousand rupees and an annual coupon of eighty rupees, so a coupon rate of eight per cent. Suppose the market demands a yield of ten per cent. The price is eighty divided by one point one, plus one thousand and eighty divided by one point two one. That is about seventy-two point seven three plus about eight hundred and ninety-two point five six, which is about nine hundred and sixty-five point two nine.
Notice three things. The price is below face value because the coupon of eight per cent is below the required yield of ten per cent. The current yield is eighty divided by nine hundred and sixty-five point two nine, which is about eight point two nine per cent, and it sits between the coupon rate and the yield to maturity, because it captures the income but not the capital gain to redemption. And the coupon rate of eight per cent told us nothing useful about the return.
Finally, accrual. If this bond paid semi-annual coupons of forty rupees and ninety days had passed in a one-hundred-and-eighty-two-day coupon period, accrued interest would be forty multiplied by ninety over one hundred and eighty-two, which is about nineteen rupees seventy-eight paise. A buyer would pay the quoted clean price plus that amount.
5. Common mistakes and how to fix them
The first mistake is treating a high coupon as a high return. Compute the yield to maturity from the price and the cash flows, and let the coupon rate be what it is.
The second is quoting current yield as though it were total return. Say explicitly that it excludes the gain or loss to redemption.
The third is forgetting the reinvestment assumption inside a yield to maturity. State that it assumes coupons are reinvested at the same rate.
The fourth is discounting a callable bond's scheduled cash flows. Read the terms for calls and puts before valuing anything.
The fifth is confusing interest rate risk with credit risk. A government bond can lose value when rates rise without any change in the probability of repayment, and a corporate bond can lose value because of credit alone. Past performance does not indicate future results, no bond or fund is safe or guaranteed, and a SEBI-registered investment adviser is the person to consult about an individual's own money.
Key takeaways
6. Board summary
A bond's value is the present value of its contractual cash flows at a rate reflecting time and risk. Coupon rate is fixed in the contract, current yield is coupon over price, and yield to maturity solves for the rate that equates price to all remaining cash flows. Price and yield move inversely because the promised cash flows are fixed. Credit risk and liquidity sit alongside the general level of rates in setting the discount rate. A buyer pays the dirty price, which is the clean price plus interest accrued under the bond's own day-count convention.
Check your understanding
7. Practice and self-check
One. A one-year zero-coupon bond repays five hundred and costs four hundred and seventy-five. Yield? Five hundred over four hundred and seventy-five, less one, which is about five point two six per cent.
Two. Its price rises to four hundred and ninety. New yield? About two point zero four per cent.
Three. Why did the yield fall? Because the promised payment is fixed and the buyer now pays more for it.
Four. A bond has a face value of one thousand, a coupon rate of six per cent and a market price of nine hundred. Current yield? Sixty over nine hundred, which is about six point six seven per cent.
Five. Is the yield to maturity higher or lower than that? Higher, because there is also a gain to redemption.
Six. A two-year bond pays a coupon of one hundred on a face of one thousand and the required yield is eight per cent. Price? One hundred over one point zero eight plus one thousand one hundred over one point one six six four, which is about ninety-two point five nine plus nine hundred and forty-three point one, or about one thousand and thirty-five point seven.
Seven. Why is that above face value? Because the coupon rate of ten per cent exceeds the required yield of eight per cent.
Eight. Semi-annual coupons are thirty and sixty days have passed in a one-hundred-and-eighty-day period. Accrued interest? Ten rupees.
Nine. Which document settles a specific bond's day-count convention and call terms? Its own offer document or information memorandum, cited with a date.