What it means
A bond's price and its yield move in opposite directions. When the price falls, the yield rises, and when the price rises, the yield falls.
Because bonds differ in coupon, maturity and other features, their prices alone say little about which is the better deal. Quoting on a yield basis puts every bond on a common scale.
A dealer might offer to buy a bond at a yield of 5.20%, and the actual cash price is then worked out from the bond's terms. Both parties agree on the yield, and the maths produces the price.
The convention is widely used in government bond, corporate bond and money market trading. It lets traders and investors compare opportunities quickly, and it makes changes in the market easy to describe as a move in yield rather than a hard-to-read change in price.
Treasurers and analysts follow the same logic when comparing the cost of different forms of borrowing. Money market instruments add a nuance.
Some, such as treasury bills, are traditionally quoted on a discount basis, which uses a different calculation from a true yield. Converting between the two is necessary to compare them fairly with each other and with longer bonds.
Calculations depend on conventions such as day count and compounding. Two quotes with the same headline yield may not be identical if one is annual and the other semi-annual.
A careful analyst checks these details before comparing figures. Yield to maturity is the most common yield used for this purpose.
It is the single discount rate that makes the present value of all the bond's future cash flows equal to its price, and it assumes the bond is held to maturity and the coupons are reinvested at the same rate. Because of these assumptions it is a useful guide rather than a guaranteed outcome.
In practice
Real-world examples.
Example
A fixed income trader receives a request from a client for a price on a 10-year corporate bond. The trader replies with a yield of 5.40% rather than a price. The client agrees, and the settlement system converts the yield into a cash price.
Example
A company treasurer compares two bonds with different coupons and maturities for investing surplus cash. She converts the quotes to yields so the comparison is fair. The higher-yielding bond has a lower credit rating, which she weighs before choosing. She also checks that both yields use the same compounding convention, so that the comparison is genuinely like for like.
Example
A finance analyst writes a market note explaining that government bond yields rose by 0.25 percentage points in a week. He then converts this into the price effect on a portfolio with a duration of 5 years. The note helps the board understand why the value of the bond holdings fell.
Formula
Calculation
Price = sum of [coupon / (1 + yield)^t] + face value / (1 + yield)^n
Suppose a bond has a face value of $1,000, pays an annual coupon of 5% ($50) and has two years to maturity. A dealer quotes it at a yield of 6%. Price = 50 / 1.06 + 1,050 / 1.06^2 = 47.17 + 934.50 = $981.67. The bond sells below face value because its coupon is lower than the yield the market demands.Case study
Seen in the real world.
Westbrook Treasury Group is an illustrative, fictional firm that invests the cash reserves of several clients. A client asked why a bond bought at a price above face value was listed at a lower price a month later, even though nothing about the issuer had changed.
The analyst explained that the market yield on similar bonds had risen from 4.50% to 5.00%. Because the bond paid a fixed coupon, its price had to fall to give new buyers the higher yield.
She showed the client the calculation on a yield basis and the matching price effect: a rise of 0.50 percentage points on a bond with a duration of 6 years reduces its price by roughly 3%. A $100,000 holding would therefore be worth about $3,000 less. The client had received the coupon throughout, so the fall was a change in market value rather than a loss of income. The illustrative lesson is that fixed income prices are best understood through yields, because the yield is what the market is actually negotiating.
Watch out
Common mistakes.
- Comparing bond prices directly, when coupon and maturity differences make yields the fairer comparison.
- Forgetting that yield and price move in opposite directions, so a rising yield means a falling price.
- Comparing yields calculated with different conventions, such as annual and semi-annual compounding, without adjusting them.
Questions
People also ask.
What does yield basis mean?
It means a bond is quoted and agreed in terms of its yield, with the price calculated from that yield.
Why not just quote the price?
Yields allow bonds with different coupons and maturities to be compared on one scale.
How is it different from a discount basis?
A discount basis quotes short-term instruments using a discount rate applied to face value, which is not the same calculation as a true yield.
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