Investments
Bond pricing and yield
A bond's price is the present value of its coupons and face value at the market yield.
Definition
A bond pays periodic coupons and repays face value at maturity. Its price is the present value of all those cash flows discounted at the yield the market demands for that risk and maturity.
When the coupon equals the yield the bond trades at par; when the coupon is above the yield it trades at a premium; below, at a discount. Price and yield move in opposite directions.
Intuition
A bond is a fixed set of promises. When the market's required return rises, the fixed promises are worth less, so the price falls.
When to use it
- Valuing a bond or a stream of fixed contractual cash flows.
- Understanding interest-rate risk in a portfolio.
When not to use it
- For bonds with embedded options or credit-dependent cash flows without adjusting the model.
Formula
Bond price
P = Σ [C ÷ (1 + y)ᵗ] + F ÷ (1 + y)ⁿ
- C
- Coupon payment per period
- F
- Face value
- y
- Yield to maturity
- n
- Periods to maturity
Formula
Current yield
Coupon ÷ Price
Worked example
Pricing a three-year bond
Face value 1,000; coupon 8% (80 a year); market yield 10%; three years left.
- 1
Year 1
80 ÷ 1.10 = 72.73.
- 2
Year 2
80 ÷ 1.10² = 66.12.
- 3
Year 3
(80 + 1,000) ÷ 1.10³ = 811.42.
Price = 950.26. Because the 8% coupon is below the 10% yield, the bond trades at a discount to par.
Common mistakes
- Mixing semi-annual coupons with an annual yield and period count.
- Forgetting the face value in the final period's cash flow.
- Assuming price and yield move together.
How it connects
requires
Learn the source first; the target assumes it.
- Time value of money: Bond pricing is a present-value sum.
relates to
Useful to study together, in either order.
- Compounding and discounting: Coupon frequency changes the compounding used.
- Bond duration and interest-rate risk: Price is the level; duration is the sensitivity.
is an advanced form of
The source extends the target once the basics are secure.
contrasts with
Often confused, but different in an important way.