Finance · level 1
Zero-coupon yield
Price and yield are the same fact stated two ways. For a zero the algebra is one root; for a coupon bond you interpolate, but the intuition is identical: yield up, price down.
Worked example: A 10-year zero-coupon bond with $1,000 face trades at $463.19. Yield to maturity?
Step by step
- 1
YTM of a zero
(F / P)^(1/n) − 1 = (1000 / 463.19)^(1/10) − 1 = 8%
- 2
Sanity
The discount is 53.7% over 10 years — about 5.4 points a year simple, so the compound yield is a little higher.
- 3
Spot rate
Zero yields are the spot rates that build the yield curve; coupon bonds are portfolios of zeros.
A 10-year zero-coupon bond with $1,000 face trades at $463.19. Yield to maturity? = 8
The theory behind it
Intuition
Finance is time and risk applied to cash: move every cash flow to the same date at a rate that reflects its risk, then compare.
Common pitfalls
- ×Discounting a nominal flow at a real rate (or vice versa).
- ×Mixing enterprise-value and equity-value numbers in the same ratio.
In the interview
Valuation, WACC, LBO and accretion rounds — where a wrong bridge is a wrong answer.