Lesson 5 of 8 · All lessons in this module
- Present value and discount (zero-coupon) bondsVideo lesson
- Coupon bonds and perpetual bonds
- Level-payment instruments: mortgages and amortizing loansVideo lesson
- Valuing shares with dividend discount models
- Implied returns on bonds
- Required return, implied growth and the P/E ratio
- Cash flow additivity, no arbitrage and forward rates
- No-arbitrage pricing of FX forwards and options
Lesson 5 of 8 · 13 min
Implied returns on bonds
When a bond's price is known, solve the valuation equation for the rate: that implied return is the market's expected return, provided its assumptions hold.
In short
- Zero-coupon bond: .
- The same formula gives an annualized holding-period return: PV = price paid, FV = sale price (plus any reinvested cash).
- Holding-period returns over consecutive periods compound to the full-period return.
- For coupon bonds, the YTM is the IRR of the promised cash flows, found by iteration (CPT I/Y).
- The YTM assumes the bond is held to maturity, every payment is made as promised, and all cash flows are reinvested at the YTM.
- A rise in yields means a capital loss for current holders but a higher return for new buyers.
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