Lesson 7 of 8 · All lessons in this module
  1. Present value and discount (zero-coupon) bondsVideo lesson
  2. Coupon bonds and perpetual bonds
  3. Level-payment instruments: mortgages and amortizing loansVideo lesson
  4. Valuing shares with dividend discount models
  5. Implied returns on bonds
  6. Required return, implied growth and the P/E ratio
  7. Cash flow additivity, no arbitrage and forward rates
  8. No-arbitrage pricing of FX forwards and options

Lesson 7 of 8 · 14 min

Cash flow additivity, no arbitrage and forward rates

Values of cash flows at the same date can be added and subtracted, so economically equivalent strategies must cost the same; implied forward rates are the rates that make this true.

In short

  • Cash flow additivity: the PV of a stream = the sum of the PVs of its parts, once all are measured at the same date.
  • No arbitrage: prices must not allow a riskless profit with zero net investment (ignoring transaction costs).
  • Two strategies are economically equivalent when the PV of their cash flow differences is zero.
  • The implied forward rate solves (1+r2)2=(1+r1)(1+F1,1)(1+r_2)^2 = (1+r_1)(1+F_{1,1}); it is the breakeven reinvestment rate.
  • If a quoted forward rate differs from the implied one, borrow at the cheap rate and lend at the dear one.
  • Upward-sloping spot rates: F1,1>r2>r1F_{1,1} > r_2 > r_1. A rise in F1,1F_{1,1} signals expected future rate rises.
  • Longer horizons chain the same way: (1+r3)3=(1+r1)(1+F1,1)(1+F2,1)=(1+r1)(1+F1,2)2(1+r_3)^3 = (1+r_1)(1+F_{1,1})(1+F_{2,1}) = (1+r_1)(1+F_{1,2})^2.

Unlock this lesson free for 7 days

Create a free account to get 7 days free: every lesson, video and flashcard, and the question bank. No card needed.

Start your 7-day free trialLog in