Lesson 11 of 11 · 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. Floating-rate coupons and spreadsheet TVM functions
  7. Required return, implied growth and the P/E ratio
  8. Cash flow additivity, no arbitrage and forward rates
  9. No-arbitrage pricing of FX forwards and options
  10. Valuing a real option with cash flow additivity
  11. Integrated cases: bills, forward rates and currency forwards

This lesson is part of the 2027 curriculum. You are following the 2026 curriculum, where it is not taught in this form. Switch if you are sitting the exam under the 2027 curriculum.

Lesson 11 of 11 · 16 min

Integrated cases: bills, forward rates and currency forwards

Short-dated bills are priced from a simple annual yield, longer zeros from a compounded one; forward rates and forward exchange rates follow from no arbitrage, and the arbitrage direction is set by comparing the quote with the fair value.

In short

  • A money-market bill quoted on a simple annual yield has price = face ÷ (1 + y × days/365). A negative yield puts the price above face.
  • Going the other way (price known, rate wanted), compute the holding period return and compound it: (1+HPR)365/t−1(1+\text{HPR})^{365/t} - 1. The two conventions give slightly different annual figures for the same bill.
  • Forward rates come from zero prices: r=(100/P)1/n−1r = (100/P)^{1/n} - 1, then F1,1=(1+r2)2/(1+r1)−1F_{1,1} = (1+r_2)^2/(1+r_1) - 1. After a rate shock, the forward rises by at least as much as the 2-year spot.
  • Fair forward exchange rate (price/base, continuous): F=S e(rp−rb)TF = S\,e^{(r_p - r_b)T}. If the quote is above it, sell the base currency forward; if below, buy it forward.
  • A real option's value is the difference between the 'with' and 'without' project values, less the present value of the exercise cost.

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