CFA Level IFixed IncomeHard
Given a one-year spot rate of 2.50% and a two-year spot rate of 3.50% (annual compounding), the implied one-year forward rate one year from today is closest to 4.51%. According to the pure expectations theory of the term structure, this upward-sloping spot curve implies that the market expects future short-term interest rates to:
- A3.00%; rates are expected to fall
- B4.51%; rates are expected to remain flat
- C4.51%; rates are expected to rise
- D2.50%; rates are expected to rise
Show answer & explanationAnswer & explanation
Correct answer: C. 4.51%; rates are expected to rise
The forward rate is (1.035²/1.025) − 1 = (1.071225/1.025) − 1 ≈ 4.51%. Under pure expectations theory, forward rates are unbiased predictors of future spot rates, so an upward-sloping curve (forward > current spot) implies the market expects short-term rates to rise.
Why the other options are wrong
- A. Incorrect direction and incorrect forward rate value.
- B. Correct forward rate value but incorrect interpretation; an upward slope implies rising, not flat, expectations.
- D. Uses the wrong rate (current one-year spot) and mismatches direction with value.
Pure Expectations Theory
A term structure theory stating that forward rates are unbiased predictors of future spot rates, so the shape of the yield curve reflects the market's expectations for future short-term rates.
- Upward-sloping curve implies expected rising short-term rates
- Downward-sloping curve implies expected falling short-term rates
- Ignores liquidity/risk premia, unlike liquidity preference theory
Memory trick: 'The curve is the crowd's crystal ball for future rates'