IAI Actuarial Core Principles · Economic Modelling · Models of the term structure of interest rates
The one-year spot rate is 4% and the two-year spot rate is 5% (annual effective). Under pure expectations theory, what is the implied one-year forward rate for the second year, to the nearest 0.01%?
The implied forward rate is 6.01%, found from 1.05 squared divided by 1.04, minus one. This equals 1.1025 divided by 1.04 = 1.0601. Simple averaging or adding the spread would give wrong figures because compounding matters.
- A5.00%
- B6.01%Correct
- C4.50%
- D5.51%
- 6.25%
Explanation
(1.05)^2 = 1.1025. Divide by 1.04 to get 1.06010, so the forward rate is 6.01%. The simple average 4.5% ignores compounding. Doubling the rise gives 6%, which is only an approximation.
Did you get it right without looking?
One question tells you little. A timed set on Models of the term structure of interest rates shows your real accuracy, how long you take and where you lose marks.
More Models of the term structure of interest rates questions
- Principal component analysis of historical yield curve changes typically finds that the first principal component is best interpreted as:
- An actuary wants a one-factor short-rate model that reproduces today's observed market zero-coupon bond prices exactly, so that it can be us…
- Annual spot rates are s1 = 4% and s2 = 5%. What is the one-year forward rate from time 1 to time 2, f(1,2), to the nearest 0.01%?
- Which of the following is a feature of an inverted yield curve?
- Which feature distinguishes the Ho-Lee model dr = θ(t)dt + σ dW from the Vasicek model?
- Continuously compounded spot rates are 4% for 1 year and 5% for 2 years. What is the continuously compounded forward rate for the year from …