FRM Part I · FRM Exam Part I · Interest Rates
Under the pure expectations theory of the term structure, the current one-year spot rate is 3.0% and the market expects the one-year rate one year from now to be 5.0%. Using annual compounding, what is the two-year spot rate (rounded to two decimals)?
The two-year spot rate is about 3.99%. Under pure expectations the two-year growth factor equals 1.03 times 1.05, which is 1.0815, and its square root minus one gives 3.99%. The simple average of 4.00% ignores compounding and is therefore slightly too high.
- A3.00%
- B3.99%Correct
- C4.00%
- D5.00%
Explanation
Under pure expectations, (1+s2)^2 = 1.03 x 1.05 = 1.0815. The square root is 1.03995, so s2 is about 3.99%. The 4.00% option is the arithmetic average, which ignores compounding. 3.00% and 5.00% are just the one-year rates.
Did you get it right without looking?
One question tells you little. A timed set on Interest Rates shows your real accuracy, how long you take and where you lose marks.
More Interest Rates questions
- A treasurer expects to borrow USD 10 million for 3 months starting in 6 months and fears rates will rise. Which position in Eurodollar/SOFR-…
- A zero-coupon bond with a face value of 1,000 matures in exactly 3 years. The yield to maturity is 5% per year, compounded annually. What is…
- A two-year bond with a face value of 100 pays a 6% annual coupon in two semiannual payments of 3. It is quoted at a yield to maturity of 8% …
- A 3-year bond with a face value of 100 pays a 4% annual coupon and is priced at par (100) at a yield of 4%. Its modified duration is about 2…
- The 1-year spot rate is 3% and the 2-year spot rate is 5%, both annually compounded. What is the 1-year forward rate starting one year from …
- A bond with a market value of USD 1,000,000 has a Macaulay duration of 7.2 years and a yield of 4% per year, compounded semiannually. What i…