FRM Part I · FRM Exam Part I · Interest Rates
A bond is priced at 100 with a modified duration of 7 and a convexity of 60. If its yield falls by 100 basis points, what is the new price estimated using both duration and convexity?
The estimated new price is 107.30. The duration effect adds 7%, and the convexity adjustment of one half times 60 times 0.0001 adds another 0.3%. Total gain is 7.3% on a price of 100. Convexity always adds to price for a yield move in either direction.
- A107.30Correct
- B107.00
- C106.70
- D107.60
Explanation
ΔP/P ≈ -D×Δy + 0.5×C×Δy² = -7×(-0.01) + 0.5×60×0.0001 = 0.07 + 0.003 = 0.073, so the price is 107.30. 107.00 omits convexity. 106.70 subtracts the convexity term (sign error). 107.60 omits the factor 0.5.
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 bank analyst observes a persistently upward-sloping yield curve. Which interpretation is consistent with the liquidity preference theory b…
- The market's 1-year and 2-year zero-coupon (spot) rates are 2.00% and 3.00% respectively, both expressed with annual compounding. What is th…
- A company will receive a FRA payoff on a USD 20 million notional. It bought a FRA at a fixed rate of 4.00% for a three-month period (0.25 ye…
- 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 …
- Annually compounded spot rates are 2.0% for one year, 3.0% for two years and 4.0% for three years. What is the implied one-year forward rate…
- 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…