FRM Part I · FRM Exam Part I · Interest Rates
Continuously compounded spot rates are 4% for 1 year and 5% for 3 years. What is the implied continuously compounded forward rate between year 1 and year 3?
The forward rate is 5.5%. With continuous compounding, the forward rate is the difference in total accumulated returns (15% − 4% = 11%) divided by the two-year forward period, which gives 5.5%. Averaging the spot rates or dividing by three years would be incorrect.
- A5.5%Correct
- B5.0%
- C4.5%
- D3.67%
Explanation
The forward rate is (5%×3 − 4%×1)/(3 − 1) = 11%/2 = 5.5%. Averaging the two spot rates gives 4.5%, which ignores the different time weights. Dividing 11% by 3 gives 3.67%, which uses the wrong time interval.
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 2-year zero-coupon bond with a face value of 100 is priced at 90.25. What is its yield to maturity expressed as a semiannually compounded …
- A manager holds a $50 million bond portfolio with a modified duration of 6.0 and wants to reduce its duration to 2.0 using Treasury bond fut…
- A 5-year bond with an 8% annual coupon and a face value of 100 trades at 105. Which ordering of the coupon rate, the current yield and the y…
- The one-year spot rate is 2.0% and the three-year spot rate is 4.0%, both annually compounded. Under pure expectations, what is the implied …
- A 2-year zero rate is 5% per year continuously compounded and a 3-year zero rate is 5.5% per year continuously compounded. What is the forwa…
- A two-year bond with a face value of 1,000 pays a 6% annual coupon and is priced at 964.33. Which is the bond's yield to maturity, compounde…