FRM Part I · FRM Exam Part I · Properties of Interest Rates
The zero curve is upward sloping, with continuously compounded zero rates rising with maturity. Which statement correctly describes the forward rate for the period between T1 and T2 (T2 > T1)?
The forward rate is higher than the zero rate for maturity T2. When the curve slopes upward, the later period must earn more than the longer-dated zero rate to pull the average rate up from R1 to R2.
- AIt is higher than the zero rate for maturity T2Correct
- BIt is lower than the zero rate for maturity T1
- CIt equals the zero rate for maturity T2
- DIt equals the simple average of the T1 and T2 zero rates
Explanation
Since the forward rate is (R2*T2 - R1*T1)/(T2 - T1), it equals R2 + (R2 - R1)*T1/(T2 - T1). With R2 > R1 the second term is positive, so the forward rate exceeds R2. It also exceeds R1, which rules out the second option. It equals the simple average only in special cases, not in general.
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