Independent CFA Level II learning guide. Original examples and exercises; not official exam questions. Use the official curriculum outline for your exam year to check coverage. These starting guides do not cover the complete curriculum.

Draw the payment timeline

Consider a default-free two-year bond with face value 100 and annual coupon 5. Its cash flows are 5 at year one and 105 at year two. With annual effective spot rates of 4% for one year and 5% for two years, value is 5/1.04 + 105/(1.05 squared), approximately 100.05. Each payment uses the spot rate for its maturity; a coupon rate is not a discount rate.

P=∑t=1TCFt(1+st)t=51.04+105(1.05)2≈100.05P=\sum_{t=1}^{T}\frac{CF_t}{(1+s_t)^t}=\frac{5}{1.04}+\frac{105}{(1.05)^2}\approx100.05
Annual cash flows and annual effective spot rates sₜ; valuation is on a coupon date.
MAKE IT PRACTICAL ↗

Recalculate the price and verify that 105 includes both the final coupon and principal. Then calculate the price if both spot rates equal 5%; it should be 100.

Infer a forward rate consistently

Under annual compounding, the one-year forward rate beginning in one year satisfies (1 + two-year spot rate) squared = (1 + one-year spot rate) times (1 + forward rate). Using 4% and 5% gives 1.05 squared divided by 1.04 minus 1, approximately 6.01%. This is an implied rate consistent with the discount curve, not a guaranteed future realized short rate.

f1,2=(1+s2)21+s1−1=1.0521.04−1≈6.01%f_{1,2}=\frac{(1+s_2)^2}{1+s_1}-1=\frac{1.05^2}{1.04}-1\approx6.01\%
The implied one-year forward rate beginning in one year, under annual compounding.
MAKE IT PRACTICAL ↗

Explain why multiplying 5% by two and subtracting 4% gives only an approximation rather than the exact compounded answer.

Separate duration from full repricing

Modified duration approximates the percentage price change for a small yield change as minus duration times the change in yield. A duration of 4 and a rise of 0.005 imply approximately a 2% price decline. This linear approximation omits curvature. Bonds with embedded options can change cash-flow behavior as rates move, so a fixed-cash-flow calculation may be inappropriate.

ΔPP≈−DmodΔy=−4(0.005)=−2%\frac{\Delta P}{P}\approx-D_{\mathrm{mod}}\Delta y=-4(0.005)=-2\%
Modified duration gives a small-yield-change approximation; 50 basis points is 0.005.
MAKE IT PRACTICAL ↗

For an initial value of 100 and modified duration 4, estimate the value after a 50-basis-point rise. Then explain why a large rate move needs more than this approximation.

State the conventions

A price calculation depends on compounding, payment frequency, settlement date, and whether the quoted price includes accrued interest. In these examples valuation occurs on a coupon date and rates compound annually. In a vignette, explicitly identify any different convention. Separate changes in benchmark rates from changes in credit or liquidity compensation before explaining a price movement.

MAKE IT PRACTICAL ↗

Write a checklist of conventions you would confirm before comparing two bond valuations from different analysts.

A QUICK KNOWLEDGE CHECK

An implied forward rate is best interpreted as what?

Keep exploring

Continue with the CFA Institute Level II outline and official candidate resources. Check the assumptions in each worked example and practise with your registered curriculum.

UP NEXTRegression interpretation
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