Free CFA Level II Fixed Income Practice Questions
Work through advanced fixed income analysis for CFA Level II. Questions test term structure models, arbitrage-free valuation, credit analysis models, and mortgage-backed securities.
Sample Questions
Question 1
Easy
The bootstrapping method is used to derive:
Solution
C is correct. Bootstrapping is a method for deriving the spot rate (zero-coupon) curve from the yields of coupon-paying bonds. The process works iteratively: starting with the shortest maturity bond (which gives the first spot rate directly), each subsequent bond's coupon payments are discounted using previously derived spot rates, and the final spot rate is solved for. This produces a complete spot rate curve from observed par bond yields.
A is incorrect because deriving forward rates from futures prices involves a different process (and may require convexity adjustments for futures). Bootstrapping specifically produces spot rates from coupon bonds.
B is incorrect because par rates are typically derived from spot rates (not the other way around using bootstrapping). Par rates are the coupon rates that make a bond price equal to par for each maturity, given the spot rate curve.
A is incorrect because deriving forward rates from futures prices involves a different process (and may require convexity adjustments for futures). Bootstrapping specifically produces spot rates from coupon bonds.
B is incorrect because par rates are typically derived from spot rates (not the other way around using bootstrapping). Par rates are the coupon rates that make a bond price equal to par for each maturity, given the spot rate curve.
Question 2
Medium
The effective duration of a callable bond is most likely to be:
Solution
C is correct. The effective duration of a callable bond is always less than or equal to that of an otherwise identical option-free bond. When interest rates decline, the price of a callable bond is capped near the call price because the issuer is likely to call the bond. This price compression (negative convexity) reduces the bond's sensitivity to interest rate decreases. Thus:
A is incorrect because the call option limits upside price appreciation, which reduces the bond's effective duration compared to the option-free bond.
A is incorrect because while it is true that when the call is deep out of the money the callable bond behaves similarly to the option-free bond, the statement says effective duration is "equal" and this is presented as a general answer. Choice C is more complete because it covers all scenarios (less than or equal to), whereas C only addresses one specific case.
A is incorrect because the call option limits upside price appreciation, which reduces the bond's effective duration compared to the option-free bond.
A is incorrect because while it is true that when the call is deep out of the money the callable bond behaves similarly to the option-free bond, the statement says effective duration is "equal" and this is presented as a general answer. Choice C is more complete because it covers all scenarios (less than or equal to), whereas C only addresses one specific case.
Question 3
Hard
In the Clearwater case, if Robert increases the assumed interest rate volatility from 12% to 18%, the most likely impact on Bond A's OAS and Bond B's OAS, respectively, is:
Solution
B is correct. The market prices of both bonds remain unchanged — only the model volatility assumption changes.
**Bond C (callable):** Higher volatility increases the call option value. A higher call option cost means the model produces a lower callable bond value. To match the (unchanged) market price, the OAS must decrease (a lower spread is needed to bring the model value up to the market price).
**Bond A (putable):** Higher volatility increases the put option value. A higher put option value means the model produces a higher putable bond value. To match the (unchanged) market price, the OAS must increase (a higher spread is needed to bring the model value down to the market price).
A is incorrect because it reverses the effects. Higher volatility hurts the OAS of the callable bond and helps the OAS of the putable bond, not vice versa.
C is incorrect because the effects are opposite for callable and putable bonds when volatility changes.
**Bond C (callable):** Higher volatility increases the call option value. A higher call option cost means the model produces a lower callable bond value. To match the (unchanged) market price, the OAS must decrease (a lower spread is needed to bring the model value up to the market price).
**Bond A (putable):** Higher volatility increases the put option value. A higher put option value means the model produces a higher putable bond value. To match the (unchanged) market price, the OAS must increase (a higher spread is needed to bring the model value down to the market price).
A is incorrect because it reverses the effects. Higher volatility hurts the OAS of the callable bond and helps the OAS of the putable bond, not vice versa.
C is incorrect because the effects are opposite for callable and putable bonds when volatility changes.
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