CFA Level II Fixed Income Practice Questions
Question 1
A bond portfolio has key rate durations of 0.60 at 2 years, 1.20 at 5 years, 2.00 at 10 years and 0.40 at 30 years. Only the 10-year par rate rises by 50 bp, and all other key rates are unchanged. What is the approximate percentage change in portfolio value?
- A. -1.00%
- B. +1.00%
- C. -0.50%
- D. -2.10%
Show answer and explanation
Correct answer: A. -1.00%
For a shift at one key rate, the approximate price change is -KRD x change in rate = -2.00 x 0.50% = -1.00%. The sum of the key rate durations (4.20) applies to a parallel shift of all key rates, not to one key rate alone.
- A. Correct: -2.00 x 0.50% = -1.00%.
- B. Gets the sign wrong; rising yields reduce value.
- C. Uses a 25 bp shift or half the sensitivity, understating the effect.
- D. Uses the 4.20 total duration, which applies only if all key rates rise by 50 bp.
Question 2
Analyst Eli builds a binomial interest rate tree to value bonds with embedded options. Which result confirms that the tree is arbitrage-free and ready to use?
- A. An option-free bond valued on the tree equals its value discounted at the benchmark spot rates
- B. The up-state and down-state rates at every date are equal, removing volatility
- C. Risk-neutral probabilities at each node sum to more than one to reward risk
- D. A callable bond valued on the tree equals the value of the same option-free bond
Show answer and explanation
Correct answer: A. An option-free bond valued on the tree equals its value discounted at the benchmark spot rates
A calibrated tree must reprice benchmark option-free bonds to the values implied by the spot curve. Once it does, it can be used to value embedded options. Zero volatility, a callable valued as option-free, or probabilities not summing to one all signal a flawed tree.
- A. Correct: repricing option-free bonds to the spot curve verifies calibration.
- B. Equal up and down rates would remove all rate volatility and make options worthless.
- C. Probabilities at a node must sum to one; they do not carry a risk reward.
- D. A callable bond should be worth less than the option-free bond, not the same.
Question 3
Analyst Priya argues that yields in the short, intermediate and long maturity ranges are set entirely by supply and demand from investors who will not leave their own maturity range, so the curve says little about expected future rates. Which theory of the term structure matches her view?
- A. Preferred habitat theory
- B. Market segmentation theory
- C. Pure expectations theory
- D. Liquidity preference theory
Show answer and explanation
Correct answer: B. Market segmentation theory
Market segmentation theory treats each maturity range as a separate market with its own investors, whose rigid demand sets yields independent of expected rates. Preferred habitat theory is similar but allows investors to move outside their habitat if compensated with a yield premium.
- A. Preferred habitat lets investors leave their range for extra yield, which Priya's investors will not do.
- B. Correct: separate markets with investors unwilling to switch maturities.
- C. Pure expectations theory ties long yields to expected short rates, the opposite of this view.
- D. Liquidity preference theory adds a maturity-related premium to expected rates and does not isolate segments.
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A bond's credit spread is 1.20% per year. The expected recovery rate on default is 40%. Using the approximation that credit spread equals probability of default times loss given default, what is the implied annual probability of default?
- A. 1.20%
- B. 0.72%
- C. 2.00%
- D. 3.00%
Show answer and explanation
Correct answer: C. 2.00%
Loss given default = 1 - 0.40 = 60%. Probability of default is about spread/LGD = 1.20%/0.60 = 2.00%. Dividing by the recovery rate is a common slip that mistakes recovery for loss.
- A. Treats the spread itself as the default probability, ignoring recovery.
- B. Multiplies spread by LGD, reversing the relationship.
- C. Correct: spread divided by LGD.
- D. Divides by the recovery rate rather than the loss rate.