CFA - Chartered Financial Analyst Fixed Income Analysis 1 — Questions and Answers
Question 1: A callable bond and an otherwise identical option-free bond have the same modified duration. When interest rates fall sharply, the effective duration of the callable bond will most likely be:
- Greater than that of the option-free bond, because the call option adds value to the issuer
- Equal to that of the option-free bond, because modified duration is invariant to embedded options
- Lower than that of the option-free bond, because the probability of the bond being called increases (Correct answer)
- Negative, because callable bonds exhibit price compression at low yields
Correct answer: Lower than that of the option-free bond, because the probability of the bond being called increases
Effective duration captures the actual price sensitivity of a bond, including changes in cash flows caused by embedded options. As rates fall, the call option moves deeper in-the-money, making early redemption more likely and capping price appreciation — effectively shortening the bond's expected life and reducing its effective duration relative to an option-free bond.
Question 2: A fixed-income analyst states: 'A bond with higher convexity will outperform a bond with lower convexity and the same duration, regardless of the direction of the interest rate change.' This statement is most accurately described as:
- Incorrect, because convexity only benefits the bondholder when rates rise
- Correct, because positive convexity causes a bond to gain more than duration predicts when rates fall and lose less than duration predicts when rates rise (Correct answer)
- Incorrect, because convexity improvements are only observable for large parallel yield curve shifts
- Correct, because higher convexity directly implies a higher coupon rate
Correct answer: Correct, because positive convexity causes a bond to gain more than duration predicts when rates fall and lose less than duration predicts when rates rise
Positive convexity is a desirable property that benefits the bondholder symmetrically: when rates fall, the bond price rises more than the linear (duration) estimate; when rates rise, the bond price falls less than the linear estimate. This outperformance holds for any non-zero rate change, which is why investors pay a premium for higher convexity.
Question 3: Key rate duration (partial duration) is most useful for a portfolio manager seeking to:
- Measure a portfolio's sensitivity to a parallel shift in the entire yield curve
- Immunize against reinvestment risk for a single horizon date
- Identify and hedge exposure to non-parallel yield curve movements such as twists and butterflies (Correct answer)
- Estimate the credit spread sensitivity of individual corporate bond positions
Correct answer: Identify and hedge exposure to non-parallel yield curve movements such as twists and butterflies
Key rate duration measures a portfolio's price sensitivity to a change in yield at a specific maturity point on the curve, holding all other points constant. This makes it ideal for quantifying and managing exposure to non-parallel shifts — such as curve steepening, flattening, or butterfly movements — that a single summary duration measure would miss entirely.
Question 4: An analyst observes a 1-year spot rate of 3.0% and a 2-year spot rate of 4.0%. The implied 1-year forward rate one year from today is closest to:
- 3.5%
- 5.0% (Correct answer)
- 1.0%
- 4.5%
Correct answer: 5.0%
The 1-year forward rate one year from now is derived from the no-arbitrage condition: (1 + S2)^2 = (1 + S1)(1 + f(1,1)). Solving: (1.04)^2 / (1.03) = 1.0816 / 1.03 ≈ 1.0500, giving a forward rate of approximately 5.0%. This reflects the additional return required in year 2 to make investing for two years equivalent to rolling over two consecutive one-year investments.
Question 5: Under classical immunization theory, a portfolio is considered immunized against interest rate risk over a single investment horizon when:
- The portfolio's yield to maturity equals the target rate of return and all bonds are zero-coupon instruments
- The portfolio duration equals the investment horizon and the portfolio has sufficient convexity to absorb parallel yield curve shifts (Correct answer)
- The portfolio's market value equals the present value of the liability and the portfolio duration equals zero
- The portfolio consists solely of Treasury securities rated AAA with maturities exceeding the horizon date
Correct answer: The portfolio duration equals the investment horizon and the portfolio has sufficient convexity to absorb parallel yield curve shifts
Classical immunization requires two conditions: (1) the portfolio's Macaulay duration equals the investment horizon, and (2) the portfolio's initial market value is at least equal to the present value of the liability. When duration equals the horizon, the capital loss (gain) from a rate rise (fall) is offset by the reinvestment gain (loss) on coupon cash flows, locking in the target return despite rate changes.
Question 6: For a bond with an embedded put option, which of the following most accurately describes the relationship between the bond's price and its yield to maturity relative to an otherwise identical option-free bond?
- The putable bond will always have a lower price and higher yield than the option-free bond
- The putable bond will have a higher price and lower yield than the option-free bond, because the put option benefits the holder (Correct answer)
- The putable bond will have the same price as the option-free bond because embedded options have no intrinsic value at issuance
- The putable bond will have a higher yield than the option-free bond to compensate the issuer for granting the put option
Correct answer: The putable bond will have a higher price and lower yield than the option-free bond, because the put option benefits the holder
An embedded put option grants the bondholder the right to sell the bond back to the issuer at a set price, providing downside protection against rising rates. Because this option has value to the holder, investors are willing to accept a lower yield (pay a higher price) for a putable bond compared to an equivalent option-free bond. The OAS of a putable bond is therefore higher than its nominal spread.
CFA - Chartered Financial Analyst Fixed Income Analysis 1
A callable bond and an otherwise identical option-free bond have the same modified duration.
When interest rates fall sharply, the effective duration of the callable bond will most likely be: