CFA - Chartered Financial Analyst Fixed Income Analysis 1

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:

Accepted Answer

Lower than that of the option-free bond, because the probability of the bond being called increases

Answer

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:

Accepted 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

Answer

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:

Accepted Answer

Identify and hedge exposure to non-parallel yield curve movements such as twists and butterflies

Answer

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:

Accepted Answer

5.0%

Answer

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:

Accepted Answer

The portfolio duration equals the investment horizon and the portfolio has sufficient convexity to absorb parallel yield curve shifts

Answer

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.

CFA Practice Test

CFA Practice Test

CFA - Chartered Financial Analyst Fixed Income Analysis 1