CFA Level III Pathway: Portfolio Management Practice Questions
Question 1
Over five months, an index fund's returns minus its benchmark's returns were +0.20%, -0.20%, +0.20%, -0.20% and 0.00%. Using the sample standard deviation of these monthly active returns and annualizing, what is the fund's tracking error?
- A. 0.20%
- B. 2.40%
- C. 0.62%
- D. 0.69%
Show answer and explanation
Correct answer: D. 0.69%
Mean active return is 0. Sum of squared deviations is 0.04x4 = 0.16 (in %-squared); sample variance = 0.16/4 = 0.04, so monthly TE = 0.20%. Annualized TE = 0.20% x sqrt(12) = 0.69%.
- A. 0.20% is the monthly figure and has not been annualized.
- B. Multiplying by 12 instead of the square root of 12 overstates tracking error.
- C. 0.62% results from dividing by n (population SD of 0.179%) instead of n-1 before annualizing.
- D. Right: 0.20% x 3.4641 = 0.69%.
Question 2
A portfolio manager holds 150 illiquid corporate bonds and wants to reduce credit-spread exposure for the next quarter without selling the bonds. Which action is most appropriate, and what risk does it leave?
- A. Sell protection on a CDS index, leaving basis risk because index constituents differ from the holdings
- B. Buy protection on a CDS index, leaving basis risk because index constituents differ from the holdings
- C. Sell Treasury futures, leaving no residual risk because spread risk is fully offset
- D. Enter a total return swap receiving a corporate bond index, leaving some tracking risk
Show answer and explanation
Correct answer: B. Buy protection on a CDS index, leaving basis risk because index constituents differ from the holdings
Buying CDS index protection gains when credit spreads widen, offsetting spread losses on the bond portfolio at lower transaction cost than selling illiquid bonds. The hedge is imperfect because the index's names, maturities and spreads differ from the holdings.
- A. Selling protection adds credit exposure rather than reducing it.
- B. Right: it is a short credit position that offsets spread exposure, with basis risk.
- C. Treasury futures hedge interest rate duration, not credit spread.
- D. Receiving a bond index return increases credit exposure.
Question 3
Two portfolios have equal modified duration of 6.0. The barbell has convexity of 80 and the bullet has convexity of 45. Yields move by a large amount in a parallel shift. Ignoring yield differences, which statement is correct?
- A. The bullet outperforms because its lower convexity limits losses when yields rise sharply
- B. They perform the same because duration alone determines price change
- C. The barbell outperforms only when yields rise, because convexity benefits losses but not gains
- D. The barbell outperforms for a large move either way because higher convexity adds gain or cushions loss
Show answer and explanation
Correct answer: D. The barbell outperforms for a large move either way because higher convexity adds gain or cushions loss
Duration estimates price changes for small moves; convexity captures curvature. At equal duration, the higher-convexity barbell gains more when yields fall and loses less when yields rise, so it outperforms for large parallel shifts, other things equal.
- A. Lower convexity gives less cushion, not more.
- B. Equal duration matches only the first-order change; the second-order term still differs.
- C. Convexity adds value to price changes in both directions, not just for yield increases.
- D. Right: positive convexity helps in both directions, and more of it helps more.
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A bond portfolio has a key rate duration of 1.20 at the 5-year point versus 0.70 for its benchmark; all other key rate durations are equal. The 5-year par yield falls by 10 bps and no other key rate moves. What is the approximate return of the portfolio relative to the benchmark?
- A. +0.05%
- B. -0.05%
- C. +0.12%
- D. +0.50%
Show answer and explanation
Correct answer: A. +0.05%
Relative return is approximately -(1.20 - 0.70) x change in 5-year yield = -0.50 x (-0.10%) = +0.05%. The portfolio is overweight that key rate, so it gains when the 5-year yield falls.
- A. Right: a 0.50 duration overweight times a 0.10% yield drop yields +0.05%.
- B. The sign is wrong; an overweight benefits from a yield decline.
- C. 0.12% applies the full portfolio key rate duration (1.20 x 0.10%) rather than the active difference.
- D. 0.50% treats 10 bps as 1%.