Fixed Income B: Portfolio Strategies

• Topic 01

  Yield Curve Strategies

  54 questions
• Topic 02

  Duration and Convexity Management

  54 questions
• Topic 03

  Currency Risk in Fixed Income

  54 questions
• Topic 04

  Global Fixed Income Portfolio Management

  54 questions
• Topic 05

  Fixed Income Factor Models

  54 questions
• Topic 06

  Liability-Driven Investing

  54 questions
• Topic 07

  Fixed Income Risk Management

  54 questions

A few questions from this unit, with the answer and a full explanation. The complete bank is available when you start practising.

1. A risk analyst builds a parametric VaR model for a bond portfolio and back-tests it against 500 days of returns. At 99% confidence, the model produces 12 exceedances. Using a binomial test framework with a 1% expected exceedance rate, what does this result suggest, and what is the conceptual implication?

   • A
     The model is over-conservative because 12 exceedances means losses are larger than VaR on only 2.4% of days, which is acceptable.
   • B
     Under the binomial framework, 12 exceedances in 500 days indicates the model overestimates tail risk, requiring a downward revision.
   • C
     Under a 1% exceedance rate, 500 days would generate an expected 5 exceedances. Observing 12 is significantly above the expected value, suggesting the model is underestimating tail risk (possibly due to fat tails or non-stationarity).
     Correct answer
   • D
     Twelve exceedances in 500 days equals a 2.4% rate, which is within acceptable tolerance because VaR models are only tested at 95% confidence for regulatory purposes.
   Explanation

   Expected exceedances: $500 \times 0.01 = 5$. The standard deviation of a binomial count is$\sqrt{500 \times 0.01 \times 0.99} \approx 2.22$. Observing 12 exceedances is$(12-5)/2.22 \approx 3.15$ standard deviations above the mean, a statistically significant result. This indicates model under-performance — the model assigns too little probability to large losses. Likely causes include fat-tailed yield distributions (excess kurtosis), non-stationarity, or parameter instability during stressed periods. Basel III's traffic-light framework classifies 10+ exceedances per 250 days as a red zone requiring capital add-ons.

2. A fixed income risk manager compares historical simulation VaR with parametric VaR for a high-yield bond portfolio during a period of market stress. The historical simulation produces a 99% 1-day VaR of USD 8.2 million, while parametric VaR produces USD 5.1 million. Which explanation best accounts for the divergence?

   • A
     The divergence reflects basis risk: historical simulation captures spread changes while parametric VaR only measures rate risk.
   • B
     Parametric VaR uses duration as a proxy for price change, but high-yield bonds have significant convexity, causing parametric VaR to understate losses for small yield changes only.
   • C
     The divergence reflects model error in historical simulation due to survivorship bias — bonds that defaulted are excluded, making the tail appear more extreme.
   • D
     High-yield bond returns exhibit fat tails and negative skewness. Parametric VaR assumes normality and therefore underestimates the probability of extreme losses, while historical simulation captures the actual empirical tail from past stressed episodes.
     Correct answer
   Explanation

   High-yield bond returns exhibit significant excess kurtosis (fat tails) and negative skewness — the left tail of the loss distribution is heavier than a normal distribution would predict. Parametric VaR imposes normality on this distribution, compressing the tails and producing a materially lower VaR (USD 5.1m vs. USD 8.2m). Historical simulation makes no distributional assumption, directly using the large spread-widening events and defaults recorded in the data. During stress periods, the ratio of historical to parametric VaR can diverge substantially, and regulators often require stressed VaR supplements to capture this effect.

3. What is the 'carry' in the context of yield curve strategies, and how does it differ from yield to maturity when the curve is steep?

   • A
     Carry = coupon income + roll-down return. When the yield curve is steep, roll-down return is substantial, making total carry higher than the bond's yield to maturity. YTM only captures the coupon income component.
     Correct answer
   • B
     Carry is the income component only (coupon / price), excluding any capital appreciation from rolling down the curve.
   • C
     Carry = yield to maturity minus the funding cost of the bond; for bonds held without leverage, carry equals YTM.
   • D
     Carry equals the bond's coupon rate divided by its price (current yield), which equals the YTM only for par bonds.
   Explanation

   In fixed income, carry = coupon income + roll-down return — it represents all the return earned by simply holding the bond without any change in the yield level. YTM measures only the coupon income component (annualised yield assuming the bond is held to maturity at constant reinvestment rates). When the yield curve is steep, a bond rolling down the curve earns substantial roll-down return in addition to coupon income, making total carry meaningfully higher than YTM alone suggests. For example, a 10-year bond with a 4.0% yield might earn 4.0% coupon + 2.0% roll-down = 6.0% total carry, making it far more attractive than a naive YTM comparison of 4.0% would indicate. Carry provides a more complete picture of the holding period return assuming no yield change.