Risk Management and Investment Management

• Topic 01

  Portfolio Construction and Risk

  45 questions
• Topic 02

  Factor Models in Investment Management

  72 questions
• Topic 03

  Risk Budgeting

  45 questions
• Topic 04

  Performance Attribution

  45 questions
• Topic 05

  Hedge Fund Risk

  57 questions
• Topic 06

  Pension Fund Risk Management

  60 questions
• Topic 07

  Alternative Risk Premia

  83 questions
• Topic 08

  ESG and Responsible Investment Risk

  46 questions

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

1. In a DB pension fund's LDI framework, the "matching portfolio" typically holds which types of assets?

   • A
     Long-dated government bonds, interest rate swaps (receive-fixed), inflation-linked bonds, and inflation swaps — instruments that hedge liability duration and inflation risk
     Correct answer
   • B
     Balanced multi-asset funds targeting the scheme's return assumption to close the deficit as quickly as possible
   • C
     Global equities, private equity, infrastructure, and alternative assets chosen for long-term capital growth
   • D
     Cash, money market instruments, and short-dated government bonds to ensure liquidity for benefit payments
   Explanation

   The matching portfolio in an LDI framework is specifically designed to hedge liability characteristics:

   | Instrument | Risk Hedged | |---|---| | Long-dated gilts / Treasuries | Interest rate risk (nominal) | | Receive-fixed interest rate swaps | Interest rate risk (extending duration beyond bond market supply) | | Index-linked gilts (ILGs) | Inflation risk (RPI-linked) | | Inflation swaps (receive RPI/CPI) | Inflation risk |

   The matching portfolio does not aim to generate excess returns — it aims to replicate the behavior of the liabilities as closely as possible. The growth portfolio (equities, alternatives, hedge funds) generates the return needed to close any remaining deficit. As the funding ratio improves, assets shift from the growth to the matching portfolio.

2. The MVaR formula is $\text{MVaR}_i = z \times \rho_{ip} \times \sigma_i$. What does $\rho_{ip}$ represent?

   • A
     The correlation between position i's return and the total portfolio's return
     Correct answer
   • B
     The proportion of portfolio VaR attributable to position i
   • C
     The information ratio of position i within the portfolio
   • D
     The correlation between position i and the benchmark
   Explanation

   In the MVaR formula, $\rho_{ip}$ is the correlation between position i's returns and the total portfolio's returns. It captures how much position i moves together with the overall portfolio. A high positive $\rho_{ip}$ means position i contributes significantly to portfolio risk (when the portfolio falls, this position tends to fall too). A negative $\rho_{ip}$ means position i tends to rise when the portfolio falls, acting as a hedge and giving it a negative MVaR. This portfolio correlation is the key input distinguishing marginal/component VaR from standalone VaR.

3. A portfolio manager interprets a positive βUMD loading in the Carhart model as evidence of which portfolio characteristic?

   • A
     The portfolio holds low-volatility stocks because UMD is the Up Minus Down volatility factor
   • B
     The portfolio is underleveraged relative to the benchmark because UMD measures use of margin debt
   • C
     The portfolio holds value stocks because UMD is the Up-valuation Minus Down-valuation factor
   • D
     The portfolio holds recent past winners (high 12-1 month return stocks) — it has a momentum tilt
     Correct answer
   Explanation

   UMD = Up Minus Down (also called WML, Winners Minus Losers): return on the portfolio of past 12-month winners minus past 12-month losers.

   A positive βUMD loading means the portfolio:

   • Tends to hold recent past winners (stocks with high 12-1 month returns)
   • Gains when the momentum factor (UMD) is positive — i.e., when recent winners continue to outperform recent losers
   • Has a momentum tilt in its portfolio construction

   This could arise from a systematic momentum-based stock selection process or from a portfolio that happens to overweight recently outperforming sectors or styles.