FRM Partie II : marché, crédit, opérationnel, liquidité

A bank backtests its one-day 99% VaR over 250 trading days.

How many exceptions should it expect if the model is correct?

A historical simulation uses 1,000 daily scenarios. The ten largest losses, in USD million, are 12.4, 11.0, 9.8, 9.1, 8.7, 8.2, 7.9, 7.5, 7.3 and 7.0. The eleventh largest loss is 6.8.

Estimating the 99% expected shortfall as the average of the losses in the 1% tail, what is its value?

A USD 10 million position has a one-day 99% VaR of USD 0.5 million. The bid-ask spread is constant at 0.4% of the mid price.

Using the constant-spread approach, what is the liquidity-adjusted VaR?

A loan has an exposure at default of EUR 5 million, a one-year probability of default of 2% and a loss given default of 45%.

What is its one-year expected loss?

A one-year corporate bond yields 5.5% and a one-year government bond yields 3.5%. The expected recovery rate is 40%.

Using the approximation spread ≈ PD × (1 − recovery rate), what is the implied one-year probability of default?

A bank’s expected exposure to a counterparty is constant at USD 10 million over the next three years. The counterparty’s marginal probability of default is 2% in each year, and the loss given default is 60%.

Ignoring discounting, what is the CVA?

A firm’s assets are worth USD 100 million, with an expected return of 6% and a volatility of 25%. Its only debt is a zero-coupon bond with a face value of USD 80 million, due in one year.

In the Merton model, what is the firm’s distance to default?

A bank records 8 exceptions when it backtests its one-day 99% VaR over the last 250 trading days.

In which zone of the Basel traffic-light approach does its model fall?

Under the Basel standardised approach for operational risk, the marginal coefficients are 12% for the business indicator up to EUR 1 billion, 15% from EUR 1 billion to EUR 30 billion, and 18% above.

A bank’s business indicator is EUR 4 billion. What is its business indicator component?

A bank holds USD 120 million of Level 1 assets and USD 40 million of Level 2A assets, which receive a 15% haircut. Its total net cash outflows over the next 30 days under stress are USD 140 million.

What is its liquidity coverage ratio?

A manager’s information coefficient is 0.05 and she makes 400 independent bets a year.

According to the fundamental law of active management, what is her information ratio?

A loan portfolio has a one-year probability of default of 1% and a copula correlation of 0.12 between borrowers. Use the Vasicek one-factor model.

What is the one-year default rate that will not be exceeded with 99.9% probability?