FRM Practice Questions
Financial Risk Manager
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View all →- Quantitative AnalysisHardPart IA GARCH(1,1) model estimated on 1,250 daily returns yields omega = 0.000003, alpha = 0.08, and beta = 0.90. Today's squared return is 0.0009 (a 3% move) and today's conditional variance is 0.000200. The 1-day-ahead variance forecast and the long-run annualized volatility are closest to:
- Quantitative AnalysisMediumPart IAn analyst applies the Augmented Dickey-Fuller (ADF) test to daily USDJPY exchange rates and obtains a test statistic of -2.15. The 5% critical value is -2.86. She then tests USDJPY daily returns and obtains a statistic of -22.8. Which conclusion is correct?
- Quantitative AnalysisEasyPart IWhich variance reduction technique involves generating each random draw alongside its mirror image to reduce Monte Carlo estimation error?
- Quantitative AnalysisHardPart ITwo assets have a correlation of 0.7. Using Cholesky decomposition to generate correlated standard normal variables, if the independent draws are Z1 = 1.5 and Z2 = -0.8, the correlated variable for asset 2 is closest to:
- Quantitative AnalysisMediumPart IDuring the COVID-19 crash in March 2020, the correlation between equity and bond returns jumped from -0.25 to +0.55 within two weeks. This phenomenon is best described as:
- Quantitative AnalysisMediumPart IA portfolio's daily returns have excess kurtosis of 5 and skewness of -0.6. Using the Cornish-Fisher expansion, the adjusted z-score at the 99% confidence level (standard z = -2.326) is closest to:
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Part I
85 questions
A GARCH(1,1) model estimated on 1,250 daily returns yields omega = 0.000003, alpha = 0.08, and beta = 0.90. Today's squared return is 0.0009 (a 3% move) and today's conditional variance is 0.000200. The 1-day-ahead variance forecast and the long-run annualized volatility are closest to:
An analyst applies the Augmented Dickey-Fuller (ADF) test to daily USDJPY exchange rates and obtains a test statistic of -2.15. The 5% critical value is -2.86. She then tests USDJPY daily returns and obtains a statistic of -22.8. Which conclusion is correct?
Part II
95 questions
A portfolio manager considers three tail risk hedging strategies: (1) 20% OTM puts costing 1.2% per quarter, (2) put spreads (20-35% OTM) costing 0.4% per quarter, and (3) a long variance swap position. Which strategy provides the MOST convex payoff in an extreme tail event (market drops 40%)?
A bank has a large portfolio of FX derivatives with an emerging market counterparty. As the EM currency depreciates, the mark-to-market value of the derivatives (owed by the EM counterparty to the bank) increases, while the counterparty's credit quality deteriorates due to the same FX move. This situation is an example of:
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