Quick reference

Cheat sheets

One printable page per built lesson: the formulas with their symbols, a worked example in three lines, the exam traps, and how to recognise the question. 44 so far; each lesson page also links to its own sheet.

R1 · Probability for risk

• Events, conditional probability and independence QTA 1
• Bayes rule: updating a probability with evidence QTA 1
• Random variables: PMF, PDF, CDF, quantiles QTA 2
• Moments: mean, variance, skewness, kurtosis QTA 2

R2 · The distributions you will meet

• Discrete families: Bernoulli, binomial, Poisson QTA 3
• Continuous families: uniform, normal, lognormal, t, chi-square, F QTA 3
• Joint, marginal and conditional distributions QTA 4
• Covariance, correlation and the bivariate normal QTA 4

R3 · From sample to conclusion

• Estimators, the law of large numbers and the CLT QTA 5
• Sample skewness, kurtosis, quantiles and covariance QTA 5
• The hypothesis-testing recipe QTA 6
• Tests on means, testing alpha, and the multiple-testing trap QTA 6

R4 · Regression, done properly

• OLS with one regressor QTA 7
• Inference on coefficients, dummies, and beta QTA 7, FRM 5
• Multiple regression, the F-test and factor models QTA 8, FRM 6
• Regression diagnostics: heteroskedasticity, outliers, specification QTA 9

R5 · Time series

• Stationarity, white noise and AR(1) QTA 10
• MA, ARMA, forecasting and model selection QTA 10
• Trends, unit roots and spurious regression QTA 11

R6 · Returns, volatility, dependence

• Returns and realised volatility QTA 12
• EWMA and GARCH(1,1) QTA 12, VRM 3
• Fat tails, Jarque-Bera and rank correlation QTA 12

R7 · Simulation and learning machines

• Monte Carlo, variance reduction and the resampling bootstrap QTA 13
• Machine learning: data, PCA, K-means and validation QTA 14
• Prediction: logit, trees, ensembles, KNN, SVM, neural nets QTA 15

R8 · Value at risk in practice

• VaR, expected shortfall and coherence VRM 1
• Historical simulation and stressed VaR VRM 2
• Delta-normal VaR and VaR for options VRM 2

R9 · Credit measured

• Ratings, transitions and hazard rates VRM 4
• Expected loss, unexpected loss and the Vasicek model VRM 6

R10 · Rates and bonds for the exam

• Pricing conventions: T-bills, bonds between coupons, par rates VRM 9–10, FMP 16
• Realised return, carry roll-down and the P&L decomposition VRM 11
• DV01, duration, convexity and the two-bond hedge VRM 12
• Key-rate 01s, bucketing and PCA hedging VRM 13
• Mortgages, prepayment and MBS FMP 18
• Bond futures, cheapest-to-deliver and SOFR futures FMP 19
• Swaps and FRAs, exam style FMP 20, FMP 16

R11 · Derivatives pricing for the exam

• Futures markets, basis and the hedge ratio FMP 7–8
• Cost of carry: financial and commodity forwards FMP 10–11, FMP 9
• Option bounds, put-call parity and early exercise FMP 13, FMP 12
• Strategies and exotics FMP 14–15
• Binomial trees and Black-Scholes-Merton VRM 14–15
• The Greeks and delta hedging VRM 16

R12 · Operational risk, insurance and capital arithmetic

• Operational risk, insurance and capital arithmetic VRM 5, FMP 1–2, FRM 1–3