Quantitative Methods
The whole Quantitative Methods reading in short lessons: the idea, the formula, one worked example with calculator keys, the exam traps and a quick check.
How this topic is tested, its exam weight and study tips: Quantitative Methods exam guide.
FlashcardsPDF · A4 · 103 pages
Quantitative Methods formula sheet
All 348 formulas of the topic, each explained. Every module page ends with its own formulas; the key formulas are here. Downloads come with a subscription or a pass; the free trial does not include them.
What an interest rate is made of, and every way the curriculum measures a return: holding period, arithmetic, geometric, harmonic, trimmed and winsorized means, money- vs time-weighted, annualised, continuously compounded, and gross, net, after-tax, real and leveraged returns.
- What an interest rate is made of13 min
- Holding period return12 min
- Arithmetic and geometric mean returns13 min
- Harmonic, trimmed and winsorized means13 min
- Money-weighted return13 min
- Time-weighted vs money-weighted returnVideo · 7 min14 min
- Integrated cases: balance tables, money-weighted and time-weighted returns16 min
- Annualised and continuously compounded returnsVideo · 6 min14 min
- Gross, net, after-tax, real and leveraged returnsVideo · 7 min14 min
- Integrated cases: from total return to what the investor keeps15 min
How to price bonds, loans and shares as the present value of their cash flows, how to read implied returns and growth rates back out of market prices, and how cash flow additivity and no arbitrage set forward interest rates, forward exchange rates and option values.
- Present value and discount (zero-coupon) bondsVideo · 6 min13 min
- Coupon bonds and perpetual bonds13 min
- Level-payment instruments: mortgages and amortizing loansVideo · 7 min12 min
- Valuing shares with dividend discount models14 min
- Implied returns on bonds13 min
- Required return, implied growth and the P/E ratio14 min
- Cash flow additivity, no arbitrage and forward rates14 min
- No-arbitrage pricing of FX forwards and options15 min
How to summarise a return series and judge what the summary is worth: where the data are centred and located, how widely they spread, what shape they have, and how two series move together, plus the pitfalls of each measure.
- Mean, median, mode and outliers14 min
- Quantiles, box plots and their uses14 min
- Range, mean absolute deviation, variance and standard deviation14 min
- Target downside deviation and coefficient of variationVideo · 7 min13 min
- Skewness and kurtosisVideo · 6 min15 min
- Scatter plots, covariance and correlation14 min
- Limits of correlation analysis12 min
- Integrated cases: describing one return series from raw data15 min
Probability tools for investment decisions under uncertainty: expected value and dispersion of a random outcome, probability trees with conditional expectations, and Bayes' formula for updating a probability when new information arrives.
- Expected value, variance and standard deviationVideo · 7 min14 min
- Conditional probability and probability trees14 min
- Conditional expected values and variancesVideo · 6 min15 min
- Bayes' formula: updating a probability with new informationVideo · 5 min15 min
- Bayes in practice: diffuse priors, missing inputs and screening tests14 min
- Integrated cases: a tree with model forecasts and a Bayes update15 min
How a portfolio's expected return and risk follow from its holdings: weights, covariance and correlation, the covariance matrix, diversification, covariance from a joint probability function, and Roy's safety-first rule for limiting the chance of falling below a minimum return.
- Portfolio expected return and varianceVideo · 6 min13 min
- Covariance and correlation13 min
- The covariance matrix and many-asset portfolios13 min
- Correlation and diversification12 min
- Covariance from a joint probability function14 min
- Shortfall risk and Roy's safety-first criterion13 min
- Shortfall probability, the Sharpe ratio and VaR12 min
Why asset prices are modelled as lognormal when continuously compounded returns are normal, how returns and volatility scale with time, and how Monte Carlo simulation and bootstrap resampling generate thousands of scenarios to measure risk and value complex securities.
How to learn about a population from a sample: the five main sampling methods and what they mean for sampling error, why sample size and a single population matter, the central limit theorem and the standard error of the sample mean, confidence intervals for the mean (z vs t), and bootstrap and jackknife resampling.
- Populations, samples and sampling error13 min
- Stratified and cluster sampling14 min
- Convenience and judgmental sampling, and choosing a method12 min
- Sample size and mixing populations12 min
- The central limit theorem13 min
- The standard error of the sample meanVideo · 6 min13 min
- Confidence intervals for the mean15 min
- Bootstrap and jackknife resampling14 min
How to use a sample to judge a claim about a population: the six-step process, Type I and Type II errors, power, critical values and p-values, tests of one mean, two means (independent and paired) and variances (chi-square and F), and when a nonparametric test is the better choice.
- The six steps and stating the hypotheses13 min
- Type I and Type II errors, significance and powerVideo · 5 min12 min
- Critical values, p-values and the decision ruleVideo · 7 min13 min
- Testing a single mean13 min
- Two means: independent vs paired samplesVideo · 6 min14 min
- Testing variances: chi-square and FVideo · 7 min14 min
- Parametric vs nonparametric tests12 min
How to test whether two variables are related: the parametric t-test on a Pearson correlation, the non-parametric Spearman rank correlation when normality is doubtful or the data are ranks, and the chi-square test of independence for categorical data in a contingency table, including how to read standardized residuals.
- Parametric vs non-parametric tests, and correlation hypotheses12 min
- The t-test for a Pearson correlation13 min
- Sample size, p-values and many correlations at once13 min
- The Spearman rank correlation testVideo · 7 min14 min
- Contingency tables and the chi-square test of independenceVideo · 6 min14 min
- Interpreting the result: standardized residuals and mosaics12 min
Simple linear regression explains the variation in one variable using one other variable. You learn how least squares fits the line, how to read the coefficients, which assumptions must hold, how to judge the fit with ANOVA, \(R^2\), the F-test and the standard error of the estimate, how to test coefficients, how to build a prediction interval, and how log transformations handle curved relationships.
- The regression model and least squares14 min
- Interpreting coefficients, fitted values and residuals12 min
- The four assumptions and residual plotsVideo · 7 min13 min
- Sums of squares, \(R^2\), the ANOVA table and the SEEVideo · 6 min14 min
- Testing the slope: t-test, correlation test and F-testVideo · 7 min15 min
- Intercept tests, indicator variables and p-values13 min
- Forecasts and prediction intervals13 min
- Functional forms: log-lin, lin-log and log-logVideo · 7 min13 min
- Integrated cases: reading a full regression printout16 min
How fintech is changing investment analysis: what makes data 'Big', where alternative data come from and what can go wrong with them, how machine learning learns (and overfits), the main types of ML, how data scientists process and display data, and how text analytics and NLP turn words into investment signals.
- Fintech and the four Vs of Big Data12 min
- Sources of Big Data and its challenges13 min
- AI and how machine learning learns12 min
- Overfitting, underfitting and model fit11 min
- Supervised, unsupervised and deep learning12 min
- Data science: processing and visualisation12 min
- Text analytics, NLP and data science tools14 min