Quantitative methods
What do the numbers mean, and how much can you conclude from a sample of them?
14 of 14 chapters published
Chapters
Beginner
- Time value of money, derivedEvery valuation in finance is one idea applied repeatedly: a rupee later is worth less than a rupee now. This derives the formulas rather than quoting them, because a formula you can rebuild is one you can check.
- Rates: nominal, effective and continuousThe same rate quoted three ways gives three different answers, and only one of them is what you actually earn. This is where most comparisons between financial products quietly go wrong.
- The statistics that actually matterMean, median, variance, skew and the one that catches people out — why the average annual return is not the return you got, and why the two differ by an amount you can calculate.
Intermediate
- ProbabilityThe rules are few and the mistakes are predictable. Conditional probability is where almost every real error lives, including the one that makes a 99% accurate fraud test mostly wrong.
- Random variables and expectationExpected value is the weighted average of what could happen, and it is the single most misused idea in finance — because almost nobody gets to repeat a bet enough times for the expectation to arrive.
- The normal distribution, and where it liesThe bell curve is the default assumption behind most of finance, and it understates extreme days by orders of magnitude. Both halves of that sentence need to be true at once.
- The lognormal case, and why returns use logsPrices cannot go negative and returns do not add, which breaks the normal model in two ways. Taking logarithms fixes both, and that single change is why option pricing works at all.
- Sampling and the central limit theoremEverything you measure in finance is a sample, and a sample is not the truth. The central limit theorem says how far off it is likely to be, which is the only reason any of it is usable.
- Confidence intervalsA range is an honest answer where a single number is not. What a 95% interval actually claims is narrower than what people hear, and the difference matters when the decision is yours.
Advanced
- Hypothesis testingA formal way to ask whether a result could be chance. It is also the machinery behind most false findings in finance, because testing enough ideas guarantees some of them pass.
- Simple regressionFitting a line through a cloud of points, and reading what it means. This is where beta comes from, and where R-squared gets over-interpreted.
- Multiple regression, and what breaks itMore explanatory variables, more ways to be wrong. Multicollinearity, overfitting and omitted variables are the three that matter, and all three produce confident, wrong answers.
- Time series, stationarity and autocorrelationData in time order breaks the independence everything else assumed. Volatility clusters, prices trend without meaning anything, and two unrelated series can regress beautifully against each other.
- SimulationWhen the maths has no closed form, generate the outcomes instead. Monte Carlo answers questions formulas cannot — and inherits every assumption you fed it, while looking far more authoritative than it is.