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Level 1 · core
Start Here: The World of Quantitative Research · What quantitative research is
Quantitative research in finance is the disciplined use of data, statistics and programming to answer investment questions. Will this signal still predict returns next year? Is this strategy’s profit large enough to survive trading costs? H
Level 1 · core
Start Here: The World of Quantitative Research · A typical day of a quantitative researcher
No two firms are identical, but most research days mix the same ingredients. The morning often starts with checks: did the overnight data load correctly, did yesterday’s live strategies behave as expected, did any model output look strange?
Level 1 · core
Start Here: The World of Quantitative Research · The skills that matter, and where you will build them
Quantitative research sits where four skills meet. The first is mathematics and statistics: probability, distributions, correlation, inference and, later, linear algebra and optimisation. You do not need to be a mathematician, but you must
Level 1 · core
Start Here: The World of Quantitative Research · Where research ideas come from, and how they become questions
Research ideas come from many places. Economic reasoning suggests that investors demand extra return for bearing certain risks. Behavioural patterns, such as overreaction to news, suggest prices can temporarily move too far. Market structur
Level 1 · core
Start Here: The World of Quantitative Research · The main families of quantitative strategies
Most systematic strategies belong to a handful of families. Trend-following and momentum strategies bet that assets which have been rising will keep rising for a while. Mean-reversion strategies bet the opposite over shorter horizons: that
Level 1 · core
Start Here: The World of Quantitative Research · Careers and compensation
Entry routes vary. Many researchers join from quantitative degrees such as mathematics, statistics, physics, computer science, engineering or economics, often at master’s or PhD level for research-heavy roles. Others move in from software e
Level 1 · core
Start Here: The World of Quantitative Research · How AI helps quantitative researchers, and where it does not
AI tools have become everyday research assistants. Coding assistants write and explain data-cleaning scripts, plotting code and test harnesses much faster than typing them by hand. Language models summarise papers, draft documentation and h
Level 1 · core
Start Here: The World of Quantitative Research · Your roadmap through Level I
Level I is built as a staircase. Module 1, Thinking Like a Quant, gives you the research mindset: how a claim becomes testable, how to report uncertainty, why every result needs a benchmark. Module 2, Financial Data and Returns, teaches the
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Thinking Like a Quant · Testable claims and falsifiable predictions
A narrative gives an intuitive reason something might happen: “Investors panic after large losses, so a rebound must follow.” A hypothesis specifies what you will measure. Define the market universe, the information available when a decisio
Level 1 · core
Thinking Like a Quant · Observations versus explanations
An observation is something measured: the sample average return after an event is 0.4%. An explanation is a proposed mechanism: temporary selling pressure reverses. A decision is a further step: allocate capital. These statements need diffe
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Thinking Like a Quant · Reporting uncertainty with a result
A sample is one realization of a process, not a promise about the next realization. Ten successful outcomes out of ten can occur under many possible success probabilities. More observations usually help, but their relevance and dependence m
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Thinking Like a Quant · Benchmarks: better than what?
A benchmark is a relevant alternative against which a claim is evaluated. A positive return alone is not proof of skill: a passive investment exposed to the same rising market might have earned more. A directional model should also face a s
Level 1 · core
Thinking Like a Quant · Prediction, explanation and the next research step
Prediction asks whether information available now improves forecasts of an outcome not yet observed. Explanation asks why an outcome occurs. A variable can forecast an event because it proxies for another variable, while a plausible causal
Level 1 · core
Financial Data & Returns · Simple returns
A simple price return is the change in price divided by the starting price. Moving from 100 to 110 produces 10/100 = 10%. The denominator matters: moving back from 110 to 100 is −10/110, about −9.09%. Equal price changes need not be equal p
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Financial Data & Returns · Compounding and multi-period returns
Returns in successive periods act on different starting amounts. Multiply the wealth factors, 1 + return, rather than add the percentages. Starting with 100, a 50% gain creates 150; a subsequent 50% loss leaves 75. The cumulative return is
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Financial Data & Returns · Log returns and when to use them
A log return is the natural logarithm of the price ratio, ln(ending/starting), or ln(1 + simple return). It is a different representation of the same positive wealth ratio. A simple 10% return is a log return of about 9.53%; converting back
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Financial Data & Returns · Dividends, adjustments and total return
An investor can receive a cash dividend while the share price falls by a similar amount on the ex-dividend date. A price-only return may then report a loss even though price plus distribution is unchanged. A one-period total return adds the
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Financial Data & Returns · Volatility and sampling frequency
Volatility is commonly measured by the standard deviation of returns, which describes dispersion around their mean. Standard deviation has the same units as the returns; variance has squared units. A daily volatility of 1% is not directly c
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Probability for Financial Markets · Conditional probability
A probability describes an event within a specified information set or population. P(up) asks how often the next outcome is up in the reference setting. P(up | signal) asks how often it is up among observations where the signal occurred. Th
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Probability for Financial Markets · Independence of events
Events A and B are independent when learning B does not change the probability of A: P(A | B) = P(A), when the conditional probability is defined. Equivalently, P(A and B) = P(A)P(B). Independence is a modeling claim, not something establis
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Probability for Financial Markets · Expected value
Expected value is a probability-weighted average of outcomes. For a two-outcome trade, combine the probability of a win, average win size, probability of a loss, average loss size, and costs on a consistent per-trade basis. A high win rate
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Probability for Financial Markets · Base rates and Bayes' rule
Bayes’ theorem combines a prior probability with how likely a signal is under competing states. In everyday terms: count true positives and false positives, then ask what fraction of all positive signals are true positives. A detector can l
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Probability for Financial Markets · From signal accuracy to expected profit
A break-even win probability follows from the same expected-payoff equation. With average gain W, positive loss magnitude L, and fixed per-trade cost c, set expected net payoff to zero and solve p = (L + c)/(W + L). This calculation assumes
Level 1 · core
Financial Distributions · Measures of location: mean, median and mode
The arithmetic mean is the sum of observations divided by their count. It uses every value, so a single extreme outcome can move it substantially. The median is the middle value after sorting, or the average of the two middle values for an
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Financial Distributions · Measures of dispersion: variance and standard deviation
Variance averages squared deviations from a mean, with a denominator depending on the convention. A common sample variance divides by n−1 when estimating an underlying variance from independent observations. The sample standard deviation is
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Financial Distributions · Skewness and asymmetric outcomes
Skewness describes asymmetry. Positive skew is associated with a more extended right tail; negative skew with a more extended left tail. A strategy with many small gains and occasional large losses can look attractive in most months while r
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Financial Distributions · Fat tails and the normality assumption
A normal distribution is symmetric and fully described by its mean and variance. It is a useful model in some settings, but financial-return samples may show asymmetry, changing volatility, and more extreme observations than a fitted normal
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Financial Distributions · Outliers: investigate before treating
An outlier is unusual relative to a reference pattern. It can be a recording error, a corporate-action problem, a genuine market event, or evidence that the model is inappropriate. These possibilities call for investigation rather than auto
Level 1 · core
Financial Performance Metrics · Compound growth and drawdowns
Compound annual growth rate, or CAGR, is the constant annual rate that matches beginning and ending wealth over a stated number of years, assuming the wealth series properly handles cash flows. It does not mean each year actually earned tha
Level 1 · core
Financial Performance Metrics · Win rate, payoff ratio and profit factor
Win rate is the proportion of trades counted as winners. Define how zero-profit trades, fees, partial exits, and trade grouping are treated. A high win rate can come from taking small profits while retaining large downside risk.
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Financial Performance Metrics · The Sharpe ratio
A conventional historical Sharpe ratio divides the sample mean of per-period excess returns over the risk-free return by the sample standard deviation of those excess returns. The numerator and denominator must describe the same periods. Us
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Financial Performance Metrics · The Sortino ratio and downside risk
A common Sortino ratio divides mean return minus a specified minimum acceptable return by downside deviation relative to that target. Under one common convention, downside deviation is the square root of the average squared shortfall across
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Financial Performance Metrics · Comparing strategies across several metrics
A fair performance review aligns dates, currency, costs, leverage, benchmarks, and sampling frequency before comparing statistics. Request growth, variability, downside, drawdown, trade counts, and confidence in the estimates. A strategy’s
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Correlation & Dependence · Covariance and Pearson correlation
Covariance summarizes whether deviations from two means tend to have the same or opposite sign. Positive covariance indicates that above-average observations in one variable tend to accompany above-average observations in the other. Its mag
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Correlation & Dependence · Rank correlation and nonlinear relationships
Spearman correlation is Pearson correlation applied to ranks, with an appropriate tie convention. It measures whether larger observations in one variable tend to go with larger or smaller observations in the other, even if the relationship
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Correlation & Dependence · Autocorrelation
Autocorrelation measures a series’ association with its own lagged values. Lag-one autocorrelation compares each observation with the previous one. Positive autocorrelation suggests persistence in deviations; negative autocorrelation sugges
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Correlation & Dependence · Spurious correlation and causality
A spurious relationship is an apparent association that does not support the intended substantive conclusion. Two trending price-level series can appear closely related because both move through time. A third factor, sample selection, or re
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Correlation & Dependence · Diversification and the effective number of bets
For two assets, portfolio variance contains both individual variances and a covariance term. With equal volatilities and equal weights, portfolio volatility is σ√((1+ρ)/2). Lower correlation can reduce dispersion under this simplified setup
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Statistical Inference · Sampling and sampling variability
A population is the collection or process you want to understand; a sample is the set you observed. An estimator is a rule such as taking the sample mean. Its value varies from sample to sample, even if the underlying process does not chang
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Statistical Inference · Confidence intervals
A frequentist confidence interval is constructed by a procedure designed to cover a fixed unknown parameter at a stated rate across repeated samples under its assumptions. In a realized 95% interval, the parameter is not assigned a 95% prob
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Statistical Inference · Hypothesis tests and p-values
A hypothesis test compares observed data with what a specified null model would imply. The null might say the population mean excess return is zero. The test statistic, alternative, assumptions, and rejection rule should be defined before u
Level 1 · core
Statistical Inference · Statistical versus economic significance
Effect size describes the magnitude of the estimated relationship. Statistical significance depends on that magnitude relative to uncertainty. With enough suitable observations, a very small effect can be distinguishable from zero, while a
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Statistical Inference · Power, error types and the research process
A Type I error rejects a true null. A Type II error fails to reject a false null. Statistical power is the probability a specified test rejects the null under a particular alternative effect and its assumptions. Power depends on the effect,
Level 1 · core
Behavioral Finance & Market Psychology · How the mind judges risk: two systems and prospect theory
Psychologists describe two modes of thinking. The fast, automatic mode (often called System 1) recognizes patterns, reacts to vivid stories and produces an answer before you ask for one. The slow, deliberate mode (System 2) calculates, chec
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Behavioral Finance & Market Psychology · Cognitive biases: errors of judgment
Cognitive biases are systematic errors in how information is processed. Representativeness judges likelihood by resemblance: a short run of good returns looks like skill, and a company with a great story looks like a great investment, even
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Behavioral Finance & Market Psychology · Emotional biases: the disposition effect, regret and herding
Emotional biases come from feelings rather than faulty calculation, and they are harder to correct because knowing about them does not remove the feeling. Loss aversion is the root of several. The disposition effect is the tendency to sell
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Behavioral Finance & Market Psychology · From psychology to prices: underreaction, overreaction and bubbles
Individual biases only matter for prices if they are shared and if arbitrage cannot fully correct them. Arbitrage is limited in practice: trading against a mispricing costs money, needs capital that can be withdrawn at the worst time, and c
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Behavioral Finance & Market Psychology · Technical analysis, briefly and without the jargon
Technical analysis studies past prices and trading volume to anticipate future price moves. Its practitioners look for trends (prices drifting persistently in one direction), support and resistance (price levels where buying or selling seem
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Machine Learning Foundations · What machine learning is, and a short history
A traditional program follows rules a person wrote: if the price falls 5%, send an alert. A machine learning program is given examples of inputs and outcomes and finds a rule that maps one to the other. In plain terms, it learns from experi
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Machine Learning Foundations · Learning from data: models, loss and gradient descent
Every supervised model has three parts. A model family proposes a shape for the rule, such as a straight line ŷ = wx + b. A loss function measures how wrong a prediction is, such as the squared error (y − ŷ)². Training searches the family f