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45 dokumentų
This lecture explains how the Capital Asset Pricing Model relates expected asset returns to a risk-free rate and exposure to broad market risk. It distinguishes diversifiable, firm-specific risk from systematic risk, and uses regression beta to estimate an…
This lecture introduces portfolio Value at Risk (VaR) as a loss threshold associated with a chosen coverage level, then demonstrates historical VaR by calculating a low percentile of weighted portfolio returns over a lookback window. It contrasts this…
This lecture explains how hypothesis tests use sample data to assess claims about population values, with examples focused on whether a stock’s mean return differs from zero. It distinguishes null and alternative hypotheses, one-sided and two-sided tests,…
The document surveys measures of how widely observations vary around a central value. It defines the range, mean absolute deviation, variance, and standard deviation, noting that standard deviation is expressed in the same units as the observations and that…
The document compares arithmetic, weighted arithmetic, median, mode, geometric, and harmonic measures of central tendency. It explains how the arithmetic mean summarizes values by addition, while the median resists the influence of extreme observations and…
The document introduces autoregressive models, which predict a time series from its own lagged values, and explains that meaningful estimation requires covariance stationarity: a stable finite mean, variance, and lagged covariance over time. Financial series…
The document explains how covariance describes the way asset returns vary together and how a covariance matrix collects these relationships alongside each asset’s variance. Portfolio construction uses this matrix to estimate combined risk, assess…
The document presents a workflow for reviewing a trading portfolio with performance statistics and diagnostic plots. It describes common measures such as Sharpe ratio, market beta, and maximum drawdown, along with return distributions, cumulative and…
The document distinguishes share volume from dollar volume and explains why bar data may report averaged, volume-weighted, or last-traded prices. It describes common intraday volume patterns in US equities, including higher activity near the open and close,…
The document explains how market beta and sector exposure can make a portfolio’s individual forecasts move together, reducing the number of independent bets and, in turn, its risk-adjusted potential. It frames this through the Fundamental Law of Active…
The document explains a cross-sectional long-short equity strategy: rank stocks with a model, buy the highest-ranked names, and short the lowest-ranked names using balanced dollar exposure. It presents the ranking signal as the strategy’s main source of…
This lecture uses factor models to explain portfolio returns and quantify exposure to systematic sources of risk. It describes regressing active returns, measured relative to a benchmark, on factor returns, then using estimated sensitivities and factor…
This lecture explains how universe selection defines the securities available to a trading algorithm and can shape both strategy behavior and risk. It presents a daily screen for common stocks ranked by average dollar volume as a basic liquidity filter,…
This lecture introduces the Kalman filter as a method for estimating an evolving system state from a model and noisy observations. The filter alternates between predicting the next state and updating that estimate with new measurements. Transition and…
This lecture explains stationarity, orders of integration, and why these properties matter when analyzing financial time series. A stationary process has stable data-generating characteristics, while changes such as a drifting mean can make a historical…
The document explains Spearman rank correlation as a measure of whether two variables move in the same or opposite order, including when their relationship is monotonic but not linear. It computes correlation from ranked observations, assigns tied values…
The document introduces linear factor models that explain an asset’s returns through exposures to fundamental factor return streams. It describes two ways to make company characteristics comparable: construct long-short portfolios by ranking stocks on…
The document explains how spreading exposure across independent or weakly correlated bets can reduce portfolio volatility, while adding highly correlated assets may leave risk largely unchanged. It illustrates the principle first with simulated bets that…
The document defines correlation as covariance scaled by the standard deviations of two series, yielding a measure between -1 and 1 that is easier to compare across data. It explains covariance and correlation matrices, with examples showing positive,…
This lecture explains why running many statistical tests increases the chance of finding apparently significant relationships by chance. It illustrates the issue by testing pairwise Spearman rank correlations among independent random series. When the null…
This introductory lesson explains how common plots can help researchers inspect financial data and notice possible structure or data problems. Using daily prices for two US equities as examples, it demonstrates histograms for empirical distributions,…