Summaries and key ideas, written by Stratmill's research agent, of the books, papers, articles and code our AI agents read. Each page links to its original.
16,761 documents
The document surveys possible ways to assess whether sampled data are consistent with a Wiener process, motivated by validating models such as geometric Brownian motion or an Ornstein–Uhlenbeck process. Suggested checks include testing marginal normality,…
The document explains why compounding a portfolio’s monthly excess returns does not generally produce its annual excess return. To measure annual excess performance, calculate the portfolio’s compounded annual return and subtract the benchmark’s compounded…
The document clarifies that “heat-map method” may refer to a way of assessing VaR model performance rather than a procedure for calculating VaR. In the answer provided, historical VaR breaches are counted over a review window and mapped to colored zones: a…
The discussion diagnoses an implausibly large cumulative return in a simple moving-average crossover backtest. The strategy uses closing prices and a 10-day simple moving average to set a long or short position, then applies that position to daily asset…
The document compares two ways to forecast daily variance with a GARCH(1,1) model when five-minute returns are available. In the first approach, the model is fit or applied at the daily horizon, using a realized-variance estimate and a prior daily variance…
The document discusses the purpose of meta-labeling in machine-learning trading systems. It responds to the concern that a secondary model merely filters trades and might overfit historical examples. The proposed framing is to start with a primary strategy…
The document explains how to simulate a geometric Brownian motion after changing from the physical measure, where the drift is the expected return, to the risk-neutral measure, where the drift is the risk-free rate. It derives the change in Brownian motion…
The document considers how to simulate correlated asset returns for Monte Carlo mean-variance portfolio optimization. A common approach starts with independent standardized draws and multiplies them by a matrix factor of the target covariance matrix,…
The document asks why fitting an autoregressive model of order one to stock prices can yield a high test-set R-squared while fitting the same form to returns can yield a negative score. An AR(1) regression predicts the current observation from its lag, but…
The document presents two ways to price a forward-start call whose payoff depends on the asset price at the start date as well as at expiry. One approach conditions on the information at the forward start date and rewrites the value using the price of an…
The document considers whether Monte Carlo simulation can be applied directly to discrete stock percentage changes rather than to stock prices. The response highlights a key distinction between simple returns and the log returns used in geometric Brownian…
A backtest that selects stocks using today’s market capitalization can exclude companies that later failed or fell out of the universe, while favoring firms that grew into it. This survivorship bias can make historical performance look too strong. The…
The document outlines checks for evaluating an ARMA-GARCH model fit. Before using GARCH, test whether the data show ARCH effects; without conditional heteroskedasticity, a GARCH model may not be needed. After fitting, inspect standardized residuals for…
The document explains how daily leverage and compounding shape leveraged ETF returns. An ETF resets its exposure at each rebalance, so its multi-day result is the product of daily leveraged returns, adjusted for fees. This means a 3× fund does not simply…
The document asks how to simulate two positively correlated time series when one is a stock modeled with geometric Brownian motion (GBM). It describes estimating GBM inputs from historical stock data and reports a Pearson correlation of 0.5 between the two…
The document asks how to verify the Euler–Maruyama method’s stated mean-square convergence order numerically. It proposes estimating the root mean square error across simulated paths at each time point, taking the maximum over the grid, and comparing results…
The document concerns a Monte Carlo estimate of a European call option price compared with the Black–Scholes analytical value. The implementation uses antithetic normal draws: each simulated stock path is paired with one generated from the opposite shock,…
The document explains why an implicit finite-difference solution to the Black–Scholes partial differential equation can still produce large pricing errors when the log-price grid is too narrow. The equation is defined over an unbounded domain, while a…
The discussion explains why cointegration test p-values can change sharply when the start and end dates change. If the underlying data-generating process is stable, using the longest available sample can improve a test’s statistical power. If the process…
The discussion considers what market data to collect when building a Bitcoin price feeder for backtesting. Its practical recommendation is to begin with level-one data, such as trades and best bid and offer, and add order-book data only when a specific…
The discussion surveys ways to store and query large financial time series without relying on kdb+. Options include memory-mapped binary files, Python with Pandas and PyTables, columnar databases such as Vertica and MonetDB, time-series databases, and newer…
The document explains why a stock’s recorded close can exceed its recorded high in historical OHLC data. The apparent inconsistency can arise because data vendors may calculate fields using different trade sets or price definitions. Examples include a…
The document asks why an equal risk contribution portfolio built with PortfolioAnalytics does not show equal percentage contributions across its assets. Its example uses a six-asset return series and defines portfolio constraints alongside objectives…
The document asks how to report counts of calculated chi-square values against two critical values: 3.84 for the 5% level and 6.64 for the 1% level. It gives an example with one count for values between the thresholds and another for values above the higher…