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 considers whether ESG can be added as a factor to the Fama–French five-factor model and how such an extension should be interpreted. It distinguishes a factor that captures exposure to priced cash-flow risk from a preference for firms with…
The document addresses a choice of risk-free rate when calculating CAPM quantities or evaluating a portfolio strategy. The question contrasts a three-month Treasury rate with a ten-year rate for a strategy whose lookback window is one year and asks whether…
The document describes a way to account for recurring time-of-day patterns when estimating volatility with GARCH on hourly returns. It recommends estimating a deterministic intraday periodicity component and filtering returns by that component before fitting…
The document considers prediction of a continuous variable when correctly ordering observations matters more than matching their values in a way that maximizes Pearson correlation. One simple approach is to transform the target into ranks and fit an ordinary…
The answer explains that an MA model represents a series using current and past shocks, rather than past observed values. It suggests comparing simulated AR(1) and ARMA(1,1) series with the same errors to see how the moving-average coefficient changes their…
The document investigates why a simulated call price comes out as zero when the Black–Scholes calculation gives a positive value. Its proposed remedy is to simulate the underlying under the risk-neutral geometric Brownian motion process, using the risk-free…
The document outlines a Monte Carlo approach for valuing performance share units whose payout depends on a company’s share-price performance relative to a peer group. It estimates daily log-return means, volatilities, and correlations from historical prices,…
The document explains how to aggregate ordinary monthly returns into quarterly returns. For each quarter, add one to every monthly return, multiply those gross returns together, and subtract one. This captures the effect of sequential returns; simply summing…
For normally distributed asset returns with known means and covariance, the document relates portfolio VaR optimization to familiar portfolio objectives. When VaR is defined as a return quantile centered on the portfolio mean, maximizing it is equivalent to…
The document considers how to specify the mean equation when forecasting stock index return volatility with a GARCH model. One workflow first selects AR and MA terms for the mean using an ARIMA procedure, estimates that equation by least squares, and checks…
The document describes a proposed way to compare an algorithm’s backtest with a simple benchmark portfolio. The benchmark buys some or all stocks in a selected universe at the start of the test period, then closes positions at the end, with transaction fees…
The document explores why historical replay alone may not faithfully test market-making or other microstructure strategies. A replay uses recorded order-book events, but cannot fully capture how other participants would react to the strategy's orders. The…
The document examines how to simulate multiple geometric Brownian motion price paths with a specified correlation structure. The attempted R approach draws independent normal shocks, applies a Cholesky factor of the input correlation matrix, and uses the…
The document addresses the lack of long histories for Treasury bond ETFs, especially leveraged funds, when backtesting portfolios over periods earlier than those products existed. It suggests using long bond futures as a proxy source of historical exposure…
The document explains why testing the CAPM by regressing individual stocks’ realized excess returns on estimated betas can produce a very low R-squared. Low fit does not by itself show the model is false: CAPM does not predict a particular R-squared, and a…
The document asks where to obtain long histories of arbitrage basis measures, such as the difference between on-the-run and off-the-run securities. It offers both direct sources for precomputed measures and sources from which researchers could assemble their…
The document raises a practical question about annualizing a Sharpe ratio calculated from a strategy that trades on five-minute or hourly bars. It contrasts the familiar daily scaling factor based on 252 trading days with scaling by the square root of the…
The document discusses how to combine long and short strategies when their signals are ranks with different scales. Directly averaging or adding those signals may not produce sensible portfolio exposures, so the answer frames the task as assigning capital…
This document explains how to calibrate a pricing model by selecting parameters that bring model prices close to observed market prices, using an error measure such as mean absolute error or root mean square error. It discusses choosing an optimization…
The document asks how to calculate a basic win percentage for a trend-following model that produces long and short signals. The proposed approach is to compare the price when a signal begins with the price when the signal changes, count a trade as a win if…
The document diagnoses why a Monte Carlo estimate of a European call price differs sharply from its Black–Scholes value. In the simulation, the stock paths use a drift parameter called mu, while the Black–Scholes calculation prices the option using the…
The discussion distinguishes computational limits by workload. For real-time trading, it argues that network throughput is often the constraint, while historical analysis is more commonly limited by memory capacity or bandwidth; ordinary CPU use may not be…
The document discusses choosing block lengths when resampling returns to simulate long investment horizons for portfolio allocation analysis. Its main principle is to choose a length that preserves dependence patterns relevant to the portfolio, including…
The document defines vol-vol breakeven as the instantaneous covariation of log implied volatilities for two options. For a local volatility model, when both options are the same contract, it gives a formula relating this quantity to the spot sensitivity of…