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.
21,023 documents
The document asks how to model prices that are pulled toward a target value but may overshoot it when momentum persists. It presents a discrete return regression with both a lagged-return term and a target-gap term, then reviews possible continuous-time…
The document compares two objective types for calibrating a one-factor Hull–White interest-rate model to caplet or similar market data. A price-based calibration minimizes differences between quoted instrument prices and prices produced by the model. A…
The document addresses an apparent conflict between the Black–Scholes relationship linking spot and forward prices and models that assign different volatility processes to forwards with different maturities. With a constant interest rate and a deterministic,…
The document clarifies that mean-variance portfolio optimization does not require every asset’s return history to have the same length. It requires a covariance matrix, which may be estimated from data, proxies, or judgment. The practical problem is how to…
The document considers whether principal component analysis of US Treasury rates should use cash yields or Treasury futures. It recommends constant-maturity par yields, which keep the maturity of each series stable as bonds and futures delivery baskets…
The document outlines a practical architecture for calculating value at risk when a trading system already generates simulated market scenarios, such as interest rate curves. In that setup, the main task is to reprice instruments under each scenario rather…
The document asks how to convert information coefficients observed at a monthly frequency into an annualized information ratio. It presents a proposed scaling formula and raises a discrepancy with a sample calculation that applies an additional factor. The…
The document considers pricing a discounted payoff that depends jointly on two equity prices at a future date. Its central point is that pricing requires a joint risk-neutral distribution; a copula is one way to construct one, but it is not the only possible…
The document concerns maximizing a portfolio's Sharpe ratio when expected excess payoffs and the covariance matrix of asset payoffs are given. It writes the objective as expected excess payoff divided by portfolio volatility, then differentiates it with…
The document discusses preparing technical indicator time series as inputs to a neural network. It presents two basic transformations: use differences between consecutive observations, or use percentage changes to express relative movement. When combining…
The document derives the exponential correction needed when expectations of products and powers of jointly log-normal variables are rewritten using their individual means. The motivating expression involves a numerator with a variable multiplied by a powered…
The document asks how to obtain a risk-neutral probability measure from a real-world model under a no-arbitrage assumption. It gives a geometric Brownian motion example in which an asset has drift and volatility under the real-world measure, while a…
The document presents a binomial pricing exercise for an American call option whose underlying is a futures contract. The stock tree is calibrated to a Black–Scholes geometric Brownian motion setup, while the option expires before the futures contract…
The document explains why a historical return histogram may compare simple returns with a normal distribution even though geometric Brownian motion implies normally distributed log returns and lognormally distributed prices. For small price changes, the…
The note addresses whether negative risk-free rates invalidate the CAPM or the use of a risk-free rate when calculating market excess returns in the CAPM and Fama–French three-factor model. Its answer is that the CAPM does not require the risk-free rate to…
The note considers cross-sectional estimation of factor returns when asset-loading columns are linearly dependent. Ordinary least squares then has no unique solution because the loading matrix’s cross-product is singular. A market factor combined with…
The document outlines a proposed workflow for applying an Ornstein–Uhlenbeck process to a pair of potentially cointegrated stocks. The suggested steps are to estimate a linear relationship by OLS, form a residual or auxiliary series, fit an AR(1) model to…
The document examines why adding risky assets can move the mean–variance frontier toward lower volatility without making it approach zero in every case. For equal-variance, uncorrelated assets, it considers an equally weighted portfolio and shows that…
The document asks how to price derivatives when the underlying follows an arithmetic Brownian motion rather than the geometric Brownian motion used in the Black–Scholes model. It starts with an additive diffusion under the physical measure, then proposes…
The document asks how to estimate a company’s pre-tax cost of debt when its borrowings include bonds with different coupon rates, maturities, and repayment schedules. The proposed method is to calculate the yield on each bond for the relevant fiscal year,…
The document discusses converting a quoted three-month Treasury bill rate into a weekly risk-free return and subtracting it from an asset’s weekly log return. It endorses scaling the log of one plus the quoted annual rate by the weekly fraction of a 360-day…
The document explains how to price a zero-coupon bond when yields differ across maturities. Its key distinction is between a bond’s maturity-specific zero-coupon spot rate and the sequence of one-year forward rates. Under annual compounding, discounting the…
The document examines negative variance-equation intercept estimates in a GJR-GARCH model with a pandemic indicator as an exogenous input. The response writes a simplified model with a regime indicator and an asymmetric term for negative shocks, then argues…
The document explains how to attribute a portfolio’s volatility to a subset of its assets, such as an equity sector, while accounting for the portfolio covariance structure. It defines an asset’s marginal risk contribution as the change in portfolio…