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 generate many asset return histories that match summary statistics from capital market assumptions, including expected returns, quartiles, volatilities, and incomplete correlation information. One response suggests initially setting…
The document asks how to adapt the differential Sharpe ratio reward used in a trading reinforcement learning system so that it instead reflects the Sortino ratio. The proposed motivation is that the traded assets are volatile and positively skewed, making…
This note distinguishes a local trading hedge from protection against large portfolio losses. For a position in one asset hedged with another, a correlation-based hedge weight can help manage small, day-to-day changes in portfolio value. A tail-focused hedge…
This note examines an apparent arbitrage in put-call parity when a stock follows a zero-drift Black-Scholes process, with no interest or dividends. For a strike equal to the current stock price, parity makes the call and put prices equal. The apparent puzzle…
The document outlines an Euler–Maruyama simulation for log asset prices under a local volatility model, using volatility that varies with time and the asset level. It asks which drift to use for option valuation versus estimating the real-world chance of an…
The document explains why Fama–French style time-series regressions use returns on factor portfolios, such as SMB and HML, rather than a stock’s size or book-to-market characteristics directly. Factor portfolio returns represent the payoffs associated with…
The document asks how the persistence coefficient in an AR(1) model for consumption growth affects the process. It identifies a zero coefficient as the case where growth has no dependence on its previous value; if the innovations are independent and…
The document presents an unfinished R simulation of traders whose buy, sell, or neutral decisions are updated using sampled decisions from other traders. Initial actions are assigned probabilistically, each trader observes a subset of peers, and the…
The document describes a user’s attempt to create a risk-return scatter plot from quarterly portfolio returns that include missing values. Replacing missing entries with zero does not resolve the problem: the assignment expression passed to the plotting…
The document considers how to balance minimum-variance portfolio construction with maximum diversification. It presents several responses: the minimum-variance and maximum-diversification portfolios are each unique and generally differ; treating both…
The document derives lower and upper bounds for a European call using payoff dominance. A call payoff cannot exceed the underlying asset’s payoff, so its price is at most the asset price. It also dominates both zero and the payoff from holding the asset…
The document studies the stochastic integral of an exponential deterministic function against a Wiener process over a finite time interval. It identifies the integral as a Wiener integral, which is normally distributed with mean zero. Its variance follows…
The document compares monthly and daily regressions of a portfolio described as 70% India and 30% USA against SMB, HML, WML, and a market excess return. It reports different coefficient estimates and significance levels across frequencies: the monthly…
The document asks how the Hayashi–Yoshida estimator for asynchronously sampled asset returns relates to realized variance and Pearson correlation. It describes realized variance as the sum of squared returns and the Hayashi–Yoshida covariance estimator as a…
The document derives a conditional expectation of cumulative inflation when nominal and real short rates follow correlated mean-reverting Gaussian diffusions. It first writes each rate as its initial value, an integrated drift contribution, and a stochastic…
The discussion separates unit-root testing from the different meanings of stationarity. An augmented Dickey–Fuller test evaluates evidence for a unit root under its model assumptions; a conclusion about that test does not by itself establish that a series is…
The document considers an OTC swap intended to offset deviations of stochastic contract cashflows from their expected values. It frames the central pricing question as determining the premium for taking on that residual variability, which may arise from…
The document explains two common ways to estimate yields for a particular tenor when several bonds have different original maturities but similar time remaining. A market data provider may use a recently issued, liquid benchmark bond for each tenor,…
The document explains why ARMA coefficients estimated together with a GARCH variance model can differ from coefficients estimated in an ARMA model alone. The variance component accounts for changing volatility, which can affect the mean-equation estimates.…
The document distinguishes daily log returns from the logarithm of a simple percentage return. For consecutive closing prices, the standard log-return definition takes the natural logarithm of the current price divided by the previous price. This expresses…
The document offers research guidance for studying whether neural networks can predict liquidity or bid-ask spreads from market depth data. It recommends preparing the data carefully, considering zero or negative spreads, and planning how limited…
The document raises a practical issue in rolling indicators built from tick data across a market close. Ticks immediately before the prior close may have different statistical properties from ticks after the next open, yet a fixed lookback such as the…
The document discusses how to normalize stock data when comparing series, such as through correlation analysis. Its responses recommend working with returns rather than raw prices because price levels are generally nonstationary, and favor subtracting a…
The document asks whether European options can be priced in closed form when the variance gamma model’s drift, volatility, and variance rate are random. It explains that unrestricted random coefficients generally do not yield a closed-form price:…