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 discusses how to choose a long-run growth or discount assumption for a perpetuity in firm valuation. One response suggests linking the rate to the valuation model and using a risk-free rate reduced by three percentage points for earnings-based…
The document discusses how to build mathematical foundations for quantitative finance and statistics. The questioner seeks rigorous, proof-based study of relevant tools such as linear algebra, probability, set theory, stochastic calculus, and measure theory,…
The discussion asks how to infer a stock price probability distribution from option prices and track changes in that distribution over time. One response identifies implied probability densities, also called state price densities, as the relevant framework.…
The document raises a portfolio selection problem: maximizing the Omega ratio for non-normal returns can favor assets with unusually high returns and produce a portfolio whose holdings have similar, correlated return patterns. The investor describes…
The answer explains how to move from a Bachelier underlying with an unspecified physical drift to a risk-neutral process for pricing a European call. It starts with the discounted asset price and uses the martingale condition to identify the required drift…
The document reviews a Heston option-pricing implementation that produces negative probabilities or prices under extreme inputs, despite giving plausible at-the-money results for other parameter choices. The implementation applies a characteristic-function…
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 explains why borrowing at the risk-free rate to scale a risky portfolio increases its expected excess return and volatility by the same factor. The Sharpe ratio uses excess return, so the leveraged portfolio’s numerator is the leveraged…
The note resolves how to obtain a short-maturity yield expansion from a Taylor expansion of a zero-coupon bond price. Starting with the price written as one plus successive powers of time to maturity, it applies the logarithm series and then negates and…
The document asks how to estimate term structures of default probabilities when market data is unavailable, including for non-listed firms. It notes that migration-based Markov chains can turn historical rating transitions into rating-specific default…
The document discusses a long-short portfolio formed by taking equal-weight average monthly returns for two groups of stocks, subtracting the mature group’s returns from the technology group’s returns, and regressing the spread on Fama-French market, size,…
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 proves that for thresholds a ≥ b, the expected value of a random variable conditional on being at least a is no smaller than its expected value conditional on being at least b, assuming the higher-threshold event has positive probability. This…
The document proposes measuring possible conflicts of interest between credit rating agencies and countries through the share of agency revenue associated with each country. The idea is to look beyond direct payments from governments and consider fees paid…
The note asks whether the expected product of increasing functions of two correlated stochastic processes rises as their instantaneous correlation rises. The response sketches an Itô-calculus argument in a simplified setting: it assumes zero drift and unit,…
The document asks whether Value at Risk at probability levels α and 1−α has a general relationship when the loss distribution is asymmetric. Using a definition based on a tail probability quantile, the answer says there is no such general relationship: VaR…
The document introduces stopping times using a filtration to represent information available over time. A decision time is a stopping time when whether it has occurred by time t can be determined from information available by t. It applies this idea to…
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 document examines whether an option and its underlying stock require risk premiums in a binomial pricing model when their payoffs can be replicated using other instruments. The central issue is a confusion between replication and hedging: constructing a…
The document asks how to infer a client’s risk-aversion parameter from an already chosen optimal portfolio of two assets under quadratic utility and a full-investment constraint. It defines portfolio utility as expected return minus a variance penalty, with…
The document considers whether an FRA rate or an interest rate futures rate is the better proxy for an expected future fixing. The two instruments can imply different values because their settlement structures create a convexity difference. The answers…
The document presents a Delphi implementation of the Black-Scholes formula for European call and put options. It calculates the standard d1 and d2 terms from spot price, strike, time to expiration, interest rate, and volatility, then applies the cumulative…
The answer distinguishes daily returns from intraday returns when calculating historical volatility. For close-to-close volatility, it describes taking the standard deviation of daily log returns and scaling by the square root of an assumed number of trading…