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.
5,922 documents
The document proposes combining annualized returns measured over several horizons with a weighted mean and weighted standard deviation. It illustrates assigning each horizon a weight that decays exponentially with its length, controlled by a chosen decay…
The document surveys possible developments in quantitative finance that could gain wider use or appear in future textbooks. It describes machine learning as a newer tool applied to established tasks, including risk analysis, risk management, and algorithmic…
The document asks how investors’ target risk might be chosen in light of wealth, future income, savings, housing, and expected expenses. It contrasts this problem with broad allocation rules and age-based target-date strategies, then proposes a questionnaire…
The document asks whether adding a derivative that depends on an otherwise unspanned source of risk makes an incomplete market complete. It sets up a continuous-time market with fewer traded risky assets than Brownian risk sources, including an example where…
The document frames a portfolio stress test for zero-coupon bonds using key-rate DV01 exposures. Each maturity bucket has minimum and maximum allowed DV01 bounds, and the sum of the bucket exposures is subject to an overall limit. Given a stress vector…
The document outlines a Monte Carlo procedure for generating joint price paths for several stocks. First, draw a matrix of returns whose asset-level observations at each time step follow a specified multivariate distribution, using a covariance structure to…
The document considers replacing a broad-market equity ETF with a portfolio of sector ETFs whose combined exposure approximates the market. At year end, an investor could sell sectors at a loss and buy similar sector funds from another provider, while…
The document clarifies whether a parametric value-at-risk estimate should be scaled by changing asset standard deviations or by scaling the final VaR. Under a Gaussian model with zero mean, VaR is a quantile multiplier times the portfolio standard deviation.…
The document asks whether portfolio factor models, such as Fama–French, reduce the estimation burden in portfolio optimization. Its central question is that although modeling covariance among a smaller set of factor portfolios can reduce the dimension of the…
The discussion interprets the Arbitrage Pricing Theory as a multifactor model in which expected returns are determined by exposure to risk factors and the premia associated with those factors. Its central point is that the cited equation has no separate…
The discussion distinguishes simple returns, logarithmic returns, and geometric returns, and considers how each applies to performance reporting, statistical analysis, and annualization. Simple returns directly express the percentage change in value over a…
The document distinguishes two tracking error calculations. The direct method takes the standard deviation of the periodic return differences between a fund and its benchmark; under this definition, zero tracking error means the fund matches benchmark…
The document examines whether gross exposure divided by capital is a useful definition of portfolio leverage. It points out that this measure omits cash and can overstate risk when offsetting holdings are highly correlated, then derives a risk-based…
The document explores whether investor reallocation can explain spillovers between asset returns. It starts from a mean-variance utility model and derives an unconstrained relationship between an investor’s holdings in two assets: the sensitivity of one…
The document explains two ways to simulate the return of a fixed-weight portfolio under a normal-return assumption. One method samples directly from a univariate normal distribution using the portfolio’s expected return and variance. The other draws asset…
The document describes a proposed stress-testing exercise for a zero-coupon yield curve built from daily observations. The curve combines a money-market-based short tenor with longer tenors interpolated from secondary-market Treasury rates. The author…
The document considers two equivalent ways to represent a complete market: state-contingent Arrow-Debreu securities and a set of complex securities whose payoff vectors span all possible states. It asks how to express the equilibrium price of each complex…
The document presents a Python example that simulates portfolios by drawing random asset weights, scaling them to a fixed total, and calculating annualized return, volatility, and a return-to-risk ratio from historical returns and covariance. It asks how to…
The discussion explains that Value at Risk (VaR) is defined for a stated time horizon and confidence level; without a horizon, a VaR figure is incomplete. It outlines a common parametric approach: estimate portfolio return volatility from historical data, an…
The document distinguishes two portfolio problems: choosing investments and sizing a group of trading strategies. For multiple strategies believed to be profitable and reasonably uncorrelated, one answer suggests allocating capital in inverse proportion to…
The document explains how portfolio theory can be adapted when holdings and weights change over time. It describes dynamic optimization as repeatedly estimating allocations at scheduled rebalancing dates, using data available up to each date, rather than…
The document considers how to measure the fit of a portfolio or linear combination of assets intended to reproduce another asset’s returns. It notes a weakness of relative error: dividing by the target return becomes unstable when that return is near zero.…
The document explains how a pension fund can use interest rate swaps within liability-driven investing to reduce the gap between asset and liability duration. Its example assumes a long-dated liability valued using a government bond yield, with only part of…
The discussion considers what an interface for monitoring an algorithmic portfolio should show. Its central design principle is to choose metrics and visualizations according to the strategy and the decisions the dashboard must support, rather than building…