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 discusses whether Euler or Constrained Aumann–Shapley allocation is preferable for attributing portfolio Value at Risk or Expected Shortfall to risk factors. Its central practical point is that capital attribution must be explainable to its…
The document compares calendar-based portfolio rebalancing with threshold-based corridors. Fixed schedules such as monthly rebalancing are simple, but weights may drift substantially between dates. A corridor approach monitors deviations from target weights…
The document shows how to calculate expected utility under a constant absolute risk aversion (CARA) negative exponential utility function. It first expresses expected utility as the integral of utility over the distribution of the outcome, then illustrates…
The document derives the discounted wealth process for a discrete-time portfolio holding a risky asset and a risk-free bond. The investor rebalances the number of risky units over time, funding each change from the bond position so that rebalancing itself…
The document asks how to express forecasts of relative stock performance in a mean-variance portfolio optimizer for a medium-frequency strategy with holding periods of about a day to a week. It frames statistical arbitrage as trading relationships among…
The document considers how to use a parametric bootstrap to assess whether a statistic comparing portfolio allocation strategies is significant. The proposed workflow fits a return model, such as GARCH, to the observed data; generates multiple return series…
The document asks whether the Merton investor’s optimal risky asset allocation changes over time when the investor must consume wealth at a prescribed rate. It gives a Hamilton-Jacobi-Bellman equation for value as a function of time and wealth, with a…
The document asks whether portfolio allocation can avoid estimates of return means, variances, and covariances. One long response frames the issue through statistical estimation, decision theory, and investor utility, arguing that applied allocation…
The post asks how to isolate equity performance from currency effects in a Brinson 1985 portfolio attribution when holdings use different currencies. It proposes expressing each holding’s value in the portfolio’s base currency before calculating its weight.…
The document asks how to measure the effect of a parallel interest-rate shift on quarterly valued, illiquid investments such as private real estate, infrastructure, and private equity. It identifies practical complications: limited observations, smoothed…
The document sets up the mean-variance portfolio problem: minimize portfolio variance subject to a target expected return and weights summing to one. It forms a Lagrangian with two multipliers, differentiates with respect to the weights and multipliers, and…
The document explains why covariance and correlation between assets are generally estimated from returns or price changes rather than price levels. Price levels can be nonstationary, with changing means and trends, so their measured co-movement may reflect…
The document asks for research on portfolio selection with robust statistics or regularization, mentioning methods such as LASSO and ridge regression. It names work on regularized portfolio selection and robust portfolio selection as examples of the topic,…
The document asks how to apply Kelly sizing to angel portfolios when investments are made in parallel, pay out at unknown times, and may have different outcomes. It proposes scaling each investment’s Kelly fraction by a decreasing schedule so that the total…
The document explains the sign of the market price of risk when risk is represented by a stochastic discount factor (SDF). In the beta representation based on SDF covariance, the price of risk is negative because the SDF variance is positive and enters with…
The document asks why institutional portfolios might hold a sizable allocation to short-term fixed-income instruments, such as repo, while also maintaining a similarly sized unfunded position in another asset class. It distinguishes this allocation from cash…
The document clarifies the role of an alpha model in quantitative equity investing. In the cited investment-process description, the model forecasts excess returns for stocks. The answer treats this as a forecast of expected return relative to a benchmark or…
The document distinguishes a mathematical property of independent, identically distributed returns from an investment conclusion sometimes drawn from it. Under the stated IID assumptions, aggregating returns across a longer horizon makes the annualized or…
The document explores how to adapt a deep reinforcement learning portfolio model, originally formulated for long-only positions, to allow positive and negative weights. The proposed representation makes positive weights long exposures and negative weights…
The document poses a portfolio theory question: given two stocks’ expected returns and standard deviations, and a correlation of negative one, how can the risk-free rate be inferred? The proposed route is to recognize that perfect negative correlation allows…
The document sets up a long-only minimum variance portfolio in Python using a covariance matrix estimated from a table of asset returns. The optimization minimizes portfolio variance subject to weights summing to one and each weight being nonnegative. The…
The document introduces Roll’s critique of empirical CAPM tests. It explains that the CAPM equation follows mathematically when a portfolio is mean-variance efficient, so testing the equation with a chosen market proxy amounts to testing that proxy’s…
The document distinguishes variance, a defined statistical measure of squared dispersion, from volatility, a term used in finance for variability that may refer to several related quantities. For return data, volatility is commonly estimated by taking the…
The document explains the link between the tangency portfolio, the capital market line (CML), and the maximum Sharpe ratio. In mean-variance theory, adding a risk-free asset creates a straight line of combinations between that asset and a particular…