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 describes a terminal-wealth portfolio allocation problem with a quadratic penalty for falling below a target wealth level. It approximates expected utility under normally distributed portfolio returns using Gauss–Hermite quadrature, then…
The document asks whether an app giving every investor the same supposedly optimal stock portfolio could distort markets. It raises two possible effects: stocks excluded from the recommended portfolio might lose investor demand, and favored stocks might…
The document describes a portfolio investor’s uncertainty about which standard deviation belongs in an annual Sharpe ratio when returns are recorded daily over a long historical period. The investor compares the dispersion of annual returns across years with…
The document explains a limit used in a Vasicek portfolio loss distribution: a binomial cumulative probability with a threshold proportional to the number of exposures converges to an indicator at the binomial success probability. The sum is recognized as…
The discussion compares principal component analysis (PCA) and clustering as ways to build risk models for portfolio optimization. PCA is presented as a method for reducing a set of risk variables to a smaller number of uncorrelated factors. Clustering…
The document discusses monthly rebalancing of commodity futures portfolios amid seasonal liquidity patterns and market microstructure effects. It argues that there is no universally suitable point in each month for rebalancing and suggests avoiding periods…
The document considers how to rank prospective trades using return, duration, liquidity, and probability of failure. It cautions that directly multiplying raw inputs can produce a misleading score because the variables may use different scales and units.…
The document responds to a request for introductory reading on concepts such as beta, global minimum variance, and the Sharpe ratio, along with basic hedging theory and basis trading. The answer points readers toward a general investments textbook for the…
The document discusses whether a trading strategy’s returns differ meaningfully from a benchmark. It outlines comparing mean returns and variances, and introduces the Sharpe ratio test: under independent, identically distributed returns, its relationship to…
The document proposes blending portfolio variance with a penalty on concentrated weights to represent a preference for naive diversification. The objective combines the covariance-based risk term with the squared length of the weight vector, subject to…
The document compares smart beta, alternative indexes, and factor investing. Alternative indexes use weighting rules beyond market capitalization, including tilts toward momentum, value, smaller companies, or lower volatility, as well as fundamental measures…
The document discusses how to represent trading costs when comparing robust and traditional portfolio allocation. It suggests testing a range of fixed cost assumptions and examining how those assumptions change optimal holdings and portfolio profitability.…
The document challenges broad claims about diversification, rebalancing, and the relationship between arithmetic and geometric means. Its answer corrects a central mathematical misunderstanding: for nonnegative observations, the arithmetic mean is at least…
The note explains how the risk-free rate enters the standard CAPM as the intercept and as the benchmark subtracted from expected market return. In the standard setup, these roles use one rate; lending and borrowing at different rates can appear in a capital…
The document distinguishes arithmetic average returns from cumulative, compounded performance. A portfolio can have a higher average periodic return yet finish with a lower cumulative value, because cumulative performance depends on the sequence and…
The document considers selecting a subset of currency pairs to form a basket subject to correlation, a second property, and a minimum basket size. Rather than enumerate every subset, the answers recommend defining a clear score or treating one target as an…
The document considers whether assets with extreme estimated betas should be excluded when using CAPM to predict expected returns and calculate residual, or idiosyncratic, returns. The proposed model estimates monthly total returns against a global equity…
The document raises questions about different James–Stein shrinkage-factor formulas used to adjust estimated asset-class returns before mean-variance portfolio optimization. One expression uses the number of observations, a grand mean, and the inverse…
The document considers whether a portfolio can be constructed to have a payoff of the form a plus b times a stochastic discount factor. The questioner proposes expressing the discount factor as a linear combination of asset returns, using a regression whose…
The document presents a theoretical case for skilled active management while distinguishing manager skill from the returns investors ultimately receive. In the equilibrium argument attributed to Jonathan Berk, investors allocate capital to capable managers…
The document asks how to calculate daily time-weighted returns for individual securities when trades occur during the day. The proposed calculation divides daily profit and loss plus dividends by the prior day’s price multiplied by the prior holding…
The document explains why the S&P 500 uses a divisor and how that divisor is maintained. The index level is calculated from constituent market capitalization relative to the divisor; the divisor is adjusted when corporate actions or changes to index…
The document asks how to convert daily portfolio and benchmark returns, contributions, and allocation and selection effects into monthly attribution while keeping the effects consistent with the portfolio’s excess return. It distinguishes compounding returns…
The document discusses how to interpret parametric value at risk and standard deviation when assessing an asset or portfolio. Its answer cautions that VaR relies on assumptions and leaves out important dimensions of risk, so it should not serve as a complete…