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 asks whether the growth of passive investing has economic effects on asset prices, despite the intuition that passive investors do not actively trade on information. It points readers to research addressing this question, including a paper…
The document compares ways to attribute portfolio risk and argues that the right method depends on the question being asked. Marginal contributions to standard deviation describe the effect of small weight changes; multiplying these by portfolio weights…
The document considers how to choose between decisions when both maximize the minimum payoff under a conservative decision rule. Its main point is that “minimum” depends on the scenarios or range of outcomes included: in continuous settings, worse outcomes…
The document asks how to annualize returns in rolling five-year estimation windows when the input data are monthly returns. It considers two possible workflows: annualize monthly returns first and then form rolling window returns, or calculate each window’s…
The discussion asks whether Berkshire Hathaway’s hypothetical dividend yield could be estimated as a weighted average of the dividend yields of companies it owns. The answer says there is no fixed calculation because the board chooses whether to distribute a…
The document examines an ETF prospectus describing a four-leg European option position intended to provide long exposure to an equity index. The structure combines a long call and short put at a strike below the current index level with a long put and short…
The note explains that a stock hedge depends on what neutrality means. Dollar neutrality is one possible target; setting expected return to zero is another, though the answer describes it as uncommon. For market or factor neutrality, returns can be projected…
The document asks how to adapt a globally diversified portfolio of US-listed funds for an investor in Europe who would prefer euro-denominated products. The portfolio spans international and emerging-market bonds, commodities, gold, global and US equities,…
The discussion clarifies the direction of subadditivity: a portfolio risk measure should assign the combined positions risk no greater than the sum of their separate risks. This inequality captures the possibility that diversification reduces measured risk,…
The document explains how to hedge a fixed position in one asset using positions in two correlated hedging assets. Write the total portfolio variance as a function of the hedge holdings, then set its partial derivatives with respect to those holdings to…
The document questions whether more sophisticated stock-return distributions, including multifractal models, materially improve portfolio work beyond the familiar lognormal assumption. It notes that the usual lognormal rationale relies on independent,…
The document explains why diversification may provide less protection in market stress than a portfolio model calibrated during calm periods would suggest. When covariance between assets rises, the off-diagonal terms in portfolio variance increase and reduce…
This question focuses on the dual representation of coherent risk measures. It states that such a measure can be expressed as the supremum of expected losses over a set of probability measures, then asks whether an example is known whose representing set is…
The document explains why investors and financial managers study portfolios with zero risk when a risk-free asset can be bought directly. One central use is derivative pricing: if a portfolio of risky securities has no risk, its return should match the…
The question compares two monthly investment plans under an assumed monthly compound return and asks whether contributing less can produce a better result. The response explains that the apparent difference comes from the way “profit” is calculated:…
The document asks whether an investor’s utility function can be inferred from observed trades when the asset’s return distribution is known and stationary and the investor’s wealth is available. It frames the task as selecting a suitable functional form and…
The note explains that an ETF’s annual expense ratio is generally accrued over time rather than collected as a single yearly charge. It gives a daily NAV-based example: for an annual fee of 0.03%, the per-share deduction is calculated as NAV multiplied by…
The question asks for research on using stochastic optimal control and Hamilton–Jacobi–Bellman methods to maximize risk-adjusted performance measures, including Sharpe, M-squared, Sortino, and Sterling ratios. The response points to Merton's continuous-time…
The document addresses how to evaluate a set of trades generated outside a backtesting package. Its key distinction is that the trade signals have already been produced; the remaining task is to calculate portfolio performance, equity, and profit and loss…
The document describes a simulation comparing equal-weight portfolios with portfolios whose weights are chosen to minimize variance. In each iteration, it selects one asset from each of several groups, uses two years of daily returns to set the optimized…
The answer recommends establishing a live performance record in a dedicated account funded with the strategy’s capital. It says to operate that account as investor money would be managed, including using the same leverage, risk limits, and instruments, and…
The document raises a statistical question about comparing the Sharpe ratios of two portfolios. One portfolio is described as holding similar stocks, while the other emphasizes companies majority owned by employees. The author wants to determine whether the…
The document shows how to construct efficient portfolios from expected asset returns and a covariance matrix. For a chosen target return, it minimizes portfolio variance while requiring the weights to sum to one and the portfolio’s expected return to equal…
The document outlines a portfolio-based approach to deciding which proposed option trades to accept. For options sharing an underlying, it recommends calculating aggregate sensitivities such as delta, gamma, and vega, then comparing them with target values…