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 shows how to backtest a portfolio of ETFs using inverse-volatility weights estimated from recent returns. A target-weight function obtains closing prices for the preceding 20 trading days, computes returns, estimates each asset’s volatility, and…
This question considers approximating a recently launched fund with a set of market indices because the fund has a short history of daily net asset values. The intended use is to build conditional return distributions for bull and bear markets from the…
This question presents a pricing equation in which a funding constraint enters the denominator alongside the risk-free rate. The constraint is represented by a Lagrange multiplier, while expected future payoffs, risk aversion, asset covariance, and optimal…
The document asks how S&P 500 ETFs such as SPY and VOO trade when an index constituent changes, using Tesla’s addition as an example. It raises questions about whether managers rely on banks, accumulate shares before the effective date, or adjust creation…
The document examines why a simplified Treynor–Black weighting expression appears to favor a call option over its underlying stock. In the example, the option’s alpha is scaled by delta while its variance is scaled by delta squared, which can make the…
The discussion distinguishes return calculations that account for external deposits and withdrawals from calculations based only on cumulative profit. For a calendar year or another measurement period, internal rate of return uses portfolio values at the…
The document explains why simulated portfolios can have an average annualized return below the arithmetic return assumed for each asset. Its central point is that annualization uses a concave transformation of compounded returns, so Jensen's inequality makes…
The document explains how to find the beta of a portfolio made from three risky assets when each asset’s beta and portfolio weight are known. The portfolio beta is the weighted average of the component betas. Using the values in the question, the accepted…
The document explains a definition from a paper on martingales and arbitrage in multiperiod securities markets. A price system assigns a linear price to attainable future consumption bundles, while a viable system requires that some agent have a preferred…
The discussion compares Cover's universal portfolio, which seeks long-run wealth growth, with Markowitz mean-variance methods, particularly the global minimum-variance portfolio, and with equal weighting. It emphasizes that the comparison depends on how…
The document raises a conceptual conflict between two uses of the term market portfolio: a value-weighted bundle of available assets and the optimal risky portfolio on the Markowitz efficient frontier. It asks how those ideas relate when changes in the…
The document discusses computing and comparing Sharpe ratios for gold, Treasury returns, and a stock index when observations have different frequencies. The reply recommends calculating each asset’s excess return at a common monthly frequency by subtracting…
The document outlines the martingale method for expected-utility maximization in a complete-market style setup. It describes replacing optimization over trading strategies with a static choice of terminal wealth subject to a budget constraint under a pricing…
The document explains why a one-factor Vasicek credit model weights its common and idiosyncratic standard-normal components by the square roots of the correlation and its complement. If each asset has unit variance and shares a common factor, the common…
The document raises a practical question about how a simulation platform calculates the total return of an alpha strategy over a long backtest. The user describes an alpha that may generate stock weights and asks how those weights become a portfolio return…
The document considers whether two portfolios' Sharpe ratios can be ranked by dividing average returns by standard deviations while omitting the risk-free rate, assuming both portfolios share the same holding period. The response distinguishes that shortcut…
The document sets up two asset returns driven by a common factor with opposite loadings, plus uncorrelated residuals of equal variance. It then defines one portfolio as the first asset and another as a weighted combination of both, with the weight tied to…
The document examines how to quantify the effect of a management fee on investor returns when two funds have otherwise identical performance. It contrasts discrete and continuous fee calculations and proposes accounting for fees at frequent intervals as the…
The document compares equal weighting, maximum diversification, and minimum-correlation approaches, then reframes them as portfolio choices that rely on different inputs and assumptions. It presents equal weighting as a deconcentration rule that can be…
The discussion proposes ways to estimate how much capital tracks an index such as the FTSE 100. One method is to identify funds whose returns closely follow the index, using regression and an R-squared threshold; a Bayesian version could assign probabilities…
The document poses a portfolio optimization problem using forecast returns and a covariance matrix for DAX stocks. The objective is to maximize forecast portfolio return while limiting tracking error for each sector. Its central lesson is that convexity…
The document explains how to formulate a portfolio that minimizes mean absolute deviation (MAD) without an expected-return objective. Under normally distributed returns, it relates MAD to portfolio volatility, so minimizing MAD is equivalent to minimizing…
The document asks how to reproduce MATLAB's maximum-Sharpe-ratio optimization in Python, referring to MATLAB's estimateMaxSharpeRatio function and its direct method. The question is whether an existing Python package offers an equivalent or whether a custom…
The document poses a portfolio variance identity for a market portfolio formed as a weighted sum of asset returns. It asks how to show that the market portfolio's variance equals the weighted sum of each constituent's covariance with the market return, then…