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 considers a portfolio problem that maximizes expected alpha subject to bounds on factor exposures, and asks how this linear formulation compares with Markowitz optimization. The responses clarify that the classical Markowitz mean-variance…
The document clarifies how a performance analytics workflow can treat the risk-free rate when calculating or plotting portfolio risk and return. A scalar input represents a constant rate, while a vector can associate a different rate with each return period.…
The document explains why logarithmic, power, and related concave utility functions recur in economic and investment models. Their appeal is mathematical tractability and the ability to express risk preferences through Arrow–Pratt absolute risk aversion, a…
The document asks why portfolio utility commonly subtracts a variance penalty instead of a standard deviation penalty. For a single risky asset, a position scales expected return linearly and variance quadratically, which can produce a finite optimal…
The document describes a two-asset risk-parity objective: compute each asset’s share of portfolio variance from its weight and the covariance matrix, then minimize the distance between those shares and equal contributions. The initial attempt uses a…
The document poses a one-year CAPM calculation for three assets. It supplies each asset’s annual volatility and market capitalization, assumes the returns of distinct assets have equal pairwise correlation, and gives the risk-free rate and expected market…
The document compares constrained minimum-variance portfolio optimization with an unconstrained objective that penalizes deviations from a target return and linear exposure constraints. It explains that choosing penalty weights by hand can make the original…
The document explains how combining two uncorrelated return streams can raise a portfolio’s Sharpe ratio. It presents a regression argument: when the streams are uncorrelated, the first strategy’s beta relative to the second is zero, so its excess return is…
The document compares three ways to estimate an annual Sharpe ratio from monthly index data: overlapping rolling annual returns, non-overlapping calendar-year returns, and annualized monthly excess returns. Its worked example uses monthly stock and risk-free…
The document considers whether a U.S. retiree can hedge a personal spending basket whose inflation runs above CPI-U, using consumer-accessible investments over a long horizon. It concludes that no single individual instrument is identified that directly…
The document asks whether a user-selected risk-aversion parameter can adjust a portfolio built with the Black-Litterman approach. Its answer describes the framework as combining a return distribution with uncertain views, then passing the resulting expected…
The document poses a research problem about predicting short-term price reversals in individual stocks and in a portfolio. The author observes that some stocks rise and then reverse, with the apparent pattern clearer in some names than others. They suspect…
The document asks how to value a stock across a two-period binomial tree when it pays fixed cash dividends. It starts with a stock price of 100, up and down factors of 1.2 and its reciprocal, and dividends of 10 and 5 in successive periods. The author…
The document raises a practical question about a statement in a diversification paper: principal component eigenvalues correspond to the variances of uncorrelated portfolios. The author compares eigenvalues from the covariance matrix of asset returns with…
The document frames return replication as a least-squares portfolio problem: choose weights on a set of assets so their daily returns track a target asset. It introduces the unconstrained regression solution, then explains that requiring weights to be…
The document describes a researcher calculating monthly Sharpe ratios for a large set of mutual funds over a ten-year sample and finding that every result is positive. The stated calculation takes each fund’s average monthly excess return and divides it by…
The document presents a finite-state price tree for an underlying asset, with zero interest and a cash dividend paid between observation dates. It sketches how to find risk-neutral transition probabilities by matching each node’s current value to the…
The document frames an optimization problem: selecting asset allocations across successive decades over a century, using a restricted set of choices among equities, cash, and bonds. Each period permits either a full allocation to one asset or an equal split…
The document distinguishes the regression meaning of alpha from the broader way traders use the term. In a single-benchmark model, portfolio returns are regressed on benchmark excess returns; beta captures market exposure, while alpha is the intercept…
The document describes a dissertation calculation of daily returns for a value-weighted portfolio of large corporations, using prior-day market values as weights to avoid using future information. It outlines normalizing market values across constituents,…
The document considers portfolio shrinkage targets that do not require expected-return estimates, including minimum-variance, risk-parity, equal-risk, equal-weight, and maximum-diversification approaches. Such targets can temper noisy return estimates used…
The discussion addresses how to obtain historical Eurozone fixed-income index data for a multi-factor study of European bond funds when Bloomberg is unavailable and replacement ETFs lack sufficiently long histories. The response names Yieldbook index…
The document addresses whether factor betas that are imprecisely estimated in time-series regressions can still produce a statistically precise risk premium in a cross-sectional regression. The answer is yes in principle, but beta measurement error works…
The document raises questions about Merton’s derivation of the security market line from the tangency portfolio. Its focus is the covariance between an individual asset and the market portfolio: the reader asks why that covariance can be written as a…