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 poses a portfolio-weighting problem: combine the returns of several models so that the resulting portfolio has as many positive periods as possible. Its objective is the fraction of periods in which the weighted sum of model returns exceeds…
The document describes how to turn a piecewise linear profit-and-loss graph at expiration into a portfolio of calls, puts, and possibly cash or the underlying. It proposes placing option strikes at the graph’s breakpoints, then solving a linear system whose…
The document asks whether a weighted combination of the Sharpe ratio and information ratio can be made convex, giving an example that assigns three times the weight to information ratio before averaging. It does not provide an answer, transformation,…
The document discusses how bond indices handle securities that mature or are redeemed between scheduled rebalances. It distinguishes indices rebalanced daily from benchmarks rebalanced monthly, noting that performance is compared with the monthly rebalanced…
The document considers how to assess long-volatility strategies with frequent small losses and occasional large gains, where mean return, Sharpe ratio, and hit rate may not capture the payoff pattern. The response recommends beginning with a long history of…
The document asks what to call the individual steps in a fund distribution waterfall, as described in a limited partnership agreement. It considers “phase,” “provision,” and “tranche,” seeking a general term that would make sense across varied agreements…
The note explains how to include long and short stock positions when calculating a portfolio correlation statistic based on pairwise asset correlations. The positions enter through signed portfolio weights, so a pair’s contribution changes sign when one…
The document explains why cumulative returns depend on how profits and losses affect the capital base. If gains and losses remain invested and change the amount exposed to later returns, calculate the total by multiplying each period’s gross return and…
This explanation clarifies why Cover’s universal portfolio does not generally remain equally weighted after its initial allocation. It starts with equal weights, then estimates the next allocation as a performance-weighted average of constant-rebalanced…
The document examines how to calculate covariance between two weighted portfolios when the underlying asset covariance matrix is estimated from log returns. The usual bilinear matrix calculation applies when portfolio returns are linear combinations of the…
The document compares holding a bond ETF with maintaining a long bond futures position, focusing on financing, collateral, benchmark fit, tracking, and operational demands. An ETF provides exposure to an actual managed bond portfolio, with management fees…
The document turns a set of bets with different success probabilities and payouts into a portfolio-optimization problem. It proposes minimizing portfolio variance using the covariance matrix of the investments, with each bet’s expected value and variance…
The document explains how an investor’s preferred portfolio changes when a risk-free asset becomes available. Without that asset, the investor selects a point on the efficient frontier where an indifference curve for their utility function is tangent to the…
The document explains why simple returns and log returns aggregate differently when a portfolio contains multiple trades and is measured across multiple days. With fixed weights for a given day, simple returns combine linearly across trades. Across time,…
The note explains how to interpret a question from Grinold and Kahn’s portfolio theory exercises about the characteristic associated with the Major Markets Index portfolio. The proposed interpretation is to identify the attribute for which the MMI portfolio…
The document asks whether the standard covariance-matrix formula for portfolio variance remains valid when some portfolio weights are negative, as they are for short positions. It presents a futures portfolio with both positive and negative contract…
The document describes a long–short factor backtest that ranks assets into top and bottom quintiles. The signal has positive performance at monthly, quarterly, and annual rebalancing frequencies, with returns improving as rebalancing becomes less frequent.…
The discussion addresses two distinct validation needs for mean–variance portfolio allocation. One reply challenges the assumptions behind mean–variance finance, arguing that return distributions may be heavy-tailed and that sample means and variances may…
The discussion asks why an equally weighted portfolio of mutual funds can have a much higher four-factor model R-squared than the average R-squared from separate regressions for each fund. The explanation is that fund-specific return noise tends to cancel…
The document considers how to compare approaches intended to address parameter uncertainty in portfolio optimization, including Bayesian methods with diffuse, asset-pricing-based, or economic-objective priors. Its response recommends evaluating forecasts…
This discussion gives two ways to calculate the correlation between two portfolios, including when one portfolio contains a subset of the assets in the other. With asset weights and the covariance matrix, portfolio covariance is obtained by applying each…
This explanation shows how to calculate the correlation between an individual asset and a weighted portfolio from asset volatilities, correlations, and portfolio weights. First, the pairwise correlation matrix is converted to a covariance matrix using the…
Mean-variance optimization can produce unstable allocations when expected returns and covariance inputs are estimated with error. The discussion surveys practical ways to reduce that sensitivity: shrink historical estimates toward common targets, use robust…
The document presents a question about translating a multi-period asset allocation problem into a dynamic programming formulation. Wealth evolves through investment returns applied to current wealth plus income, while the investor chooses portfolio fractions…