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 how to balance hedge quality against bid–ask costs when hedging an exotic instrument with liquid instruments. It proposes measuring the cost of an imperfect hedge as a high percentile of losses over a chosen risk horizon, so the…
The document explains how the Black-Litterman model blends market-implied prior returns with investor views, with the view covariance matrix Ω controlling their relative influence. When the pick matrix is the identity and Ω equals τ times the market…
This discussion asks whether correlations change more slowly than volatilities and whether clustering affects the two quantities differently. It cites the use of longer rolling windows for ex-ante correlation estimates than for volatility estimates in…
This document addresses how to choose starting capital so that a portfolio funds a specified stream of annual expenses and reaches zero at a chosen horizon. It describes a forward recurrence: grow the remaining investment by a fixed rate, then subtract each…
The document asks how correlations affect diversification and the minimum-variance portfolio as the asset count grows. It gives the two-asset condition under which the higher-volatility asset receives a positive weight, then asks whether an analogous…
The document explores using the Ledoit–Wolf estimator to reduce sampling error in a covariance matrix used for a market-neutral portfolio. It describes shrinkage as blending the sample covariance matrix with a structured target, with an intensity that…
The document considers a one-period market with two risky assets and three possible future states. After arguing that the market is arbitrage-free, the question is how to establish that every contingent claim can be replicated without solving explicitly for…
The document examines why equal-dollar long and short positions are sometimes compared with cash-like benchmarks, while emphasizing that dollar neutrality does not make a portfolio riskless. A long-short portfolio can reduce broad market exposure and seek…
The document considers whether a country’s aggregate market capitalization can exceed the wealth of its residents. It presents two competing explanations: foreign ownership can add demand for domestic shares without adding to residents’ wealth, while a share…
The document explains why a multi-factor equity model might use market-cap-weighted means when converting factor values into Z-scores. In a universe with many small companies and a few very large ones, an unweighted cross-sectional regression can let the…
The document starts from a two-asset allocation rule that sets the risky asset’s weight using its expected excess return, variance, and the investor’s risk aversion. It asks how sampling bias in estimated variance affects that weight. Bessel’s correction can…
The document considers how to combine several trading strategies with similar returns and volatility when their trades rarely or sometimes overlap. Equal cash allocations produce a weighted average return, while allocating the full capital to whichever…
The document formulates a portfolio rebalancing problem with quadratic risk, expected-return benefits, proportional transaction costs based on absolute weight changes, and constraints on weights, turnover, concentration, and beta. It asks how to express the…
The document asks how to derive expected cross-sectional variation in returns from a mean vector and covariance matrix, rather than estimating it from noisy historical observations. For a multivariate normal model, it expresses the returns as a mean vector…
The document explains why reaching a target portfolio percentage requires recalculating both the bond holdings and the total portfolio value after new money is invested. The example starts with a £40,000 portfolio holding 40% in bonds and asks how much…
The document asks how to estimate covariance when optimizing a minimum-variance portfolio over weekly or fortnightly cumulative returns. It contrasts calculating covariance directly from returns sampled at the target frequency with scaling a daily covariance…
The document considers how to handle missing monthly returns for stocks selected into a portfolio. It outlines simple treatments, including assigning zero, the risk-free rate, or a strategy-neutral return, and skipping months across assets. It also describes…
The document raises whether annualized volatility estimated from monthly returns is typically lower than estimates based on daily returns. The questioner considers using daily observations to increase the sample size, while worrying that the measured…
The document examines whether a small historical sample can support fitting a Generalized Pareto Distribution (GPD) for extreme-tail risk estimates. The motivating example uses monthly portfolio data to estimate Expected Shortfall at the 99% level, and asks…
The document raises a question about dynamic programming when asset returns are serially independent. A cited book says wealth can connect one period to the next as a single state, and the question asks why independence makes the other states at a stage…
The document surveys proposed principles for assessing asset values, including price discovery and market efficiency, no-arbitrage pricing, discounted cash flows, time value, capital structure, factor-based risk models, and the option-like relationship…
The document considers how a new investor’s subscription can change portfolio weights when some holdings cannot be increased or traded. Its example starts with a portfolio containing liquid assets and an illiquid holding, then allocates the incoming cash to…
This question examines how to manage simultaneous pair trades that each use the same ETF as a hedge. One signal calls for a long position in a stock against a short ETF position, while another calls for a short stock position against a long ETF position. The…
The document considers a portfolio optimizer that maximizes expected return subject to a Value-at-Risk limit, then adds borrowing to permit leveraged positions. It asks how VaR should be calculated once debt is included. The response says borrowing costs…