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
State prices are the current values of claims that each pay one unit in exactly one state and nothing in the others. To infer them from traded assets, each state-specific payoff must be replicable by a portfolio of those assets. The example has a bond paying…
The question concerns a boundary in an investment problem with proportional transaction costs. At the boundary, it is optimal to pay a cost and move into another region of the value function. The paper reportedly imposes a first-derivative condition there,…
The document describes a portfolio-construction task using monthly average quoted spreads for a broad set of companies over a long sample. The intended procedure is to rank stocks by a liquidity measure at the start of each year, divide them into ten equally…
The document explains why portfolio optimization commonly produces fractional target holdings even though some investors must trade whole shares. Integer constraints make optimization substantially harder than the continuous-weight problem, while larger…
The document explains how dated private equity cash flows enter an internal rate of return calculation. Capital calls and management fees are outflows and should be recorded as negative amounts; distributions are inflows and should be positive. For an…
The document addresses whether portfolio assets should be negatively correlated or mostly uncorrelated. Its central lesson is a mathematical constraint: correlations across many assets cannot all be moderately negative while still forming a valid correlation…
The document presents a question about the two risky asset tangency portfolio formula. It explores how the calculated weight of one asset changes as the assets’ correlation rises, holding expected excess returns and volatilities fixed. The example reports a…
The document compares two approaches to empirical stock return prediction: estimating a panel regression with stock-level characteristics and sorting stocks into portfolios. Portfolio sorts are popular because their results are easy to explain and can be…
The document considers how to construct a probability density for portfolio returns when the sample mean, variance, skewness, and kurtosis are known. It collects several suggested routes: estimate parameters for a chosen distribution, use a generalized…
The document asks how to express ordinary statistical views in the scenario-based form used by Entropy Pooling. It sets up a matrix of simulated outcomes for two variables, assigns equal prior probabilities to the scenarios, and describes a view matrix whose…
The document sets up a portfolio of long and short European calls and puts on one underlying, with a common expiry and different strikes. It calculates initial cost by multiplying each option position by its quoted price and summing across contracts. A…
The discussion asks why risky portfolios are sometimes compared by cash equivalent rather than by expected utility alone. For a given utility function, the cash equivalent is the certain amount that gives the investor the same utility as the risky portfolio.…
The document addresses why ordinary percentage returns can become misleading when a long-short strategy’s recorded P&L or value crosses zero. It presents a net asset value approach: account for the value of long holdings, short-sale proceeds, and the current…
The document examines why a covariance matrix for a large stock universe may remain singular after applying Ledoit–Wolf shrinkage. It suggests checking whether securities are duplicates or nearly perfectly correlated, since multicollinearity can make the…
The document considers whether annual portfolio volatilities can be combined to estimate volatility over a shorter span crossing calendar years. One reply presents a parallel variance algorithm: combine the observation counts, means, and variances of two…
The document explains why the Hansen–Jagannathan bound constrains attainable Sharpe ratios rather than the individual means, volatilities, or factor betas of assets. A beta can be bounded using a covariance inequality when asset-return volatility is bounded…
The document asks how to reward diversification in a fixed-income portfolio whose holdings vary by currency, yield, tenor, and class. It raises portfolio-weighted correlation and the Herfindahl index as possible ingredients, but does not develop either into…
The document surveys learning resources and possible uses of quantum computing in quantitative finance. It highlights optimization and simulation as areas of interest, including quantum annealing for constrained graph problems that may help represent…
The document considers whether each point on the capital market line (CML) identifies a unique portfolio. It describes a mean-variance argument: for a target expected return, minimize portfolio variance subject to a return constraint. The Lagrange conditions…
The document answers a question about commercial services that model how global events may affect asset classes and portfolios. It points to major factor risk model providers as an alternative to a macroeconomic scenario service, noting that these providers…
The document considers how to construct a long-only mean-variance portfolio with a limited number of holdings. Instead of directly imposing a cardinality constraint, the suggested first step adds an L1 penalty on portfolio weights to the optimization…
The document addresses how to backtest a strategy that trades a list of cryptocurrencies on a daily schedule. It recommends considering Backtrader, which supports event-driven strategies across multiple assets, and mentions Zipline as another possible…
The document derives the variance of an equal-weighted portfolio from the covariance terms between its assets. The key correction is that the double sum contains two kinds of terms: each asset’s variance on the diagonal, where the asset is paired with…
The document asks whether optimal risky-asset weights move in a predictable direction when correlations are removed while individual variances, expected returns, risk aversion, and the risk-free rate are held fixed. It contrasts the general unconstrained…