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 asks how to estimate the degrees of freedom for a multivariate Student t distribution used to simulate asset returns. The questioner already has a sample mean vector and covariance matrix and notes that, when the degrees of freedom exceed two,…
The document addresses whether Conditional Value at Risk (CVaR) is convex or concave and what that means for optimization. The response explains that the answer depends on the quantity used as the function’s input and the sign convention: CVaR expressed as a…
The document raises a portfolio-optimization problem: an Excel Solver calculation intended to maximize the Sharpe ratio produces very large long and short weights. The author asks what constraints might be appropriate, why unconstrained extreme positions may…
The document examines a disconnect between improving a statistical forecasting model and improving the portfolio built from its estimates. In a hypothetical two-asset example, returns are usually at a baseline volatility, but one asset experiences a…
This collection of practitioner observations links asset returns to discount-rate and cash-flow shocks, aggregate risk, and changing economic regimes. It argues that risk depends on how returns covary with investors’ circumstances, and that regime shifts can…
The discussion presents several quantitative ideas for changing portfolio exposures across assets or building active portfolios. Momentum-based timing is introduced as a way to switch between major asset classes. Other suggestions include combining valuation…
The document considers a cross-sectional equity mean-reversion idea: rank index constituents by past returns, pair the strongest performers with the weakest, and allocate more capital to the most extreme pairs using a linear weighting scheme. The main sizing…
The document sets up a portfolio problem that minimizes variance while constraining weights to sum to one and expected return to equal a chosen target. It describes applying Lagrange multipliers to express the portfolio weights using the expected-return…
The document outlines two ways to create return samples for Monte Carlo analysis of mean–variance portfolios. One approach resamples rows from historical multivariate returns: collect asset prices, convert them to returns, use a lower frequency suited to the…
The document surveys the role of skewness in portfolio optimization and distinguishes it from the standard mean-variance framework. Higher moments become relevant when asset returns are not normally distributed and investors care about properties of return…
The document explains when skewness can matter in portfolio construction: asset returns must depart from normality, and investors must care about asymmetry beyond expected return and volatility. Positive skewness may be desirable to investors with that…
The document outlines a Monte Carlo procedure for estimating portfolio Value at Risk, using correlated stock returns generated from a historical covariance matrix and a Cholesky factorization. Simulated terminal prices are used to revalue the portfolio; the…
The document contrasts how corporate and public pension plans account for liabilities and asks whether public plans need tail-risk protection. Under the simplified description, corporate plans discount liabilities using market interest rates, so rate changes…
The document considers how to combine a coupon bond and a perpetuity to create a portfolio with zero duration. It identifies an error in multiplying weighted durations and replaces it with a linear duration condition: the sum of each bond’s weight times its…
The document raises the problem of interpreting portfolio turnover when market stress causes trading activity to rise. It asks whether a turnover threshold should be adjusted for market or portfolio volatility, perhaps using a benchmark and beta, while…
The document explains why a mean-CVaR portfolio optimization may fail to meet a specified return: the target can be infeasible given the return scenarios and portfolio constraints. In the example, the assets have daily returns, so a 4% daily target exceeds…
The document proposes a general-equilibrium approach to modeling a small economy and its stock market. In its simplified exchange economy, a fully equity-financed firm has one share and pays dividends at a stochastic rate. A representative risk-averse agent…
The document asks whether portfolio theory can accommodate weights that change frequently, including at a tick-level timescale. The answer describes a rolling mean-variance procedure: estimate asset returns and their covariance matrix from historical data,…
The question concerns the Bates–Granger combination of two forecasts and asks why its optimal weight can produce expected squared error below the smaller of the two individual forecast variances. The answer treats the combined error as a quadratic function…
The document explains CRSP’s value-weighted return series as returns on a market portfolio proxy. In a value-weighted portfolio, securities contribute according to their market values, so a defined set of traded stocks can be combined into an aggregate…
The document introduces coherence as a set of properties for portfolio risk measures: zero risk for an empty position, subadditivity, positive homogeneity, and translation invariance. These axioms express expectations such as diversification reducing…
The discussion asks whether correlated Brownian motions are an appropriate way to simulate correlated geometric Brownian motion (GBM) stock prices. It describes using a Cholesky decomposition to generate Brownian drivers with a chosen correlation matrix,…
The document presents a long-short risk-budgeting formulation attributed to a UBS paper on trend-following and risk parity. It maximizes a signal-weighted sum of logarithms of absolute portfolio weights, limits portfolio volatility, requires each position’s…
The document distinguishes portfolio exposure from the capital invested by showing a common gross leverage measure for long-short portfolios: the sum of long and short position values divided by equity. In the example, an investor with $100 of equity holds…