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 note explains why a Black–Litterman model does not itself prevent negative portfolio weights. The model combines a prior return estimate with investor views to produce expected returns; weight constraints belong to the subsequent portfolio optimization…
The document shows how to calculate daily returns for a portfolio whose target weights are reset monthly. Begin with the capital allocated to each asset at the start of the month, apply each asset's daily return to its current dollar value, and sum the…
The document sets up an approach for choosing a debt-to-equity ratio by minimizing weighted average cost of capital (WACC). It combines the tax-adjusted costs of debt and equity, estimates the cost of equity with CAPM, and adjusts unlevered beta for leverage…
The document formulates sector performance attribution as a constrained fit of S&P 500 returns using sector return time series. The proposed coefficients sum to one and are each restricted to the interval from zero to one. The author interprets larger…
This collection surveys apparent contradictions and counterintuitive results in quantitative finance. Its most detailed example is post-crisis interest-rate valuation: pricing swaps may require separate curves for discounting cash flows and projecting…
The question asks whether consistent covariance estimates require every asset’s volatility to use the same model and parameter values, and what to do when assets appear to follow different volatility processes. The responses point toward a full multivariate…
The document addresses how to calculate liquidation tracking error in an equity fund liquidity stress test. Under horizontal, or waterfall, liquidation, assets are sold according to available daily capacity, which can distort portfolio weights. The proposed…
The document derives how the mean-variance tangency portfolio depends on expected asset returns, their covariance matrix, and the risk-free rate. With a riskless asset available for borrowing or lending, the optimal risky-asset weights are proportional to…
The document sets up a long-only portfolio with weights summing to one and distinguishes period-by-period price returns from cumulative returns measured since the start of a sample. Under its fixed-weight setup, portfolio cumulative returns are linear in the…
The document identifies the described portfolio risk calculation as Delta-Normal Value at Risk. It combines portfolio weights with a forecast covariance matrix to obtain predicted portfolio variance, then scales a distribution quantile by the resulting…
The document asks how to backtest a modern convertible bond arbitrage strategy, with particular interest in R or Matlab packages and affordable data. The response separates strategy research tools by task: fPortfolio for simpler weight-based allocation,…
The document examines a counterintuitive property of return-to-risk ratios such as the Sharpe and Treynor ratios: when excess returns are negative, dividing by a larger risk estimate can make the ratio less negative and appear better. It presents an…
The document contrasts a Total Portfolio Approach (TPA) with strategic asset allocation (SAA) based on mean-variance optimization. The question describes TPA as using equities and bonds as a reference portfolio, with other allocations treated as active…
The document examines whether ranking portfolios by the smoothness and risk-adjusted performance of their historical returns can identify future winners. The questioner groups daily results into 20-day intervals, accumulates the interval returns, and applies…
The document explains that fixed-income spreads serve several purposes, including quoting bonds, comparing relative value, attributing profit and loss, and measuring or hedging market risk. Simple yield spreads compare a bond’s yield with a selected…
The document asks how to interpret asset-level volatility contributions in a portfolio built from return covariance and asset weights. It contrasts a conventional long-only case, where contributions are expected to guide weight changes for raising or…
The document presents a portfolio allocation problem involving three assets, with expected returns, volatilities, and a correlation specified for two of them. One asset is described as having zero volatility. The questioner writes a portfolio variance…
The document asks whether downside deviation has practical value for measuring risk or guiding portfolio allocation. The only response describes it as a coherent risk measure and notes its connection to Markowitz’s work. It says practitioners use the…
The question asks whether mean-variance portfolio weights have a closed-form solution when weights must sum to one and each asset weight must lie between zero and one. The response gives the familiar inverse-covariance expression for the global…
The discussion outlines a basic historical-data workflow for choosing portfolio weights: calculate asset returns, estimate their covariance matrix, and optimize for minimum variance or for minimum variance at a target expected return. It also points to…
The document addresses whether maximum Sharpe ratio portfolio weights have a closed-form solution when short selling is allowed. It presents the result that, for risky asset returns with covariance matrix Σ and expected excess returns, the tangency portfolio…
The document introduces the Treynor–Black model, which combines a market portfolio with an active portfolio that is assumed to offer alpha. It gives formulas for the active allocation using the active portfolio’s alpha and residual variance, along with…
The exchange connects mean-variance portfolio choice to the CAPM decomposition of asset returns into market exposure and idiosyncratic residuals. Under the answer’s assumptions that residuals have zero mean and are mutually independent, the covariance matrix…
The document compares two ways to revalue a composite index after changing the values of its underlying indices. One formula takes the ratio of shocked to base weighted totals; the other adds each underlying index’s percentage change multiplied by its…