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 outlines two main decisions when building corporate bond yield curves: how to group securities into curve subsets and how to fit a curve to each subset. Grouping can reflect credit quality, sector, issuer, currency, coupon type, seniority, or other…
The document models a pension fund as the accumulated value of periodic contributions, where income grows continuously and each contribution earns a continuously compounded return until the valuation date. It derives sensitivities of the fund value to the…
The document derives the fully invested tangency portfolio from the unconstrained mean-variance solution. Maximizing expected excess return minus a risk-aversion-weighted variance penalty yields weights proportional to the inverse covariance matrix…
The document explains how covariance and correlation matrices can both support generation of correlated normal samples through Cholesky factorization. Using the covariance matrix applies the variables’ scales directly; using the correlation matrix requires…
The document considers a portfolio that invests one unit in each of several stocks whose future prices are modeled as independent squared standard normal variables. Since each squared standard normal variable has a chi-square distribution with one degree of…
The document asks how to calculate daily returns and weights for a stock portfolio that rebalances monthly, using a ranked-beta strategy as context. It distinguishes the weights assigned at the start of a month from the weights that result after the stocks…
The document explains how Johansen trace-test statistics and critical values indicate the number of cointegrating relationships among three instruments. In the example, the null of no cointegration is rejected, while the next rank null is not, which points…
The document explains how to interpret principal component analysis applied to a matrix of asset returns. Selecting the leading eigenvectors creates a lower-dimensional representation: multiplying the original observations by those vectors produces component…
The document asks what numeraire corresponds to the real-world probability measure and presents answers for both a simple stock-and-cash model and a broader factor-based setting. In the Black–Scholes geometric Brownian motion example, a change-of-measure…
The note explains why dividing one negative portfolio value by another can produce a return sign that conflicts with the economic result. Its example starts with a short position that makes the securities value negative, then shows the liability shrinking as…
The document poses a mathematical finance question about a market with one risk-free asset and several risky assets. It defines arbitrage in terms of a portfolio with nonpositive initial cost and a nonnegative payoff that is sometimes positive, and defines…
The document explains how to calculate parametric Value-at-Risk for a portfolio holding equities and a correlated short futures position. Its central point is that portfolio volatility and exposure must use the same normalization. Using the net market value…
The document shows how to calculate a portfolio’s one-year expected credit loss when it contains bonds with different ratings, default probabilities, and recovery rates. For each bond group, it multiplies exposure at default by probability of default and…
The document considers whether stocks must be sorted into portfolios when estimating Fama–French factor models. With only three companies available, the accepted answer recommends running separate regressions on each stock’s excess returns using the factor…
Factor models explain shared movements across assets with a smaller set of common drivers. Because stocks often move together, treating their returns as independent can overstate the diversification benefit in a portfolio. A factor representation captures…
The document explains a two-step Bloomberg workflow for retrieving an index’s members and then collecting return data for those securities. It says there is no single field that returns constituents together with their data: first request the member list,…
The document contrasts two stylized betting approaches. A convergent strategy increases exposure after losses and takes gains after wins, producing frequent small gains alongside the possibility of a very large loss. A divergent strategy increases exposure…
The document asks how to assess uncertainty in an estimated information ratio based on portfolio returns relative to a benchmark. It explains that the information ratio resembles a t-statistic and can be used to test whether average active returns differ…
The document examines a proposed rule for deciding whether to add an asset to a portfolio. The rule compares the candidate asset’s expected return per unit of volatility with the existing portfolio’s corresponding ratio, adjusted by their return correlation.…
The document develops a two-asset quadratic hedging example for returns that are negatively correlated and may have different volatilities. Assuming zero expected returns, it writes portfolio risk as the variance of a weighted combination of the two returns,…
The document is a literature guide for studying Bayesian methods in portfolio management. It responds to a reader who finds the mathematical treatment in an early Bayesian regression paper difficult and is looking for a suitable learning path, especially one…
The document explains how to calculate an external cash inflow that moves a portfolio toward target weights without selling overweight holdings. It distinguishes this approach from conventional rebalancing, where assets above target are sold to fund…
The document addresses a learner seeking a small, detailed Black-Litterman portfolio example that can be worked through by hand. It points to a step-by-step guide as a resource for understanding the model, rather than presenting the calculations directly. No…
The document asks how to turn estimated coefficients from a three-asset cointegration relation into dollar allocations for a mean-reversion trade. Its example models the log price of one security as a linear combination of the other two log prices, then…