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 shows how to choose the 5-year and 10-year weights in a 5s/7s/10s interest-rate butterfly so its exposure to the first two principal components is zero. It represents the portfolio’s key-rate sensitivities in PV01 terms, sets the 7-year position as…
The document asks about statistical properties of a sample estimator for average value at risk, also called conditional value at risk. It presents the population objective as a minimization over a threshold parameter, with expected tail loss beyond that…
The document poses a quadratic minimization problem with a positive-definite matrix and constraints requiring each linear form in the decision vector to have magnitude greater than one. Although the objective is convex, the feasible set is non-convex because…
A portfolio’s dollar volatility is unchanged when every position is reversed: variance is sign-insensitive, so a short portfolio with the same absolute value as a long portfolio has the same standard deviation. The discussion distinguishes this total risk…
The accepted answer explains how to raise a portfolio’s volatility by combining a tangency portfolio with a risk-free asset. Since the risk-free asset has zero volatility and is uncorrelated with the tangency portfolio, the combined portfolio’s volatility is…
This note explains how to build a constant-correlation covariance target from a sample covariance matrix, then blend that target with the sample estimate using a chosen shrinkage weight. It first converts each off-diagonal covariance into a correlation,…
The document considers whether a portfolio should rebalance less often when its return forecasts cover a longer horizon. It explains that more frequent rebalancing can incorporate updated views and potentially improve alignment with target exposures, while…
The document offers a basic principle for market makers managing quotes across multiple securities: adjust prices in response to inventory in the quoted asset, and also account for inventory in assets considered similar. This extends single-instrument…
The document explains how to interpret the Treynor ratio, which measures a portfolio’s excess return per unit of beta, alongside the CAPM market risk premium. Under CAPM with zero alpha, a portfolio’s expected Treynor ratio equals the market risk premium.…
The document derives the cash account needed to keep a portfolio self-financing when its stock holding changes over time. Portfolio value is written as the shares held times the stock price plus the balance in an interest-bearing account. Applying the…
The document surveys practical ways pension plans can set investment risk appetite within an asset-liability management framework. It presents examples from public pension investors: risk limits can include relative performance measures against a reference…
The document explains how principal component analysis (PCA) is used to summarize yield curve movements. In the example, the first three components account for 58%, 85%, and 93% of cumulative variance, and their coefficient patterns are commonly interpreted…
The document asks how to assess three portfolios against the Capital Market Line (CML) and how to allocate capital to achieve a target return. With a 2% risk-free rate and a market portfolio expected to return 10% with 20% standard deviation, the CML slope…
This document introduces notation used to describe a jointly normally distributed vector of financial variables. It presents a multivariate normal density built from a mean vector and a variance–covariance matrix, then asks how to interpret the density and…
This discussion outlines how optimal control concepts apply to quantitative finance. In dynamic portfolio construction, an investor allocates capital across instruments while accounting for expected returns, risk, and the costs of changing positions over…
The document asks how researchers should estimate correlation matrices from historical financial data. It highlights choices that can affect the result, including observation frequency, sample size, and the method used to extract correlations from time…
The document raises modeling and portfolio attribution questions about minimum lower partial moment hedging with order two, in the setting of currency hedges for international equity portfolios. It contrasts downside co-moments with covariance matrices,…
The document formulates portfolio liquidation as a continuous-time optimization. It balances a trading cost that depends on the rate of position change against a penalty for holding portfolio variance, represented using positions and their covariance matrix.…
The document examines whether a two-asset minimum-variance portfolio can determine how much of one stock to buy or short against a holding in another. It describes calculating the portfolio weight from the assets’ return volatilities and correlation, then…
The document solves a two-asset allocation problem for an investor with quadratic utility over terminal wealth. The investor begins with $100 and chooses a share to place in a risky asset, with the remainder earning the risk-free rate. The risky asset has…
The document compares two ways to estimate hedge positions for replicating a signed, equal-weighted portfolio of stocks with other instruments. One approach runs a separate rolling regression for each constituent and averages the resulting hedge…
The document explains why a portfolio value written as holdings in a stock and a risk-free asset can be modeled using only the gains from those assets under a self-financing strategy. Applying the product rule to each holding reveals additional terms…
The document addresses whether portfolio weights should be optimized using asset returns or returns measured relative to a benchmark. Its answer favors raw portfolio returns when the goal is to evaluate a complete investment strategy without a specific…
The document explains how to calculate account performance when deposits, withdrawals, and currency conversions can occur at any time. It recommends treating the account like a fund: track the number of units outstanding and the net asset value per unit in a…