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 explains how to calculate the correlation of each of two portfolios with a combined portfolio. Given the covariance matrix of the two subportfolios, define the combined portfolio as a weighted blend of them. The covariance of the first portfolio…
The document asks how to convert portfolio weights into capital allocations, contrasting a long-only formula with a long-short set of weights. One answer explains that weights whose positive and negative components are large can have a net exposure near the…
The document explains a way to remove a portfolio’s estimated exposure to a Fama–French factor. First, regress the portfolio’s excess returns on the chosen factor to estimate its beta. Then combine the portfolio with a short position in the factor…
The document outlines how to infer Stock Z’s expected return under CAPM when the market portfolio is composed of three stocks with equal weights. It proposes first calculating market variance from the component variances and covariances, then finding each…
The document outlines ways to combine an allocation produced by a quantitative model with an allocation informed by qualitative judgments. It distinguishes blending portfolio weights from blending expected returns: direct weight combinations may remain…
This discussion examines why a risk-parity optimizer may return nearly equal asset weights when its inputs use a Ledoit–Wolf shrunk covariance matrix. The proposed explanation is that strong shrinkage reduces differences in the covariance estimates, leaving…
The document addresses how to keep a stock portfolio beta-neutral when holdings change over time and may consist only of long or only of short positions on a given day. Its proposed approach is to estimate the stock portfolio’s beta against an index, then…
The document distinguishes calculating a bond’s yield to maturity from realizing that yield as an investor. YTM is the discount rate that equates a bond’s dirty price with the present value of its scheduled cash flows. Solving that equation does not require…
The discussion distinguishes literal transfers of capital from the shorthand of money flowing into or out of an asset class. In secondary markets, a seller’s shares are acquired by a buyer, so trading alone does not reduce the number of outstanding shares or…
The document evaluates a portfolio objective that adds portfolio variance and a correlation-based term while requiring weights to sum to one. It explains that the formulation is mathematically permissible, but the two terms have different scales. Without an…
The document presents a portfolio optimization problem in which trades should either be zero or exceed a chosen minimum absolute size. The proposed objective combines active risk with a turnover penalty, while portfolio weights and auxiliary buy and sell…
The document asks how to construct a factor from stocks ranked by idiosyncratic volatility after accounting for the Fama–French market, size, and value factors. The proposed long–short return subtracts the returns of low-volatility stocks from those of…
The document poses a one-year holding-period return problem for a coupon bond using annual spot rates today and a projected spot curve one year later. The calculation must combine the coupon received during the year with the bond’s sale value after that…
The document addresses a geometric-return calculation that appears to fail when a dataset includes a reported return below negative one hundred percent. The key issue is that the spreadsheet formula treats the observations as arithmetic simple returns, even…
The document explains how an equal-weight portfolio can end up with a higher Sharpe ratio than a portfolio selected to maximize Sharpe. The tangency portfolio is chosen using information available at the investment date, such as historical returns and…
The document considers minimizing an objective formed from two quadratic terms, one associated with price returns and another with income returns. The central algebraic observation is that both terms share the same coefficient vector, so they combine into a…
The document explains how to construct a mean-variance efficient frontier when expected returns and asset volatilities are forecasts rather than a historical return series. It emphasizes that asset volatilities alone are insufficient: portfolio risk also…
The document explains how to calculate the portfolio where a capital market line from a risk-free asset touches the efficient frontier. It derives the weights from expected asset returns, the covariance matrix, and a risk-free rate. With unconstrained…
The discussion considers how to interpret portfolio exposures to the market, size, and value factors in the Fama-French three-factor model. One response characterizes portfolios through their individual loadings: exposure to size and value distinguishes a…
The discussion explains why portfolio VaR should be calculated against current positions and historical or simulated changes in market factors. Historical simulation revalues today’s portfolio using past factor moves; Monte Carlo simulation generates…
The document explains how to calculate returns and risk for a long-short portfolio using asset weights. Portfolio return is the weighted sum of component returns, with short positions represented by negative weights and long positions by positive weights.…
The document considers how to allocate a limited portion of a portfolio to puts as a tail-risk sleeve. It asks how option maturity, renewal frequency, and distance out of the money affect the strategy, noting that longer-dated options have greater vega…
The document describes a mean-variance optimization setup for an account manager allocating capital among multiple subportfolios with different, potentially overlapping asset universes. Each subportfolio has its own budget constraint, while assets not…
The document derives how an investor’s wealth changes when a fraction is allocated to a risky asset following geometric Brownian motion and the remainder earns a risk-free rate. Applying Ito’s lemma transforms the wealth process into a stochastic process for…