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
A negative average SMB return does not establish that large stocks outperformed small stocks: the observed estimate may be statistically indistinguishable from zero. The response illustrates this with Swedish market data, where the estimated monthly SMB…
The document explains how to combine two portfolios when their Sharpe ratios and correlation are known. Under the Markowitz framework, it gives a formula for the maximum achievable Sharpe ratio and a corresponding vector of portfolio weights, expressed using…
The document explains why, without a risk-free asset, any portfolio on the mean-variance frontier can be represented as a linear combination of two distinct frontier portfolios. Its main explanation uses an orthogonal decomposition of returns: expected…
The document formalizes the value of a two-stock portfolio conditional on one stock finishing below a specified level at a future time. It represents the condition as an event and uses its indicator to restrict portfolio outcomes. The conditional expected…
The document explains how to combine the Macaulay durations of two bonds into a portfolio duration. Its key concept is that the portfolio duration is the market-value-weighted average of the individual bond durations. Each bond’s duration is multiplied by…
The discussion explains why missing entries in a return covariance matrix can arise when asset histories have no overlapping observations. Pairwise covariance estimates can use the dates available for each asset pair, but if two series never overlap, their…
The document frames a stress-testing problem for a portfolio exposed to an equity index through short autocallables and other worst-of basket products, short exchange-traded puts, and long underlying holdings. It lists potential risk drivers: falling prices,…
The document sets up a spot portfolio containing two stocks whose prices are related by a proposed cointegration expression. It assigns coefficients to the two prices, defines a position indicator that can take long, flat, or short values, and writes the…
The document raises a question about principal component analysis applied to several fund return series. The author reports that the first component has much higher volatility than the funds used to construct it and wonders whether the component might…
Fama–French portfolio breakpoints are thresholds calculated from NYSE-listed stocks and then applied to stocks listed on the NYSE, AMEX, and NASDAQ. The explanation links this choice to differences in market capitalization across exchanges and the addition…
The discussion asks whether the Capital Asset Pricing Model requires a large set of risky assets so investors can diversify away idiosyncratic risk. One response argues that the answer depends on the risk-free-rate assumption: without a known risk-free rate,…
The document explains why dividing each asset’s variance contribution by total portfolio variance gives additive percentages, while dividing standalone standard deviation components by portfolio standard deviation does not. It rejects normalizing those…
The document asks how to assign a parametric portfolio Value at Risk (VaR) across three assets. It contrasts allocating VaR by portfolio weights, which ignores differences in volatility, with allocating it in proportion to each asset’s standalone VaR, which…
The note explains how a risk-free asset changes the efficient frontier into the Capital Market Line (CML), which connects the risk-free return to the tangency portfolio. The Sharpe ratio measures the slope of this line: excess expected return over the…
The document asks whether shrinkage estimators can improve estimates of expected returns outside mean-variance portfolio optimization. It contrasts calculating a separate sample mean for each return series with jointly estimating a vector of means using a…
The note surveys ways to identify changes in correlation between asset return series and cautions against assuming that one historical window will always be suitable. Suggested diagnostics include formal changepoint analysis, shifts in covariance…
The document outlines several ways cointegration can inform trading and portfolio analysis. For two traded securities, a stable long-run relationship can motivate a pairs strategy: estimate the relationship, monitor the spread, and take opposing positions…
The document answers which market capitalization to use when calculating a value-weighted portfolio return for a period. When securities are selected or the portfolio is formed at the start of the month, the starting market capitalizations provide the…
The document examines why asset-level contributions across multiple periods may not sum to a portfolio’s cumulative return when contributions are calculated with fixed weights or by compounding each asset’s standalone contribution. Its central explanation is…
The document explains how a constituent that does not trade for a day affects a market-capitalization-weighted index such as the S&P 500. Its central point is that a company’s market capitalization does not automatically change when trading pauses; index…
The document considers whether a risk-aversion parameter can be inferred from a target value at risk under a continuous-time portfolio model. The risky-asset allocation follows the Merton rule, linking weight to expected return, the risk-free rate,…
The document explains how a portfolio variance expression separates into contributions from individual asset variances and from covariances between different assets. In the covariance matrix, the variance terms lie on the diagonal, where an asset is paired…
The document considers how bond spreads should evolve in asset-liability management and economic scenario generation models. A spread is first calibrated at the valuation date so the model price matches the bond’s market value. The question is whether to…
The discussion clarifies the meaning of the drift vector in the unconstrained Kelly portfolio formula, where allocations depend on the inverse return covariance matrix and excess drift over the risk-free rate. The answer says the objective is long-run…