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 an annual geometric return from a sequence of monthly simple returns and how to check two seemingly different methods. First, compound the monthly gross returns within each year, then take the geometric mean of the…
The example distinguishes dollar-weighted return from time-weighted return when an investor changes the number of shares held during a multi-year investment. For dollar-weighted return, it translates purchases and liquidation into dated cash flows and…
A short position’s cash flows and liability can produce a marked value or P&L that crosses from negative to positive. Applying the ordinary percentage-change formula directly to that signed series can give a misleading result, so the discussion considers…
The document explains a mismatch between an analytical mean-variance portfolio solution and a numerical optimizer. The portfolio objective combines covariance-based risk with expected return, while the weights must sum to one. An unconstrained formula that…
The document sketches an early timeline for formal portfolio selection theory. It identifies Harry Markowitz’s 1952 work on mean-variance portfolio selection as a foundation of modern portfolio theory, emphasizing how diversification affects portfolio…
The document explains how to choose portfolio weights so each stock contributes equally to total portfolio variance. It defines each asset’s contribution using its weighted variance plus its covariance interactions with other holdings, divided by total…
The document outlines the two stages of Fama–MacBeth regression for testing whether factor exposures explain stock returns. First, time-series regressions estimate each security’s factor loadings. Then monthly cross-sectional regressions use those estimated…
The document raises a basic accounting question about two definitions of net asset value: assets minus liabilities, and that net amount divided by the number of outstanding units. It asks which definition applies to a hedge fund and what outstanding units…
The document considers whether entropy pooling can be used when returns have a nonlinear, time-varying drift. One answer says it can be applied to simulated log returns or resulting prices at the investor’s horizon, then used as input to portfolio…
The document discusses how to choose the market weights and asset universe when calculating the Black–Litterman implied return prior. One response recommends selecting a representative benchmark, then using the portfolio securities’ weights within that…
The discussion explains why a pricing equation with an expectation of one can appear as an equation with an expectation of zero. For a payoff priced today, the Euler equation states that its price equals the expected discounted payoff under the real-world…
The document explains why separate factor regressions for two portfolios do not establish that one has a higher alpha than the other. Each regression tests its own alpha against zero; comparing the estimates requires a statistical model that explicitly links…
The document considers a portfolio optimization problem with a fully invested constraint and a risk-adjusted return constraint involving the square root of portfolio variance. It describes converting that square-root expression into a quadratic form, which…
The document presents a simplified Basel Pillar 2 granularity adjustment that adds a concentration-sensitive component to capital assessment. Its formula combines squared exposure shares with exposure-level terms involving default probability, loss given…
The document explains a practical way to estimate a covariance matrix for a portfolio containing a stock and multiple calls on that stock, with a common maturity and different strikes. Rather than relying on historical return data, simulate the stock forward…
The document frames a multi-period funding problem: choose among borrowing sources to cover forecast cash shortfalls while minimizing interest expense. The example includes fixed-rate borrowing with a short maturity, a capped source available across a range…
The document raises a portfolio-allocation problem for an algorithmic trader running several stock-market models that may generate signals at the same time. With a finite wallet, committing all capital to one model can prevent acting on another signal and…
The document discusses how to estimate the covariance matrix needed to construct a Markowitz efficient frontier. It names maximum-likelihood estimation from historical returns as a standard approach, then describes alternatives: shrinkage of the covariance…
The document sketches a two-investment portfolio model inspired by a time-dependent Polya urn. The portfolio is split between two assets, and one asset is monitored at each step with probability proportional to its current portfolio weight. If the monitored…
The document outlines how to assess whether an ESG score behaves like a priced equity factor. It cautions that correlating ESG scores with established characteristics such as size or value does not establish a risk premium. Instead, it proposes sorting…
The document explains why assets can receive large or small weights in a mean-variance portfolio. The allocation balances expected returns against portfolio variance, so an asset’s own risk and return matter, as do its correlations with the other holdings.…
The document explains why combining two managers’ returns using fixed allocation weights each quarter can produce a misleading annual result. That calculation assumes the portfolio is restored to its target equity and fixed-income weights after every period.…
The document presents two ways to incorporate skewness into portfolio optimization alongside expected return and variance. One derives a third-moment term from a third-order Taylor approximation to a constant absolute risk aversion exponential utility…
The document clarifies that a Sharpe ratio calculated from daily returns is a daily estimate, regardless of how many observations were used, and that converting it to a monthly or annual figure depends on the return interval. Under the usual…