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.
21,023 documents
The document explains how covariance-matrix inversion affects the standard mean-variance portfolio solution. In an eigenvector decomposition, each direction’s contribution is scaled by the reciprocal of its covariance eigenvalue. Consequently, directions…
The document shows how to calculate a money-weighted rate of return for a pension fund with dated inflows and outflows. The method sets the future value equation to zero at the fund’s closing date, compounds the starting balance over twelve months, adjusts…
The document discusses how to evaluate residuals when comparing time-series forecasts, including volatility forecasts from models such as GARCH. It recommends examining autocorrelation: if errors contain predictable structure, the model may be missing a…
The document asks for the stochastic differential of an exponential built from an integral involving a diffusion process. The questioner applies Itô’s formula to the exponential, but assumes the integral has differential equal only to the integrand at the…
The document poses a conceptual question about the efficient market hypothesis (EMH): if prices reflect available information and investors are rational, why should prices change or investors expect returns? It considers three possibilities: no new…
The document resolves a confusion between variance as a function of a probability parameter and portfolio variance as a function of asset weights. A Bernoulli variable’s variance can be concave in its probability parameter, but portfolio variance, expressed…
The note derives the range of a common off-diagonal correlation that makes a matrix with unit diagonal entries a valid covariance or correlation matrix. It corrects a variance calculation: when summing pairwise covariances in the variance of a sum, each…
The note asks why a CAPM generalized method of moments specification does not add a separate moment equating the factor’s sample mean to its expected value. It explains that the cross-sectional pricing moments compare each asset’s expected excess return with…
The document asks what changed in Monte Carlo methods for pricing American options between 2005 and 2016, following earlier machine-learning work on optimal stopping. One answer argues that the period brought few groundbreaking Monte Carlo advances and that…
The document considers a finite-difference approximation to the Black–Scholes equation and asks how coefficient sign conditions can establish a maximum-norm bound. The proposed argument rewrites each value at one time level using the neighboring values and…
The document introduces mean-variance portfolio optimization, including a minimum-variance portfolio and a variance-minimizing portfolio constrained to a target expected return. It then describes practical variations: long-only holdings, caps on individual…
The document discusses the economic meaning of the intercept, or alpha, in regression-based asset pricing models. In a return regression, the intercept represents the component of return not explained by the included factors when their returns are zero. For…
The document explains how to obtain a quantile of an exponentiated normally distributed variable. If the logarithm of a positive variable is normal, its quantile is found by taking the exponential of the corresponding normal quantile. Because the exponential…
The document raises a problem in simulation-based testing of investment strategies that use valuation measures such as price-to-book or dividend yield. A simulation that generates prices while retaining historical values for accounting variables may create…
The document examines why selecting the top decile of S&P 500 stocks by price-to-earnings ratio can produce fewer names than an expected count. One proposed explanation is that some companies had negative earnings during the measurement period. Since the…
The document asks for a route from beginner-level C++ to quantitative trading, from a learner who already programs professionally in Visual Basic and has trading experience. The response suggests starting with a general C++ text, then studying resources…
The document examines how the value of an inflation-linked payment can differ from expected inflation multiplied by a discount factor when inflation and interest rates are correlated. It presents a simplified convexity adjustment for a fixing paid after a…
The document examines limitations of variance as a portfolio risk measure, especially when return distributions are not well described by a stable normal model. One example compares two hypothetical single-stock portfolios with the same variance: one has…
The document asks whether investors who understand asset pricing should hold only portfolios on the mean-variance efficient frontier. It presents a relation between an asset’s expected return, its volatility, its correlation with the stochastic discount…
The document explains how to maximize expected return for a portfolio subject to a limit on expected shortfall (ES), also called conditional value-at-risk. It describes an auxiliary function of portfolio weights and a threshold variable: the function is…
The document explains why spot forex historical data cannot be interpreted like exchange consolidated equity data. Spot foreign exchange is fragmented across dealers and electronic venues, so there is no single source that captures all quotes, orders,…
The document applies Itô’s lemma to an exponential function of an integrated short rate under the Vasicek model. It derives the stochastic differential of the intermediate process, then uses its drift and diffusion terms to obtain the dynamics of the…
The document explains how the Lévy measure determines whether successive jump times and their gaps can be treated as discrete events. When the Lévy measure has finite total mass, jumps form a compound Poisson process, with rate equal to that total mass; the…
The document considers how to compute an exponential moving average across a large universe without replaying every observation since each security began trading. It explains that the recursive form needs only the prior EMA, while the equivalent direct form…