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 asks how to enforce a minimum terminal wealth in a continuous-time consumption and investment problem with CRRA utility. It presents a proposed construction: scale down the unconstrained Merton strategy and use the remaining initial capital to…
The note explains why a sample covariance matrix may have unreliable or zero eigenvalues and summarizes ways to address the problem. Even with balanced observations drawn independently from one distribution, sample eigenvalues differ from population values.…
The note discusses the practical challenge of obtaining low-frequency historical and ongoing data across index providers, including index levels, constituents, and weights. The response highlights licensing as a central constraint: agreements may limit how…
The note explains why Joel Greenblatt’s Magic Formula uses a roughly one-year holding period. It cites the book’s tax rationale: in taxable accounts, selling losing positions just before the one-year mark and winners just after it can give losses short-term…
The question asks how to separate the approximate return of a coupon-bearing bond into yield income, roll-down, duration-driven price change, and pull-to-par effects. The response gives a compact decomposition: return is associated with yield minus repo over…
The document explains a practical way to price several fixed-rate bonds described in a pandas table. A row-wise function converts each bond’s dates and coupon into a QuantLib bond object. The bonds are assigned a shared discounting engine built from a flat…
The document addresses a practical portfolio selection problem: several backtested strategies may produce more stock picks than can be traded in live operation. The response suggests ranking candidate strategies or setups using risk-adjusted performance…
The document explains how to choose a fixed-size, equally weighted basket from a larger asset universe using estimated returns and a covariance matrix. It formulates the selection as a binary optimization problem: indicators represent whether assets are…
The document explores whether a one-step binomial model must use the option’s underlying stock in a replicating portfolio. The response explains replication from the seller’s perspective: construct and, where possible, rebalance a portfolio so its future…
The document describes a portfolio robustness exercise using a Markowitz model. The author estimates expected returns and covariances from historical monthly stock data, finds portfolios associated with minimum and maximum expected returns, and then perturbs…
The document addresses a two-asset portfolio problem: how to allocate a fully invested portfolio between independent stocks to minimize volatility. Under the independence assumption, portfolio variance is the sum of each asset’s variance weighted by the…
The document gathers suggested books and papers for learning quantitative alpha design and advanced quantitative finance. Its starting list includes texts on active and quantitative portfolio management, expected returns, financial machine learning,…
The document asks why a regression of an unequally weighted stock portfolio on a market index produces a lower R-squared and a beta nearer zero than a regression of one constituent stock. The response offers possible explanations rather than a definitive…
The document considers whether an empirical covariance matrix calculated from returns imputed by an expectation-maximization procedure can be trusted. Although the questioner reports good covariance estimates in simulations with substantial missing data, the…
The document explains how to obtain the locally optimal portfolio control in the finite-horizon Merton expected-utility problem. In the Hamilton–Jacobi–Bellman equation, the control is chosen to maximize a function of the value function’s first and second…
The document asks how to calculate the correlation between two portfolios built from the same three assets. It provides each portfolio’s weights and the assets’ pairwise correlations, and the questioner has already calculated portfolio means and variances.…
The document explains what a quoted basket correlation can mean when a trader gives a single percentage instead of a matrix of pairwise correlations. For a weighted basket, its variance depends on each component's variance and on the weighted contributions…
The document asks how to simulate returns for an allocation among equities, bonds, and cash, including how to handle a lower bound of zero for cash returns and how to combine return and risk assumptions for the two defensive assets. An answer suggests…
The document raises a portfolio construction issue for arbitrage strategies that rely on mean reversion. Price deviation indicates the potential profit if a position is held until convergence, but it does not show how quickly that profit may be realized. The…
The document compares two common mean-variance formulations: minimizing variance for a target return and minimizing variance minus a weighted expected return. With an equality constraint on target return, Lagrange multipliers show how the return constraint’s…
The document explains an algebraic rewriting of a covariance matrix formed from a shared random effect and independent residual noise. The key object is the matrix that projects onto the direction of the all-ones vector; with a vector of length T, its…
The document raises the problem of calculating coskewness and cokurtosis for a multivariate lognormal distribution from the parameters of an underlying multivariate normal distribution of log returns. The motivation is portfolio optimization: these…
The document surveys ways to use the eigenvalues and eigenvectors of an estimated covariance matrix to improve portfolio optimization. It points to random matrix theory as a way to distinguish noisy eigenvalues from informative structure. In particular, the…
The document considers portfolio annualization when assets trade on different calendars, using traditional stocks and cryptocurrency as examples. Its central recommendation is to annualize each asset's expected return and covariance contributions using the…