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 combine monthly Fama–French factor returns into multi-month returns. Rather than taking an arithmetic average, the response compounds the monthly returns: convert each percentage return to a growth factor, multiply those factors…
The document describes an R error that occurs when the PerformanceAnalytics Return.portfolio function is asked to rebalance a portfolio on a calendar frequency. The reported call fails with a subscript error, while the function works when rebalancing is…
The document asks how to make the absolute position weights in a six-stock long-short portfolio as equal as possible while respecting gross exposure, long exposure, and beta-adjusted net exposure limits. It proposes minimizing the variance of absolute…
The document asks whether an efficient-frontier portfolio must also lie on the capital market line (CML), and whether a portfolio’s standard deviation can be inferred from its expected return using the CML equation. It presents a CAPM setup with a risk-free…
The document discusses how to calculate a portfolio’s cumulative return from asset prices and weights that change monthly. It distinguishes a portfolio rebalanced to target weights every day from one whose holdings are allowed to drift between monthly…
The document asks why Harry Markowitz described algorithms for finding efficient portfolios without deriving a closed-form equation for the efficient frontier in the unconstrained case. It contrasts this approach with a later analytical derivation by Robert…
The note explains how to interpret a portfolio weight greater than one in a combination of a risky market portfolio and a risk-free asset. A positive risky-asset weight above 100% is funded by a negative weight in the risk-free asset, which represents…
The document asks how to infer expected asset returns from observed portfolio weights, a covariance matrix, risk aversion, and weight limits. Its response first considers the unconstrained mean-variance problem with weights summing to one. The first-order…
The discussion challenges the claim that cost of capital alone determines whether a business should invest. It distinguishes profit maximization from utility maximization: decision makers may value power, reputation, innovation, or other personal and…
The note gives an intuition for approximating a portfolio’s log return by the weighted sum of its assets’ log returns. For portfolio weights that sum to one, it expands each asset’s gross return, represented by the exponential of its log return, around zero.…
The document explains why classical portfolio construction usually takes asset return estimates as inputs rather than starting from a portfolio return distribution. In the Markowitz mean-variance framework, historical asset returns are used to estimate…
The document explains rolling correlation for two asset return series: calculate correlation over successive windows and plot the resulting time series. It clarifies that the choice of window depends on assumptions about stationarity. If returns are weakly…
The document asks whether a stock forecast based on real-world return probabilities can support decisions among owning shares, buying protective puts, or substituting calls, and what risk-neutral pricing adds. Its proposed real-world model extrapolates…
The document shows how to formulate a search for arbitrage as an optimization problem using asset prices and state-contingent payoffs. A linear program can minimize portfolio cost subject to nonnegative payoffs in every state. A negative-cost solution…
The document explains why a portfolio built through mean-variance optimization for a target expected return may finish a holding period with a different realized return. It addresses whether the gap between the target and the outcome is necessarily caused by…
The document defines portfolio variance as the quadratic form of asset weights and their return covariance matrix. It then proposes using a matrix square root multiplied by the weight vector to obtain signed asset contributions whose squared values sum to…
The document explains scenarios as market outcomes used to assess or optimize a portfolio. One approach takes asset returns from a historical window and applies that return pattern to the portfolio under consideration. Rolling or overlapping windows can…
The document addresses how to use PortfolioAnalytics in R to run portfolio optimization on intervals such as semiannual or nine-month schedules. The question describes attempts to pass a spacing parameter through the rebalance setting, which continued to…
The document asks whether an agent trained to play Atari games from screen images and scores could learn to trade by observing market data and choosing actions. It introduces deep Q-networks as an example of reinforcement learning, where the agent improves…
The document raises a factor-investing question about the divergence in equity factor performance around the final quarter of 2016. It reports that low volatility had recently outperformed broad capitalization-weighted indices before weakening after the US…
The document asks how to extend mean-variance portfolio optimization to include skewness and kurtosis. It presents an objective with expected return, a variance penalty, and a third-order co-skewness term based on the portfolio weights and co-skewness…
The document frames a portfolio-selection problem in which rows represent candidate bets and columns represent binary win-or-loss scenarios. Because bets may be correlated, selecting the highest individual win rates is not necessarily sufficient. The author…
The document asks why a self-financing strategy’s discounted wealth remains a local martingale when the discounted asset price is a local martingale under an equivalent martingale measure. It frames the gain process as a stochastic integral of the trading…
The document clarifies that the standard Markowitz framework is broader than a single portfolio objective. Its original formulation considers risky assets, forbids short selling, and uses expected returns and covariances to describe the risk-return…