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 why a quadratic programming portfolio optimizer may use twice as many decision variables as there are assets. Each asset’s exposure is represented by a positive part and a nonpositive part, which together reconstruct the signed…
The document compares two ways to construct portfolios that track observable macroeconomic factors. Its naive proposal regresses each factor’s time series on returns from a base universe of assets; the resulting coefficients define weights that minimize…
The document examines why compounding the asset’s period returns does not match the holding-period return of a short position when the short is evaluated using its initial notional. Its example uses a price path of 5, 6, 4, and 2.5, with the short asset…
The document asks which portfolio optimization methods are considered most robust out of sample, especially when assets have price histories that begin on different dates. It points to a 2002 paper on robust portfolio selection as a possible approach, but…
The document discusses calculating average portfolio turnover from beginning-of-period and end-of-period weights. It warns that random return data can produce extreme or unrealistic results because the simulated asset returns include very large losses. In an…
The discussion explains why options strategies often lack a standard benchmark: each strategy may trade a different basket of contracts, and the VIX is a price index rather than a return index. For a long-only strategy, it suggests building a custom index…
The document distinguishes a leveraged ETF’s net asset value from its market exposure. NAV per share comes from the market value of assets, less liabilities, divided by shares outstanding. Cash, cash equivalents, stocks, and liabilities such as margin loans…
The post asks whether the ratio of upside deviation to downside deviation can guide portfolio weights. Its author informally calls the ratio “acceleration” and imagines using it to size a momentum strategy, on the intuition that upside variation represents…
The document explains why calculating beta in both directions between a portfolio and a benchmark does not generally produce reciprocal values. It defines beta as the covariance of the two return series divided by the variance of the variable used as the…
The document clarifies why different Ledoit–Wolf covariance estimators can produce different diagonal values. Shrinkage is not one unique procedure: the result depends on the target matrix. The constant-variance approach used by scikit-learn shrinks toward a…
This discussion collects learning resources on applying hidden Markov models to financial markets. Suggested applications include detecting market regimes and forecasting changes in turbulence, inflation, and economic growth. The references describe…
The document considers how to determine whether a fund or portfolio has momentum exposure or tends to add to positions after strong past performance. It assumes access to a year of monthly holdings and returns. The question proposes regressing portfolio…
The document gives a brief orientation to calculating portfolio risk and return in R from historical holdings data. It points to computational finance materials and portfolio analytics resources, and names common tasks: measuring the standard deviation of a…
The document addresses whether two Markowitz portfolio formulations are equivalent when one requires expected return to equal a target and the other requires it to be at least that target. Its argument considers a candidate minimum-variance portfolio whose…
The document presents the common-factor and specific-risk components of covariance between a portfolio and the market in a predicted beta framework. Common covariance is expressed through portfolio and market factor exposures and a factor covariance matrix.…
The document explains how to build a time series of portfolio log returns from constituent stock returns when portfolio weights are specified. Because log returns do not combine linearly across assets in the same way as simple returns, directly taking a…
The document explains how to calculate portfolio risk when asset weights can be negative. For independent or uncorrelated assets, portfolio variance is the sum of each asset’s variance multiplied by the square of its weight; standard deviation is the square…
The document distinguishes portfolio choice among risky assets from allocating wealth between a risky portfolio and a risk-free asset. It explains that adding a tradable risk-free asset creates a capital allocation line from the risk-free return through the…
The document considers what expected return to assign a momentum strategy when using mean-variance portfolio optimization. It presents empirical estimation by backtesting the strategy, then updating the estimate with live trading results. Estimates may also…
The document discusses how to choose weights for two risky assets to maximize the portfolio Sharpe ratio when short selling is prohibited. One answer expresses the unconstrained optimum using each asset’s Sharpe ratio, volatility, and the correlation between…
The document asks how to construct industry portfolios for markets such as the UK and Japan when a familiar US industry classification may not be available or current. The intended use is to study relationships between stock returns and economic variables at…
The document explains how to recover portfolio weights after solving a transformed optimization problem for the maximum Sharpe ratio. In Markowitz portfolio theory, the tangency portfolio is associated with the highest ratio of expected excess return to…
The document asks how a common equal-risk-contribution (ERC) objective compares with a formulation that maximizes the sum of log weights under a unit variance constraint. The first method computes each asset’s share of portfolio variance, then minimizes…
The document considers the set of portfolio weights that sum to one and produce a specified volatility under a given covariance matrix. It explains that the target-volatility condition is a quadratic constraint, so the solution set is generally a continuous…