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 examines a result for equal risk contribution portfolios when every pair of assets has the same correlation. Under that assumption, equal contributions imply that each asset’s weight multiplied by its volatility is equal across assets. The post…
The document considers how to reconstruct the historical performance of a stock portfolio. It contrasts a daily return based on prior portfolio value and current holdings’ weights with the simpler calculation of summing each holding’s quantity times its…
The document discusses using principal component analysis to understand portfolio exposures and construct hedge baskets. It corrects an example that applies PCA to equity and ETF returns: the code uses a correlation matrix, while the stated method expects a…
The document explains that portfolio optimization determines asset weights under a chosen objective; it does not automatically identify a small set of stocks expected to outperform. In mean-variance optimization, the inputs include expected returns,…
The document presents a proxy hedge for a company expecting Norwegian kroner while seeking to manage the dollar value of that future receipt. Because a direct kroner-dollar hedge is assumed unavailable, the company uses euros as a correlated substitute. The…
The document explains when a portfolio’s conditional beta can be calculated from the conditional betas of its holdings. For ordinary beta, covariance is linear in portfolio returns, so the portfolio beta equals the sum of each asset’s beta multiplied by its…
The note frames value averaging as an investment rule that specifies how much wealth to commit over time to reach a chosen portfolio value path. It characterizes the approach as mean-reverting in spirit: contributions respond to the difference between the…
The document asks why a mean-variance optimization formulation uses a cost exponent of five-thirds when incorporating a square root market impact model. The author suspects the exponent may result from converting impact costs between units, but does not…
The document raises a question about using exponential differential Shannon entropy as an uncertainty measure in portfolio selection. It asks whether the measure of a sum of random variables is bounded by the sum of their individual measures, and compares…
The document explains why a two-asset portfolio’s standard deviation is not automatically zero when the assets have correlation of negative one. Substituting that correlation into the variance formula yields a perfect square: the absolute difference between…
The document shows a maximum-return portfolio optimization with a covariance penalty and intended limits on individual asset weights. Although the author creates absolute-value bounds and a full-investment constraint, the reported portfolio contains…
The document poses a methodological question about applying principal component analysis to daily yield curve changes. It compares using observable par rates, as in influential work on common factors in bond returns, with first bootstrapping a curve and…
The discussion considers how to estimate risk and return for a portfolio whose current holdings are known but whose assets have price histories of unequal lengths, shorter than the desired measurement horizons. One response annualizes estimates from the data…
The document examines how many observations are needed to estimate a covariance matrix for portfolio analysis. It distinguishes the sample count needed for a matrix to be full rank from the larger amount of data that may be needed to estimate its entries and…
The document explains how to calculate covariance between portfolios, including a global minimum variance portfolio and a mean-variance efficient portfolio. The same covariance definition used for individual securities applies: use the portfolios’ returns…
The document raises a sample-selection question for a value-momentum asset allocation strategy. Its in-sample period includes the global financial crisis, and the strategy optimizes a value cutoff for allocating across asset classes. The concern is that…
The note considers applying Black–Litterman in an ongoing portfolio rebalancing process. It asks whether previous portfolio weights can serve as the prior when new expected return forecasts arrive. The response says the framework can incorporate market views…
The document surveys reported portfolio construction approaches at several robo-advisors and asks whether firms rely only on Modern Portfolio Theory or use other methods. The cited descriptions include Black-Litterman expected returns, asset-weight…
The discussion derives how to obtain the two multipliers in the first-order condition for a mean-variance efficient portfolio when its target return and fully invested constraint are known. Recasting the condition as the first-order condition of a…
The document explains why a two-asset portfolio’s usual return versus standard-deviation curve depends on asset means, variances, and covariance. With those quantities fixed, Pearson correlation determines the covariance term, so additional nonlinear…
The document asks how to divide an annualized XIRR among dividends and stock-sale gains, using an example with an initial stock purchase, an interim dividend, and a later sale. The replies distinguish calculating an overall money-weighted return from…
The discussion examines whether least-squares regression of Nasdaq-100 component prices, returns, or price changes against the index can recover its constituent weights. The original analysis used about 168 market days of adjusted prices for the index’s…
The document distinguishes the feasible set of randomly sampled portfolios from the efficient frontier. Randomly generated weights populate a cloud of possible risk-return outcomes; points inside that cloud are generally dominated, while its efficient…
The document asks whether combining a volatile underlying asset with options can improve portfolio diversification, measured by a higher Sharpe ratio than holding the asset alone. It motivates the question with a position consisting of one share and one…