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 why a portfolio’s simple return is expressed as a weighted sum of its assets’ simple returns, since directly comparing portfolio value at the start and end appears to produce a different formula. The resolution is that portfolio weights…
The discussion corrects an annualized Sharpe ratio calculation based on 36 monthly observations. For monthly returns, the risk-free rate should also be expressed monthly, and the monthly Sharpe ratio is conventionally scaled by the square root of the number…
The document asks whether portfolio optimizers should reshape the covariance of expected-return forecasts, given that forecast covariance can be transformed independently of the market-return risk matrix. The response cautions that raw forecast covariance is…
The document raises a question about factor exposures when constructing equal-weighted and value-weighted benchmark portfolios from a cleaned set of U.S. listed firms. The portfolio universe contains firms across AMEX, NYSE, and NASDAQ, with membership…
The document considers a Monte Carlo portfolio analysis in which changing the weights and strikes of put options reduces measures such as expected return and volatility, while Value at Risk sometimes rises. The response says this outcome can be plausible…
The discussion explains why a long-short portfolio can have a higher market beta than a long-only portfolio. Scaling exposure to the market scales beta, while short positions can offset some of that exposure. The example compares a portfolio beta of 0.5 with…
The post asks whether the volatility of a stock portfolio can be compared with the volatility of the S&P 500 when one is calculated from constituent volatilities and correlations and the other from observed index returns. The accepted answer says the direct…
The document presents a Markowitz-style mean-CVaR portfolio optimization setup. It defines scenario losses from portfolio returns, uses a confidence level to form CVaR, and balances expected return against tail risk with a risk preference parameter. The…
This note considers how to estimate value-at-risk for a stock-and-bond portfolio when one stock has only a short post-IPO return history. It raises two possible workarounds: bootstrap the stock's observed returns to create a longer series, or substitute…
This note describes the gap between theoretical online portfolio selection (OLPS) models and live implementation. It points to assumptions often used in research, such as no transaction fees or market impact, ample liquidity, and the ability to trade…
The discussion considers back-testing a portfolio of individual stocks intended to track an equity index or ETF. It emphasizes that matching constituent trades alone is insufficient: a faithful simulation must reproduce the index’s rules, rebalance timing,…
The document asks whether performance statistics such as profit factor and Sharpe ratio should be computed for each leg of a pairs trade separately or for the combined position. Its example shows that the measured profit factor differs depending on whether…
The document explains how to evaluate a history of overlapping trades as a portfolio, including cumulative profit and loss, drawdowns, and period returns. Its central method is to value each open position over time using market prices, then aggregate the…
This document presents a bond portfolio duration calculation and asks how to hedge its interest-rate exposure with a fourth bond. The accepted answer distinguishes Macaulay duration, which measures the weighted timing of cash flows, from modified duration,…
This document describes a question about how realized returns from a Constant Proportion Portfolio Insurance strategy change as its floor is varied. The investor compares a fully bond-invested portfolio at a 100% floor, a fully risky-market portfolio at a 0%…
The document explains why a global minimum variance portfolio has the same covariance with any fully invested asset or portfolio. Its algebra starts with the GMV portfolio weights, proportional to the inverse covariance matrix applied to a vector of ones.…
The response offers several theoretical research areas for someone seeking mathematical finance problems grounded in analysis, probability, and optimization rather than statistical modeling. It suggests investigating convergence questions in simulation-based…
The discussion addresses portfolio analysis when stocks have different listing dates and incomplete monthly return histories. It warns that interpolating irregular observations to create an even time series, often by linear interpolation, can introduce…
The document presents a validation question for a machine-learning portfolio strategy evaluated out of time against a strong benchmark. Its custom rolling metric reflects portfolio value and additional state variables such as inventory and time. The observed…
The document explains why the Fama–French model represents size and value effects with portfolio returns such as SMB and HML instead of using firm characteristics directly. In the asset-pricing framework discussed, expected returns are linked to covariance…
The document asks how to handle bonds that mature while backtesting a fixed-income portfolio strategy, particularly when trying to reproduce a published study. It focuses on how a maturing bond contributes to returns and how the portfolio should account for…
The document compares two portfolio optimization objectives: expected return penalized by variance, and expected return penalized by standard deviation. It derives a parameter mapping, δ = η divided by the portfolio’s standard deviation, that makes their…
The document discusses unstable coefficient estimates when returns-based style analysis uses many correlated indices or factors. Suggested tools include ridge and lasso regression, which add penalties to coefficient estimates; lasso can also encourage factor…
The document distinguishes return measures according to their use. To summarize a monthly portfolio series as an annual growth rate, it recommends compounding the simple monthly returns and converting that compounded growth into an annualized simple return.…