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 whether commonly accepted ranges exist for risk-aversion parameters in power and exponential utility functions. Its author describes simulating stock returns over multiple weeks and comparing optimal portfolios across different values of…
The document discusses a long-short macro momentum portfolio whose positions are adjusted so that the portfolio has a specified forecast volatility. The cited research describes estimating risk from a rolling window of monthly returns and scaling the…
The document explains how a portfolio return function can combine asset returns with a dated series of portfolio weights. It describes aligning the return and weight data, selecting the matching asset columns, and starting the calculation only once initial…
The document considers how to evaluate simulated weekly stock returns with volatility, tail-risk, and downside-risk measures. It contrasts simple percentage returns with log returns and arithmetic with geometric averaging. The accepted answer recommends…
The document addresses how to represent a stock portfolio that is rebalanced periodically while daily positions need to be recovered over time. It presents a trade-journal approach: record each instrument, transaction amount, date, and price, then derive…
This discussion derives the first-order condition for a risk-neutral investor who maximizes expected portfolio return subject to a bound on return variance. It clarifies that the constraint in the question limits standard deviation, so squaring it gives an…
The document surveys research on whether cryptocurrencies differ quantitatively from currencies and other assets. It describes proposed distinctions such as decentralized transaction records, market-specific drivers, high volatility, and limited history. The…
The document uses monthly regressions on a benchmark market return and style factors to interpret two portfolios' return patterns. It reads coefficient t-statistics as evidence of factor exposures: both funds show market sensitivity, while the second has…
The document addresses how a credit union might estimate the funding benefit of equity in a funds transfer pricing or risk-adjusted profitability model. The proposed calculation multiplies the target capital ratio by the loan’s risk weight and by the cost of…
The document offers a concise way to extend a principal component analysis hedge-ratio method from two instruments to a basket with multiple legs. It proposes building the covariance matrix for the instruments, finding its eigenvectors, and selecting an…
The document discusses fund-level risk measures for long-short equity portfolios, including volatility, risk-adjusted returns, drawdown, and long and short exposures. The answer adds market beta or correlation to an appropriate equity index and exposure to…
The document derives the optimal portfolio for a mean-variance objective with a full-investment constraint. It sets the first-order conditions, represents them as a block linear system, and applies block-matrix inversion to eliminate the Lagrange multiplier.…
The note considers a derivative paying an exponential function of a stock’s terminal price and asks whether a static portfolio of stock and a zero-coupon bond can guarantee at least that payoff. Such a portfolio has a payoff linear in the terminal stock…
The document considers how to estimate risk and correlation when one asset has far less price history than the rest of a portfolio. It outlines two approaches: exclude assets with histories too short for reliable estimation, or estimate their covariances…
The document describes a factor model in which factor returns are estimated by weighted least squares from asset returns and known exposures. It derives the corresponding factor mimicking portfolio weights as a matrix involving the exposure matrix and the…
The document explains that mean-variance portfolio optimization does not require normally distributed returns; it requires finite second moments. For returns with finite variance, including the stated Fréchet example, mean-variance allocation remains…
The document discusses how to include swaps, FX forwards, and other non-equity derivatives in Monte Carlo Value at Risk simulations. It contrasts sensitivity-based approximations with full revaluation under simulated market scenarios. Sensitivity methods…
The note derives a way to divide a total fund among people who retire at different times so that each allocation grows to the same value at that person’s retirement. It assumes a constant return and annual compounding. Each person’s share is set in…
The document raises a question about a constrained expected-utility problem: maximize expected utility of terminal wealth while requiring discounted wealth to have a specified risk-neutral expectation. It focuses on a textbook exercise involving the function…
The document explains how the variance of a trader’s wealth can be calculated from the risks and co-movements of the assets held. If wealth is a fixed dollar-weighted sum of asset prices, its variance is the sum of each holding’s price variance scaled by…
The document explains why an unconstrained full Kelly portfolio can have the same relative asset weights as a mean-variance tangency portfolio. Its central claim is that maximizing long-run growth leads to maximizing the portfolio’s Sharpe ratio, so the…
The document raises a practical portfolio-construction question: whether a long-short equity portfolio can reduce risk by balancing its exposures to factors such as value, momentum, size, and volatility. The motivation is that a covariance-matrix optimizer…
The document asks how to calculate beta-weighted delta and gamma for a portfolio of options on different stocks. Its answer gives a relationship for an individual option’s beta: multiply the underlying price by the option’s delta and the underlying asset’s…
The document examines whether the covariance matrix supplied to R’s quadratic programming solver should be doubled when constructing a mean-variance efficient frontier. The question arises because the solver’s objective includes a one-half factor on its…