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 how an efficient frontier based on expected return and Entropic Value-at-Risk (EVaR) should compare with frontiers built using variance or Conditional Value-at-Risk (CVaR). It notes that EVaR is an upper bound on VaR and CVaR, then asks…
The document proposes a mean–variance model for a static portfolio of assets quoted at bid and ask prices. It represents each asset’s long and short exposure as separate nonnegative variables, calculates expected returns and covariances for those positions,…
The discussion examines why fundamental equity risk models, such as Barra-style models, often assign securities a binary exposure to their country, industry, or world factors. A one-zero membership indicator is a simple way to define exposures and estimate…
The discussion compares position sizing in proportion to inverse volatility with sizing in proportion to inverse variance. In a simple portfolio of normally distributed assets, inverse volatility sizing is associated with risk parity: it treats assets as…
The document explains ways to identify a portfolio with zero beta when no risk-free asset exists. One practical approach begins with a portfolio of assets, estimates its beta by regressing its returns on market returns over a chosen horizon, then offsets the…
The document shows how to derive the price of a 10-year zero-coupon bond from two 10-year coupon bonds with different coupon rates and known prices. The replication scales a long position in the lower-coupon bond and a short position in the higher-coupon…
The document frames portfolio construction as choosing weights across return series to maximize the Sharpe ratio, defined in the question as average portfolio return divided by its standard deviation. It provides a small sample return matrix and a CVXPY…
Reverse stress testing starts with an unacceptable outcome, such as a specified portfolio loss or capital shortfall, and works backward to find market scenarios that could produce it. When many combinations could reach the threshold, assumptions about how…
The document explains why the Kelly criterion chooses a position size by maximizing expected logarithmic wealth growth rather than expected wealth or simple return. Because wealth compounds multiplicatively across repeated bets, log returns add across…
The document addresses how risk managers can respond when portfolio managers argue that tighter limits kept them from benefiting from rallies or rebounds. Its central recommendation is to agree with senior management on a clear mandate for each trader,…
The document discusses how to broaden a mathematical finance reference sheet that is focused mainly on stochastic calculus and derivative pricing. The responses suggest adding topics that serve distinct parts of quantitative finance: risk management,…
The document describes an R approach to minimizing a linear portfolio objective while imposing limits on net exposure, individual asset weights, total absolute exposure, and portfolio volatility. It suggests using the nonlinear optimizer in Rsolnp, even…
The document discusses how to perform Markowitz mean-variance portfolio optimization in R when expected returns and risk estimates are supplied by the researcher rather than computed directly from a return history. It notes that the `portfolio.optim`…
The document considers how to classify mutual funds into low, medium, and high volatility groups without choosing fixed volatility thresholds in advance. The answer proposes unsupervised clustering with k-means: provide the funds’ volatility measurements and…
The document explains the Carr–Madan formula as a way to represent a sufficiently smooth payoff as a linear position in the underlying, a cash amount, and integrals of European put and call payoffs across strikes. The decomposition expands the payoff around…
The document raises a practical problem in estimating covariance for portfolio construction when asset price histories have different gaps. Missing observations arise from holidays, isolated data omissions, and longer stretches without quotes, leaving…
The document discusses using the PerformanceAnalytics Return.portfolio function to apply a time series of portfolio weights to daily asset returns. The author observes that specifying different rebalance_on frequencies appears to produce identical portfolio…
The document considers how to select and prepare market and macroeconomic time series for a portfolio return regression. The portfolio example is denominated in Swiss francs and includes global equities, fixed income, gold, commodities, currency pairs, and…
The document asks for methods to manage asset allocation across discrete transition states, with attention to liquidity, trading costs, and delayed cause-and-effect relationships. It contrasts moving from cash directly into an asset with transitions between…
The document explains how the risk-aversion coefficient in mean-variance utility affects portfolio choice. A low coefficient places less weight on variance and permits greater risk exposure; a high coefficient penalizes risk more heavily. Varying the…
The document describes a proposed liquidity-adjusted asset pricing analysis using monthly turnover, defined as average daily volume relative to shares outstanding. Because the measure is persistent, the author plans to model each stock's liquidity with an…
The document presents a portfolio measurement problem involving two funds with different valuation schedules and cash-flow rules. One fund is valued monthly, allows cash flows only at month-end, and can use time-weighted returns. The other is valued…
The document asks whether portfolio plots built from combinations of several stocks are plausible and why they show few portfolios with both low returns and high standard deviation. The portfolios use weekly return and volatility estimates, with the asset…
The document considers how to hedge a government bond portfolio using available short- and long-maturity futures. It cautions that a single quoted risk measure or maturity match is not enough to determine an effective blend: DV01 is nonlinear, and duration…