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.
4,613 documents
The document explains the basic construction of a bull spread using European calls with a common expiration. For the two-call example, the proposed position buys the lower-strike call and sells the higher-strike call. The intuition offered is that the…
The document asks how to size a short position in one asset to hedge a long position in another using their betas. The accepted answer gives a dollar-weighting rule: make each position’s market value inversely proportional to its beta. It illustrates the…
The document explores how to set asset-level risk contribution budgets while also requiring a portfolio to meet a target volatility. It presents an optimization that minimizes squared differences between each asset’s share of portfolio variance and its…
The document considers whether a proposed Kelly fraction is appropriate for a trading record described by a win rate and average win and loss sizes. One response gives the standard expression for the special case where every win has the same size and every…
The document explains how a trading system can update position quantity, cost basis, average price, and realized and unrealized profit and loss incrementally as fills arrive. Under average-cost accounting, the update uses the prior position and cost, plus…
A return regression can help estimate a strategy’s Sharpe ratio, but the regression alone does not determine it. The result depends on how the signal is converted into positions and, for portfolios, on the conditional covariance among assets. A tangency…
The document examines when optimizing expected utility leads to an investment fraction proportional to expected return divided by variance. It writes the first-order condition for an investor choosing a fraction of wealth in a risky asset, then identifies…
The document explores how to allocate capital among models that trade different instruments, strategies, and holding periods. One proposed starting point is to treat each strategy–instrument combination as a portfolio component and apply mean–variance…
The problem asks how to choose a fraction of current wealth to stake each day in an even-money game with a favorable win probability, so as to maximize the chance of reaching a target within a fixed horizon. One answer proposes a target-seeking sequence: bet…
The document asks how to choose a stop-loss boundary automatically from a trade log containing entry and exit times, profit or loss, maximum adverse excursion, and maximum favorable excursion. The suggested approach frames threshold selection as an…
The note addresses how to size a long breakeven inflation position using an individual inflation-linked bond and a nominal Treasury of similar maturity. It describes a common starting assumption: real yields and nominal yields have a beta of one. Under that…
The document compares ways to allocate capital between two strategies when only their average daily P&L and Sharpe ratios are known. It infers daily volatility from those inputs, then distinguishes three objectives: maximize expected profit, minimize…
The document distinguishes a positive expected payoff from an arbitrage. In its energy investment example, each unit of generation capacity costs 70 euros and earns either 230 euros or loses 60 euros, depending on the electricity price. The stated…
The discussion considers whether triple-barrier labeling should use a flexible vertical horizon alongside volatility-scaled profit and loss barriers. One response frames the vertical barrier as a practical limit on how long a trade event can remain tied to…
The document considers how to target a desired portfolio volatility when optimizing a dollar-neutral long-short portfolio with leverage and per-asset weight limits. Scaling optimized weights afterward by the ratio of target volatility to recent realized…
The discussion compares a leveraged ETF with borrowing on margin to increase exposure to an equity ETF. Its central point is that margin borrowing leaves the investor responsible for managing leverage as the asset value changes, while a leveraged fund resets…
The document asks how to maximize expected portfolio return while keeping risk, such as value at risk, under a chosen ceiling. The answer points to an R package with portfolio optimization routines for expected shortfall and its long-short variant,…
The document considers how a market maker with no initial inventory might submit orders to capture the bid-ask spread, and whether submitting both sides is preferable to sequential or one-sided strategies. One response explains that market makers generally…
The document considers a mean-variance portfolio optimization with short positions allowed, linear equality constraints, and a bound on the absolute size of each position. It asks whether an auxiliary variable and a large penalty are needed to express the…
The document considers an investor whose primary concern is whether portfolio value ever falls below the initial investment, even if the strategy later earns a positive return. It explains why variance, Sharpe ratio, maximum drawdown, and tail-loss measures…
The document outlines a supervised learning setup for choosing positions in a single instrument. At each point in time, past prices are summarized as features such as momentum, volatility, and other technical indicators; fundamental information could also be…
The document frames a bankroll-sizing problem for poker cash games, where returns over a fixed number of hands are treated as approximately normally distributed rather than as discrete tournament payouts. It gives an example with a stated mean and standard…
The document poses a practical question about measuring a foreign-exchange forward hedge when the value of the underlying portfolio holding changes. It describes a USD exposure that is intended to be converted into EUR in one month and a forward contract…
The document surveys ways quantitative methods from finance and statistics can apply to sports betting. It compares bookmakers managing event odds with market makers quoting binary options: both may adjust prices in response to their existing exposure and…