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 derives an expected-utility rule for deciding whether to accept a two-outcome investment. An investor with logarithmic utility receives one return with probability 0.6 and incurs a loss with probability 0.4. The investment is avoided when the…
The document walks through a numerical example of a long futures position whose daily gains and losses are settled in cash. Because the position controls many units while the trader posts only an initial margin deposit, a modest percentage move in the…
The document considers how to connect a forecast driven trading system to Kelly sizing. The example code estimates probabilities from forecast data, derives candidate stakes for long and short positions, updates a bankroll sequentially, and calculates…
The discussion explains why replacing variance with semivariance in the familiar Kelly fraction does not preserve the usual log-utility objective. The mean-over-variance expression relies on assumptions such as normally distributed returns and follows as an…
The document discusses defending a short out-of-the-money strangle by entering a futures position when the underlying reaches a short strike. The proposed approach aims to respond before the option reaches breakeven, but the response explains that hedging…
The document considers how a market maker should choose the quantities displayed on bid and ask orders. Its central guidance is to define an acceptable inventory range and size orders in relation to the risk of reaching its limits. One response proposes…
The document examines why the Merton portfolio formula can produce a large recommended allocation to equities. The fraction depends on expected excess return, volatility squared, and risk aversion. Using historical equity returns, a risk-free rate, and…
The question asks how to size a variance swap as an imperfect hedge for an asset return that tends to weaken when its variance rises. It proposes modeling returns with a GARCH-in-mean relationship and setting swap notional to offset the estimated sensitivity…
The document discusses a bullish LEAPS call spread: buy an out-of-the-money call and sell a call at a higher strike, with both options expiring more than a year away. The proposed plan is to close the short call partway through the trade if the outlook…
The document considers a portfolio constraint under which each asset must either have zero weight or meet a positive minimum allocation. This creates a non-convex feasible set, so an ordinary continuous portfolio optimizer cannot represent the choice…
The document explains relative risk aversion as absolute risk aversion scaled by wealth. The scaling makes the measure invariant to a change in the units used to express wealth. It also relates the measure to utility curvature: marginal utility and its rate…
The document asks how the Merton portfolio choice problem relates to Kelly sizing, which selects a bet size to maximize expected logarithmic wealth. It presents the familiar Merton risky-asset fraction in terms of excess expected return, return variance, and…
The document shows how to express a joint allocation across multiple portfolios as one quadratic program. It stacks each portfolio’s asset weights into a single decision vector, then writes constraints for distributing each asset’s total holdings, matching…
The document considers how to reallocate capital when a fund manager breaches a drawdown limit, but it does not provide a direct optimization rule for distributing the withdrawn money among managers whose allocations cannot be reduced. Instead, its answer…
For a futures position, exposure should be measured using the contract’s own price, since changes in that price determine the position’s profit and loss and daily variation margin. The contract size multiplied by the futures price is therefore the relevant…
The document discusses how to train a trading model intended to operate only in low-volatility conditions. The question contrasts supplying volatility as a feature with explicitly excluding unsuitable market states. The response recommends retaining…
This explanation clarifies how to size a position to offset market exposure when an asset’s return sensitivity is described by a regression beta. The key step is to distinguish percentage returns from dollar profit and loss: beta scales the asset’s…
The document considers portfolio weights chosen to bring portfolio variance close to a target while meeting a minimum expected-return requirement and a fully invested budget constraint. It discusses solving the resulting optimization at each rebalance date.…
The document explains how to represent leveraged trading in an account model. Borrowed funds can be represented as negative cash: buying shares reduces cash, potentially below zero, while selling shares increases it. The account’s equity is the sum of cash…
The document asks how to use constant relative risk aversion utility to calculate the payment a person would accept to avoid an even-odds gamble. It also poses a second question about when a person with CRRA preferences rejects a gamble with a possible loss…
The document compares selecting a betting fraction by maximizing the terminal wealth from one simulated sequence with choosing a fraction under the Kelly criterion. In a repeated even-odds coin game with a stated win probability, it calculates the classical…
This document asks how much future company information, especially accounting results and profits, could explain subsequent stock returns if it were known in advance. It contrasts that hypothetical question with conventional factor research, which uses…
The example estimates one-day Value-at-Risk for a large position in at-the-money European call options on a non-dividend-paying stock. It uses a first-order approximation: convert annualized volatility to a daily standard deviation, take the adverse return…
The document considers a cross-sectional equity mean-reversion idea: rank index constituents by past returns, pair the strongest performers with the weakest, and allocate more capital to the most extreme pairs using a linear weighting scheme. The main sizing…