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 describes a US company that bills a German client in euros while funding payroll in Egyptian pounds. Its cash flows span USD, EUR, and EGP: funds are converted for payroll in Cairo, client invoices are paid in euros on net terms, and the bank…
The document considers how to combine several trading strategies with similar returns and volatility when their trades rarely or sometimes overlap. Equal cash allocations produce a weighted average return, while allocating the full capital to whichever…
The document explains why reaching a target portfolio percentage requires recalculating both the bond holdings and the total portfolio value after new money is invested. The example starts with a £40,000 portfolio holding 40% in bonds and asks how much…
This question examines how to manage simultaneous pair trades that each use the same ETF as a hedge. One signal calls for a long position in a stock against a short ETF position, while another calls for a short stock position against a long ETF position. The…
The document considers a portfolio optimizer that maximizes expected return subject to a Value-at-Risk limit, then adds borrowing to permit leveraged positions. It asks how VaR should be calculated once debt is included. The response says borrowing costs…
The document raises a portfolio-construction question: how should raw signals that produce instrument positions be combined into a final portfolio? It considers averaging or weighting signals within each instrument, then applying a portfolio method such as…
The document derives the time needed for an account with an initial balance and regular monthly deposits to reach a target under compound interest. It models the balance recursively: each month’s opening balance earns interest, then a deposit is added.…
The document asks why trading research does not more often estimate conditional return distributions from data, update them with Bayesian methods, and use those distributions to solve for expected-value-optimal position sizes. It notes that normality…
The document poses a currency risk management exercise for a Czech company with a euro payable due at month end and an expected euro receipt halfway through the month whose arrival is uncertain. It asks how to hedge the exposure using futures, calculate the…
The document frames a trading problem in which an oracle repeatedly predicts whether an asset’s price will be higher or lower at a fixed future horizon. Each forecast has a stated accuracy rate, and the question assumes that absolute price-change magnitudes…
The document discusses mean-variance portfolio optimization with a target return, a fully invested constraint, and a limit on the sum of absolute portfolio weights. That absolute-weight constraint limits gross leverage while allowing short positions. It…
The document presents an R simulation intended to reproduce a Kelly capital growth example. It defines a set of bets with different win probabilities and odds, assigns probabilities to selecting each bet, and associates each with an optimal Kelly stake. The…
The document explains how to translate mean-variance portfolio weights into holdings. Given total capital and asset prices, allocate capital in proportion to each optimized weight, then divide each allocation by the asset price to obtain the number of…
The document asks how to choose a log-growth-maximizing allocation for a portfolio holding a stock and an option through expiration, without continuous hedging. It contrasts the familiar single-asset Kelly formula with the harder joint problem and describes…
The document examines how to obtain long-term leveraged exposure to a single stock with a stable leverage factor, no knock-out, and no fixed end date. Suggested structures include European factor certificates, bespoke total-return swaps or contracts for…
The document analyzes a game with fourteen cards that double a bankroll and one card that sharply reduces it. A player chooses how many cards to draw, and the discussion contrasts the expected value of the choice with its variance and Sharpe ratio. The…
The document explains the return of a hedged position that holds one unit of stock A and shorts h units of stock B. The portfolio’s return is written as rA − h rB: stock A contributes its return, while the short position contributes the negative of stock B’s…
The document explains two ways to estimate interest rate swap PV01 and infer a notional from a target risk amount. For an exact sensitivity, it recommends pricing with unbumped market data, bumping the market curve, repricing, and measuring the change. When…
The document shows how to calculate a running net amount for a short-selling backtest when positions are added over time. The proposed recurrence updates the previous net amount by the next period's short-sale price change, then adds the value of any new…
The document raises an implementation question about the differential Sharpe ratio in an online setting. It contrasts this approach with calculating Sharpe over a sliding time window and notes that the method updates two recursively maintained quantities,…
The document explains why Kelly sizing maximizes expected logarithmic wealth rather than expected terminal wealth. In a repeated favorable coin-toss game, betting all available capital can maximize expected wealth but carries a high risk of ruin. Betting a…
The document addresses how to calculate portfolio weights as they drift under buy-and-hold returns, an operation used in a Monte Carlo stress-testing workflow. It states the recursive update: each asset’s prior weight is multiplied by its gross return and…
The document asks how to estimate the price change that would make a risk-adjusted trading system add one share. The proposed procedure estimates annualized return volatility at the latest price, calculates the current position, then holds volatility fixed…
The exchange considers how to choose whole-share quantities under a cash budget to approximate target portfolio weights. It critiques an objective that minimizes squared differences in share counts: equal share-count errors can represent very different…