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 asks how to turn a sequence of predicted future prices into an optimal trading plan for a single asset and cash pair. Its proposed setting removes bid–ask spreads, restricts the trader to long-only exposure, and fixes the asset position size, so…
The document asks how to choose among portfolios on a modern portfolio theory efficient frontier when the objective is long-run growth. It points readers to research on Kelly-optimal portfolios, including work on applying the Kelly criterion to stock…
The document asks how to set leverage separately for a short-only crypto strategy that trades many coins, holds positions from hours to days, and uses signal-based exits without fixed stops or profit targets. Its central risk is that sharp upward price…
The document explains why the euro profit from an XAUUSD trade cannot be calculated from the gold price movement alone. A trade denominated in dollars creates exposure to the EUR/USD exchange rate when the account balance is in euros. The response describes…
This note explains how to interpret an initial margin requirement when calculating the stock price that triggers a maintenance margin call. The requirement is the investor’s equity contribution to the purchase, so the financed portion is the complement of…
The document explains the signs and relative sizes of mark-to-market changes for credit default swaps when spreads move. Selling protection loses value when spreads widen, while buying protection gains value. The cited example gives risky annuities and…
The discussion explains why hedging agency mortgage backed securities with Treasuries alone can leave substantial spread risk. Treasury yields may move independently of mortgage spreads, while mortgages also have duration and prepayment related convexity:…
The document asks how to construct a fair buy-and-hold comparison for a strategy that accumulates shares over several days, sells the accumulated position, and later repeats the process with a different trade size. The central challenge is that the…
The document presents a question about how realized profit and loss, average opening price, and unrealized profit and loss behave when a trade crosses through zero and reverses direction. Its included answer proposes a fill-by-fill accounting procedure that…
The document applies the Kelly criterion to a repeated trade with equal probabilities of gain and loss but different payoff sizes. It chooses the fraction of current capital that maximizes expected logarithmic wealth, using the two possible post-trade wealth…
The document asks how estimated factor exposures can guide weights across a universe of securities. Its answer describes a high-minus-low construction: rank assets on a selected factor, form upper and lower groups, and take opposing positions in those…
The document examines why a Kelly bettor may stake a larger total fraction after first taking a bet at shorter odds and then being offered a second bet at longer odds on the same outcome. It starts from the Kelly criterion, which chooses a wager fraction to…
The note explains how to define portfolio weights when a long position is fully funded by an equal-sized short position. For a $200 long in Apple and a $200 short in Google, it uses signed weights of +1 and −1, calculated relative to the portfolio’s net…
The document considers whether to size the long and short legs of a pairs trade in proportion to each stock’s price variance. The proposed intuition is to allocate more capital to the more volatile asset, which may move more as the spread converges. The…
The document explains that a minimum variance hedge ratio can exceed one. It gives the relationship between the hedge ratio, spot-to-futures price correlation, and the ratio of their price-change standard deviations. Since correlation cannot exceed one, a…
The document examines how to choose a Kelly bet fraction when returns are not Gaussian. It notes that the familiar mean-over-variance estimate is exact only under Gaussian assumptions, and frames the general problem as maximizing expected logarithmic wealth…
The document asks whether the Kelly fraction, which maximizes expected log wealth, has a closed-form solution for finite discrete payoff distributions bounded between a full loss and a full gain. It gives the symmetric two-outcome case, where the optimum…
The document contrasts the discrete Kelly formula for sizing a binary wager with the continuous Kelly rule used for strategies whose returns vary continuously. For a strategy with mean excess return and return volatility, the continuous rule expresses…
The note derives the price elasticity of an investment’s return when return is defined relative to initial wealth. With initial wealth normalized to one, return is price minus one, so elasticity is price divided by price minus one. The apparent mismatch with…
The document explains a two-asset mean-variance allocation in which the risky asset receives a weight greater than one and the risk-free asset receives a negative weight. For an investor with a fixed amount of capital, the interpretation is to invest the…
The document considers how to compare backtested strategies when returns are not normally distributed, especially when negative skew and leverage make a Sharpe ratio an incomplete description of risk. It raises maximum drawdown as a possible measure of…
The document examines a simulation of a portfolio that borrows to double its exposure, repays the loan daily, and estimates a Sharpe ratio from repeated annual trials. The central modeling issue raised in one answer is the simulated asset return: for…
The discussion explains why a machine-learning model with lower mean squared or root mean squared prediction error can still earn less in a backtest. Prediction accuracy evaluates numerical closeness to observed returns, whereas profit depends on how…
The document explains the conversion-factor adjustment in a duration hedge using bond futures. With a single cheapest-to-deliver bond and no delivery optionality, the futures price is the CTD bond delivery price divided by its conversion factor.…