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 why idealized leverage leaves the Sharpe ratio unchanged. If borrowing and lending occur at the risk-free rate, leverage scales excess return and volatility by the same amount, so their ratio remains constant. The statistical argument…
The document answers a question about calculating weekly turnover for a portfolio that rebalances regularly. It gives a basic measure: take the smaller of total purchases or total sales and divide by the portfolio’s market value. This convention measures one…
The document examines how to choose a position when forecasts provide expected returns and volatility over multiple future horizons. It starts with the growth-oriented rule of sizing in proportion to expected return divided by variance, then considers…
The document considers how much of a $1 million bankroll to wager on a coin game that pays a stated amount on tails and loses the stake on heads. It compares a single play with repeated plays and discusses Kelly sizing, which maximizes expected logarithmic…
The document discusses how to hedge a long American put in a two-period binomial stock and cash market while repaying a loan used to buy the option. The central method is dynamic replication: calculate the option's stock hedge at each node, then rebalance as…
The document examines whether a mortgage-backed securities book should include 30-year Treasuries in its curve hedges. The proposed setup bootstraps a yield curve, models prepayments and option-adjusted spread, and calculates key-rate DV01s before sizing…
The answer explains how the sign of a hedge-adjusted spread can guide the direction of a pair trade. Under the stated spread definition, a positive spread prompts a short position in the first asset and a long position in the second; a negative spread…
The answer treats a cointegration spread as a synthetic position: going long the spread means buying one leg and shorting a hedge-ratio-weighted amount of the other, with the reverse positions for a short spread. It then discusses practical sizing across…
The document asks whether binary options can produce a position that doubles on success and halves on failure when the event is close to equally likely. Its algebra shows that the desired payoffs imply a particular option quantity and purchase price, but…
This discussion considers quoting strategy in market-making games where the counterparty may know more about the eventual payoff. It distinguishes ordinary uncertainty from informed trading. When both sides lack an information advantage, the questioner’s…
The document considers how to choose among many Kelly-based betting strategies after testing a UFC fight prediction model. The model outputs win probabilities, and the user evaluates parameter combinations using bookmaker odds, return on investment, and…
The document explains why bond duration is not a straightforward measure for Eurodollar futures. A bond’s duration relates its percentage price change to a yield change, while a futures contract has no meaningful cash value at inception for calculating that…
The document describes a proposed way to evaluate a multi-asset portfolio using weekly returns and a time-varying matrix of portfolio weights. The intended test samples start dates, measures performance over a one-year period, rebalances at regular…
The document shows how to backtest a portfolio of ETFs using inverse-volatility weights estimated from recent returns. A target-weight function obtains closing prices for the preceding 20 trading days, computes returns, estimates each asset’s volatility, and…
The question compares the long-run behavior of leveraged exchange-traded funds with a buy-and-hold portfolio using borrowed money, especially when the underlying asset ends a period near its starting price. The replies challenge the claim that leveraged…
The discussion addresses sizing long and short stock positions generated by a daily strategy when trades overlap and signals arrive unevenly. One proposed approach budgets exposure using the number of concurrent long and short positions. If a signal has an…
The document investigates whether Vince’s optimal f can be used for futures position sizing without look-ahead bias. The author assumes log utility and is reluctant to estimate expected returns, then reproduces a historical profit-and-loss example in which…
The note examines how to hedge an inverse-price product using a second instrument whose payoff changes linearly with the same underlying. It distinguishes a finite-period payoff, based on the change in the reciprocal of price, from a possible continuously…
The document frames a mortgage from the borrower's perspective, expressing the value of the house less the present value of remaining mortgage payments. The original question asks how down payment, interest rate, and maturity affect that value, and how to…
The document asks whether machine learning needs to predict option gamma when a trader can rebalance delta hedges over time. It frames a portfolio containing a call, shares, and a second option, with target conditions for zero delta and zero gamma at a later…
The document discusses a mixed-integer formulation for rebalancing a stock portfolio toward mean-variance target weights while limiting the number of traded positions. It represents each trade with a signed change variable and uses a binary indicator to mark…
The discussion addresses how to estimate a trading strategy’s capacity using historical data and market depth. The question notes that standard broker market-impact tools may not capture strategies with complex entries and exits or those whose opportunities…
The document clarifies how to calculate portfolio turnover from monthly asset weights. It considers the absolute changes in each holding’s weight between consecutive months and explains why their sum should be divided by two for a one-way turnover measure.…
The document distinguishes forecasting a security’s daily high and low from deciding how to trade on those forecasts. The author reports using an ensemble of forecasting methods and evaluating historical errors, including their dispersion and frequency of…