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 note explains a relationship between the Sharpe ratio of an actively managed portfolio, the benchmark’s Sharpe ratio, and the manager’s information ratio. It derives the result by scaling active bets and expressing portfolio return as benchmark return…
The document asks how to convert daily return forecasts and their forecast variances from a Kalman-filtered stock-market model into an investment allocation. It defines forecast return, realized return, and forecast error, and assumes realized return is…
The document frames position sizing as a choice of how risk changes with account capital. It describes a daily strategy with normally distributed returns and compares candidate sizing rules, including fractional sizing, where each trade risks a fixed share…
The document works through a market hedge for a 50,000-share stock position using index futures. Given the stock value, futures price, contract multiplier, and a beta of 1.3, it calculates a short position of 26 contracts. The cited textbook solution says…
The document asks how to size two equity legs when a mean-reversion strategy trades their price ratio. Rolling estimates of the ratio’s mean and standard deviation produce a z-score, with entry beyond an outer threshold, exit near the mean, and a more…
This note explains the description of an option as “purer” in its risk: the risk is concentrated into exposure to a particular outcome, which can make the option’s value more responsive to market moves than owning the underlying asset. It uses a stock and an…
The document asks whether a martingale betting strategy can be designed so it never explodes or exhausts its capital. The main response argues that in a fair, zero-sum game with a finite capital base, any sequence of positive bets can eventually accumulate…
The document presents a stock-pair strategy that selects highly correlated financial shares during a formation window, then trades a price-ratio z-score during a later period. It describes entering opposing long and short positions when the ratio moves…
The document considers why a trader might buy a cash-settled quarterly bitcoin future instead of holding bitcoin in the spot market. Its main explanation is leverage: a spot purchase requires paying the full asset value, while opening a futures position…
The document argues that a machine-learning trading model has no universal target success rate. The proportion of winning trades matters only in relation to the sizes of wins and losses, the trading horizon, and the strategy’s payoff structure. A…
The document explains what strike price multiplied by contract units and multiplier represents: the underlying notional exposure if the option is exercised. It illustrates this with a standard equity option and distinguishes that notional amount from the…
The document considers how to calculate daily performance for a strategy that continually sells call options and replaces them at expiry. It points out that holding one contract is not a stable measure of portfolio exposure: the option’s dollar exposure…
The document explains how to form a monthly long–short portfolio from a universe of ten stocks. At each rebalance, calculate each stock’s average return over the chosen lookback period, rank the results, short the three weakest performers, and go long the…
The document compares two ways to set portfolio weights to a target ex-ante volatility. Mean-variance optimization uses the inverse covariance matrix to adjust the signal and chooses a risk-aversion parameter to reach the target. Direct risk scaling instead…
The document derives the decline in stocks that would move a portfolio away from its target stock allocation far enough to trigger a rebalance. It assumes stocks begin at allocation X₀, bonds remain unchanged, and the trigger occurs when the stock share of…
The document examines the argument that a trader with enough capital to meet margin calls can hold a leveraged stock-index futures position through a severe decline and eventually recover when the market rebounds. The replies challenge the assumption that…
The document considers how variance affects optimal growth under Kelly betting. It defines the objective as expected log wealth after investing a fraction of the portfolio in a risky return, with the remainder earning a risk-free rate. The author presents a…
The document derives the leverage that maximizes expected continuously compounded wealth when returns follow a normal model. It starts with an asset whose returns have mean 5% and standard deviation 10%, then shows that leverage scales the mean linearly…
The explanation addresses a step in a derivation used in Kelly-style growth analysis: why the expected square of an outcome can be approximated by the variance when the mean is small. It writes each outcome as its mean plus a zero-mean deviation, then…
The document explains the relationship between borrowing, risk-free investment, and a portfolio’s market beta. Scaling exposure to a risky portfolio scales its market sensitivity: borrowing to enlarge the position raises beta, while holding some wealth at…
The discussion frames starting capital as a tradeoff between potential return on invested capital and the chance that losses force a strategy to stop. It gives a normally distributed daily profit example to illustrate why a small account may face a…
The document models a pension fund as the accumulated value of periodic contributions, where income grows continuously and each contribution earns a continuously compounded return until the valuation date. It derives sensitivities of the fund value to the…
The document asks how to calculate daily returns and weights for a stock portfolio that rebalances monthly, using a ranked-beta strategy as context. It distinguishes the weights assigned at the start of a month from the weights that result after the stocks…
The document develops a two-asset quadratic hedging example for returns that are negatively correlated and may have different volatilities. Assuming zero expected returns, it writes portfolio risk as the variance of a weighted combination of the two returns,…