This article explains how stochastic control models can set dynamic positions in a mean-reverting spread. It outlines two investor preference models: constant relative risk aversion over terminal wealth, and Epstein–Zin recursive utility, which can account…
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This document surveys methods for estimating and adjusting covariance matrices used in portfolio risk analysis. It covers the empirical estimator, robust Minimum Covariance Determinant, basic and data-driven shrinkage methods, semi-covariance, exponentially…
This article explains why a multi-asset mean-reverting portfolio may be easier to trade when it uses a small number of assets. Sparse baskets can improve interpretability and reduce trading costs; they also avoid the ambiguity that can arise when combining…
The article surveys four online portfolio selection methods that seek to profit from mean reversion: Passive Aggressive Mean Reversion (PAMR), Confidence Weighted Mean Reversion (CWMR), Online Moving Average Reversion (OLMAR), and Robust Median Reversion…
The document introduces Modern Portfolio Theory and explains how asset correlation shapes the risk and return of a portfolio. Expected portfolio return is a weighted sum of asset returns, while portfolio variance also depends on covariances. When assets are…
The document reflects on Quantopian’s closure through the strengths and constraints of its research platform. It describes benefits for systematic traders, including a team environment for exchanging ideas, training, research technology, peer feedback, and a…
The document contrasts two possible trading outcomes for a strategy described as having a known, substantial edge: a favorable run and an unfavorable run. Its central lesson is that realized profit and loss can vary considerably even when the underlying…
This article demonstrates a vector autoregression (VAR) model using daily returns for a basket of U.S. homebuilding stocks. It fits the model on a rolling historical window, forecasts each asset’s next return, and converts the cross-sectional forecasts into…
This short article uses the long-run nominal growth of US stocks and bonds as a starting point for discussing risk premia. It reports that stocks rose 48,000 times in value and bonds 300 times from 1900 to the article’s present. Its explanation is that…
This article demonstrates a convex optimisation workflow for a crypto perpetual futures portfolio. It combines expected returns estimated from cross-sectional momentum and carry features with a breakout signal, then uses a covariance estimate to represent…
This article addresses whether publishing a trading edge causes it to disappear. It uses an end-of-month Treasury demand effect as an example: price-insensitive buying may temporarily move prices away from fair value, so a trader could enter ahead of the…
This short discussion considers the role of foreign exchange in a systematic trading portfolio. Its central claim is that FX does not offer an inherent risk premium that can provide a persistent return tailwind, so traders must seek returns through active…
The article presents a research philosophy for systematic trading centered on identifying genuine market mechanisms and combining modest opportunities. An edge should have an explanation for why another participant accepts the other side of the trade, such…
The article examines practical limits of traditional market-neutral pairs trading. Each trade consumes capital on two legs, incurs spreads and commissions on both, and may use capital on a fairly valued leg even when the opportunity is concentrated in the…
The article explains why covariance estimates matter for portfolio risk: pairwise asset covariances combine with portfolio weights to determine portfolio variance. Using adjusted-price returns for SPY, TLT, and GLD, it first compares rolling-window…
This article explains how to combine overlapping pair spread signals to infer which individual stocks appear rich or cheap relative to peers. Each spread acts as a relative vote; aggregating votes across a network can help distinguish a likely outlier from a…
The article illustrates how a put option can limit downside on an equity holding and shows how the premium changes the portfolio’s payoff. It first models a position in an index-tracking fund, identifying the price level associated with a chosen loss and…
The article explains how to assess candidate equity pairs and estimate a spread for mean-reversion trading. Using XOM and CVX as an example, it fits an ordinary least squares hedge ratio, forms a residual spread, and applies an Augmented Dickey-Fuller test.…
The article distinguishes risk premia, which compensate traders for bearing unwanted risks, from inefficiencies caused by participants who must trade for reasons other than price. Forced liquidations, redemptions, reporting practices, index changes, and…
This introductory page presents a research philosophy for independent systematic traders: begin by identifying a plausible market edge, then use tools such as backtesting to investigate it. A backtest can show how a set of rules performed historically, but…
The article defines a trading edge as positive expected value: across many trades, the probability-weighted gains should exceed the losses. A strategy can lose often and still have an edge, or win frequently while carrying occasional losses large enough to…
This article weighs gold’s theoretical status against its observed portfolio behavior. Since gold produces no cash flow and has no clear cash-flow-based valuation anchor, the author argues it does not fit a conventional academic account of a risk premium. In…
The article addresses how to distinguish a durable strategy effect from luck, while acknowledging that certainty is impossible. It recommends starting with a credible economic explanation, such as compensation for bearing risk or a structural imbalance in…
The article introduces tidy data principles and shows how to represent financial returns in long and wide formats. In tidy form, each column represents a variable, each row an observation, and each cell one value. Its example uses dates, tickers, and…