Equity Curve and Return Conventions for Pairs Trading

Summary

The document explains how to form and evaluate long-short stock portfolios, focusing on pairs trading. It compares hedge-ratio methods: ordinary least squares minimizes portfolio variance under a correlated random-walk and Gaussian framework, while total least squares minimizes geometric distance to observations. It also mentions cointegration methods and dollar neutrality, distinguishing dollar-neutral exposure from market neutrality.

For positive-value portfolios, it compounds strategy-weighted daily returns into an equity curve. For a spread that can cross zero, it instead accumulates daily P&L per spread unit, since conventional returns and return on capital may not be meaningful. For portfolios trading several pairs, return on committed capital includes capital allocated to inactive pairs, while fully invested return assumes capital can be concentrated in pairs that traded. The document gives formulas and conceptual comparisons, not empirical performance tests. Its methods depend on assumptions about price behavior, hedge selection, and capital allocation; it leaves sizing and conversion of P&L into returns to the researcher.

Key ideas

• OLS estimates a hedge ratio that minimizes spread variance under its distributional assumptions.
• TLS accounts for variation in both assets but shares OLS assumptions and may be less stable.
• Cointegration methods can provide hedge ratios for price series, while dollar neutrality does not by itself remove market beta.
• Positive-value portfolios can be evaluated by compounding strategy-weighted daily returns.
• For spreads that may be negative, cumulative P&L per unit is more suitable than conventional returns.
• ROCC includes the cost of capacity reserved for inactive pairs, while fully invested return assumes flexible capital allocation.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.