medium · Quantitative Finance microstructure-arb
In a pairs trade, if the spread S = ln(P_A) - β ln(P_B) is used instead of the raw price difference, what is the primary advantage?
- It eliminates the need to run a Dickey-Fuller stationarity test on the raw price spread beforehand.
- The spread is interpreted in terms of percentage returns, which is more stable across different price levels.
- Logarithms will mathematically transform any non-stationary series into a fully stationary one on their own.
- The hedge ratio beta will always equal exactly 1.0 for any pair once both prices are converted to logarithms first.
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