hard · Quantitative Finance microstructure-arb
A pairs-trader identifies that the log-prices of Stock A and Stock B are cointegrated. The spread S_t = ln(A_t) - β ln(B_t) is modeled as an Ornstein-Uhlenbeck process with mean reversion speed κ = 14 per year.
What is the half-life of a deviation in the spread, and what does this imply for the strategy?
- 2.5 days; the high speed of reversion κ=14 implies that most trades are closed within a single trading week.
- 14 days; the half-life is exactly 1/κ in units of days, making it a fortnightly rebalancing strategy.
- 0.0495 years (approx 18 days); the trader should expect deviations to revert halfway to the mean in about 3 business weeks.
- 0.0714 years (approx 26 days); the strategy is higher frequency and requires execution within minutes to capture the mean reversion.
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