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Spread (statistical)

The combination of two or more instruments that a relative-value trader actually holds, constructed so the combined series mean-reverts.

Bid-ask spread in an order bookSell orders stacked above buy orders with a gap between the best of each.SELLERS (asks)50.0690050.051,40050.0460050.011,10050.002,30049.99800spread = 0.03BUYERS (bids)
The bid-ask spread. Buy orders sit below, sell orders above, and the gap between the best bid (50.01) and best ask (50.04) is the spread you pay to cross. Bar length shows the size resting at each price.

For a pair the spread is typically A - h x B, where h is the hedge-ratio. Its level in dollars is arbitrary, so traders normally track its z-score and enter when it is stretched, exiting near zero.

The two choices that decide everything are h and the lookback used for the mean and standard deviation. Both should be checked for parameter-sensitivity, and both should be estimated only on data available at the time, or you have invented a beautiful look-ahead-bias.

Worked example: A at 52.00, B at 39.00, h = 1.25. Spread = 52.00 - 1.25 x 39.00 = 3.25. If the 60-day mean is 2.10 with a standard deviation of 0.46, the z-score is 2.5, a typical entry threshold for a short-A long-B position.

Related: cointegration, hedge-ratio, z-score, mean-reversion

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