Get a Half-Life

What is the half-life of a spread and how do you use it in practice?  For a mean-reverting spread, half-life is the time it takes for the spread to revert to half its initial deviation from the mean.  It is measured in trading days.  Half-life can be derived from  Ornstein-Uhlenbeck’s mean-reversion equation.  It is calculated as

 

Half-Life =- ln(2)/theta

where theta is the estimate of the rate of mean-reversion. The half-life of a spread has two main purposes.  First it can be used to determine whether or not to enter a spread.  We prefer spreads with a half lives under 50 days.  There are no real rules for this however and if you don’t mind holding positions for a longer period you can use a longer half life.  Half life can also be used to determine the holding period for a mean-reverting spread.  In other words it can be used as a stop loss criterion.  If a spread hasn’t hit its exit target within the period given by the half life, the trader would exit the trade.  Again there is no rule that says a trader has to exit a position at the end of the half life, but it is a useful indicator as to whether the relationship between the two securities has changed.

Written by Norm Winer. Follow me on Twitter and StockTwits.