# Avoiding negative spread in pairs trading

I'm constructing money-neutral spread by this formula:

Spread = log(P1) - log(P2), where P1 and P2 is prices of two instruments


But sometimes spread can get into negative zone, when log(P1) < log(P2). How to avoid this and make spread always positive?

• Adding additional information may help us understand your needs. I mean: why not a simple value? – pincopallino Apr 10 '14 at 6:57
• spread sign is not important. P&L will be determined by change in equity line. – Wisentgenus Apr 10 '14 at 7:17
• My backtesting program accepts only data with positive quotes. I want to backtest this spread like standalone instrument. – Eldar Agalarov Apr 10 '14 at 8:05
• Multiply it by $-1$. – user2763361 Apr 10 '14 at 8:48
• but if spread sometimes is positive, sometimes is negative? – Eldar Agalarov Apr 10 '14 at 9:17

## 2 Answers

Solution is following:

• Calculate the spread: spread = log(P1 / P2)
• Find minimum value of spread: minVal = Min(spread)
• If minVal < 0 then do transformation for spread: spread = spread + Abs(minVal) + 0.01

Now we have spread with positive values.

My understanding is following:

Spread = Log(P1) - lambda * Log(P2) Lambda is the hedging ratio to eliminate market risk

Assuming the two securities are cointegrated, if Spread is positive, security P1 is relatively more expensive than P2. As a trader, you might want to consider short P1 and long P2.

If Spread is negative, security P1 is cheaper than P2 in relative term. So one might want to long P1 and short P2.