Dollar neutral or beta neutral?

Beta is a greek letter that shows the relation between one stock and its market. For instance, if we check out Johnson & Johnson in Reuters we see that Beta=0.56, so when the DJI goes up 1%, JNJ goes up 0.56%, or when the DJI goes down 2%, JNJ goes down 1.12%.

When we build a Long-Short Portfolio (buy some stocks and at the same time bet on a bearish movement in others), we can use the same amount of money for the long leg and the short one (dollar neutral). However, perhaps, the short stocks have a higher beta and in fact our portfolio is not market neutral (our profits don´t depend on the market movement). How can we create a market neutral portfolio? A beta neutral strategy targets a zero total portfolio beta (i.e., the beta of the long side equals the beta of the short side). While dollar neutrality has the virtue of simplicity, beta neutrality better defines a strategy uncorrelated with the market return.

Imagine we want to buy 3 stocks and go short in other 3. Each stock has its beta. Imagine that we want to use the same amount of money for each long stock (XL) and for each short one (XS).
For instance, imagine we have 40.000 GBP to invest:
  • Long: JNJ (0.56), WMT (0.22), KO (0.59); SUM=1.37
  • Short: PG (0.57), AAP (0.67), TNT (1.02); SUM=2.26
  • XL/XS=2.26/1.37=1.65
  • If XL=5000, Long position=+15000, Short position=-9090