short extension

If I have a portfolio, and I go short 30% of any other stocks, and use the proceeds to buy any stocks, it called short extension strategy, am I right?

Yes, that’s called Short Extension 130/30 Strategy

No restriction on which stocks to be long and short?

Yes, no restrictions. The 130/30 is managed as a single portfolio which is way different than 100/0 + 30/30.

IMO, here you short some % of your long portfolio

say 20% of your current market value 100 is shorted to generate 20 which is used to go long on other stocks worth 20. As a result your long portfolio has a value of 100+20 & short -20…So it may be called as 120/20 short extension strategy. Here only PARTIAL relaxation allows manager to capture value based on his views/information which is otherwise not available on long-only portfolio…

The concept seem simple. But I don’t understand why textbook said " in a short extension strategy, the manager could start out with a beta of 1.0…" what does beta of one mean? and why beta is one?

They are contrasting it with Market neutral long short strategy which has a zero beta.

In short extension, manager MAY start with Beta 1 & end up with 1. meaning no extra exposure due to short position. In other words they may be able to RETAIN there original beta or a different net porfolio beta as they desire.