Hedging is rarely perfect (Basis risk ) - dervative

Can someone shed light on this.

When effective beta is higher than the estimated one ( also when you will need to buy certain contracts to hedge) ,please explain basis risk when portfolio and contract increase by the same amount acted as if their betas were the same and did not reflect INITIAL ESTIMATES OF BETAS. so what will be this INITIAL ESTIMATE?Can someone explain this whole thing?