portfolio mgnt: stability of beta

where I could find conclusion about the stability of beta? high-beta portfolio tend to decline over time toward beta 1.0, why? betas ar emore stable as portfolio size increase. if there is direct relationship between the stability of betas and the lenght of the estimation period, is it positive correlation or negative? why beta estimates for small firms tend to be too low? dose that equal to say, new IPO issue tend to be over priced? price too high than suppose to be? Thanks.