Does anyone know the reasoning behind the beta for Value. It says in the text that a negative value for value beta means its a growth stock. But I thought a positive value for value beta would mean growth stock? Thanks

It’s based on the Fama French Factors, and the factor HML, is High Book to Price minus Low Book to Price. This is essentially Value minus Growth, so the factor portfolio lambda would be the excess of return of Value over Growth. Therefore, a positive beta is a positive relationship with value, so a negative beta is a negative relationship with Value, which is the same as growth.