Although many studies have found a non-trivial incidence of beta instability for individual common stocks, there exists controversy over the beta stability characteristics to expect in portfolios formed from these stocks. The extent is examined to which portfolio formation can diversify away beta instability. Specifically, although a constant beta for the market portfolio is acknowledged as the trivial limiting case, particular attention is devoted to shedding light on the speed with which diversification can deliver a reasonable expectation of stable portfolio betas. The issue is examined by forming portfolios which mix together constant beta stocks and varying beta stocks. The evidence is generally consistent with the presence of a diversification effect, but as the portfolio size increases, results do show a greater proportion of constant beta stocks are needed to maintain the relative stability of the portfolio.