A *beta* of a stock generally means its relation with the market, how many percent move we should expect from the stock when the market moves one percent.

Market, being a somewhat vague notion is approximated here, as usual, using the S&P 500. This aforementioned relation (henceforth, *beta*) is detrimental to many aspects of trading and risk management. It is already well established that volatility has different dynamics for rising markets and for declining market. Recently, I read few papers that suggest the same holds true for *beta*, specifically that the *beta* is not the same for rising markets and for declining markets. We anyway use regression for estimation of *beta*, so piecewise linear regression can fit right in for an investor/speculator who wishes to accommodate himself with this asymmetry.