Today most investors who peer across Bear Valley assume that once stocks finally stop falling, they will promptly climb back to previous heights. Few contemplate a third alternative -- an extended period when stocks frustrate both the bulls and the bears and remain at low levels. In this type of market environment, convertible securities may be worth a new look. The public has been chronically indifferent to convertibles because they are fraught with complex mathematics and difficult to trade. The math surrounding convertibles is complicated, but the concept is simple: A corporation issues bonds or preferred stocks that are convertible into a predetermined number of shares of the issuer's common stock whenever the holder chooses. The convertibility--or exchangeability--feature means that when a company's stock rises, it pulls the convertible's price up with it. If the stock drops, it drags the price of the convertible down, but only to the point where its value as a plain vanilla bond (determined by quality, coupon and maturity) provides a floor. If the stock continues to drop, the floor protects the convertible investor against continuing losses.