IN A 1968 ARTICLE, Weil, Segall, and Green (hereafter WSG) suggest that the riskprotection feature of convertible bonds (CB's) may not contribute to the determination of market values for conversion privileges.' In their paper WSG define the premium on a CB as the excess of its market value above the market value of the stock into which it is convertible. A more general definition, however, would identify the premium as the difference between the CB market price and the greater of either the underlying conversion price, as above, or the underlying bond price. This bond, or "theoretical," value is defined as the price of an ordinary bond (OB) which has all features of the CB (amount, timing, and risk of interest and principal payments) except the conversion feature.Previous literature on this topic had predicted that a CB would sell at a premium because a CB holder could share in potential common stock appreciation, while at the same time retaining a bond value "floor" on his investment value. Other possible reasons for CB's selling at a premium are carefully discussed in the WSG paper. This note, however, will address only their argument related to the floor or "insurance" explanation for CB premiums. This argument observes that the holder of stock in the CB-issuing company can place a floor under his asset value by executing a stop-sell ("stop-loss") order when he purchases the stock. The availability of this alternative insurance against market decline leads the authors to conclude that, "since a stop order is cheap, the floor should play little role in determining the premium" (p. 461).An initial problem lies in the asymmetry of the stop-sell order. The holder of a CB has a floor which not only protects against stock price declines but also allows the CB holder to participate in subsequent stock price resurgences, while the stop-sell floor does not allow this subsequent market participation. (The theoretical value as a bond serves as a reflecting barrier to price movements, whereas a stop-sell order is an absorbing barrier.) The stop-sell strategy can only be made symmetrical by following its execution with an immediate decision to buy at the same floor price. This amendment is necessary if the stop-sell technique is to replicate the position of the CB holder.We may now consider an example of the stop-sell strategy. Assume that Company X's CB is convertible into 20 shares of X common, and that X common is presently selling at $50. Also assume that the value of a similar non-convertible bond is $1,000, so both the current conversion value and bond value of the XCB are equal, $1,000. A possible pattern of behavior of X stock prices from the present until the last date at which the conversion privilege can be exercised is illustrated in Figure 1. These price data are superimposed on the expected bond value of the XCB, which is, in turn, the price of an equivalent OB. For simplicity, the bond value is assumed constant over time.2
