The sensitivity of a convertible’s delta to changes in the underlying share price (mathematically, it is a second-order partial derivative of the convertible price with respect to changes in the underlying common stock). It is often expressed as the change in delta for a one basis point change in parity. However, it’s sometimes measured as the sensitivity of the delta to a 1% change in the share price. For substantial moves in share price, delta is not an accurate yardstick of the sensitivity of the convertible. Characteristically, the convertible is more equity sensitive in bull markets and less sensitive in bear markets. Its gamma measures the intensity of this effect.
The total risk in a given position cannot be only defined by changes in the delta- it is vital that the gamma is also taken into account. For instance, a convertible with a delta of 0.8 and a gamma of 0.4 doesn’t have the same level of risk as a convertible with a delta of 0.8 and a gamma of 0.2. Convertibles that are deep in-the-money have low values of gamma, as do convertibles that are far out-of-the-money. In contrast, convertibles that are at-the-money have higher levels of gamma.
