An investor considering the addition of options to his investment portfolio must consider the effect an option will have on portfolio risk. The “beta” of an option at any point in time can be calculated from the beta of its underlying stock and the option’s risk elasticity—a measure of the percentage change in the value of the option for a small percentage change in the value of the underlying stock.
An option’s beta will change in a predictable fashion with changes in the underlying stock’s price and variance rate, the option’s exercise price and time to expiration, and the risk-free interest rate. A call option’s beta will decrease with increasing stock price and exercise price and increase with an increasing risk-free rate; its sensitivity to variance and time to expiration will depend on the stock price to exercise price ratio. Nomograms provide a quick and easy way to estimate option betas from these readily observable underlying parameters.
Option betas will also change, often drastically, with the passage of time. Graphs indicate that, in general, call betas will increase as time to expiration increases. The ultimate impact will depend, however, on the parameters of the contract and on changes in the underlying stock’s price.
