Consider a stock that is trading at $50, has a volatility of 0.5, and pays no dividends. The risk-free rate is 4%. If the beta of the stock is 1.1, what is the beta of a 52-strike, one-year call option on this stock?
A) 0.55
B) 1.1
C) 3.3
D) 4.4

Question

Quizplus · Accepted Answer

The beta of a call option can be significantly higher than the beta of the underlying stock due to the leverage effect of options. Given the parameters, the Black-Scholes model (or similar option pricing models) would show that the delta of the option (sensitivity of the option price to changes in the underlying stock price) is less than 1 but the leverage effect (given by the option's elasticity, which is the percentage change in option price divided by the percentage change in stock price) amplifies the beta of the option compared to the beta of the stock. Without doing the exact calculation, which requires the Black-Scholes formula or numerical methods, we know the beta of the option will be higher than the beta of the stock due to this leverage effect. Among the given choices, 3.3 is a plausible amplified beta for the call option, reflecting the increased sensitivity of the option's value to market movements.

Consider a Stock That Is Trading at $50, Has a Volatility