Question #44

of 111 Zetion Inc stock (current price $28) has 1-year call options with an exercise price of $30 trading at $2.07. The stock can increase by 15% or decrease by 13% over the next year and the risk-free rate is 3%. Arbitrage profits are most likely: A) not possible. B) possible by purchasing 28 shares and writing 100 calls. C) possible by purchasing 100 calls and short selling 28 shares. Ronald Franklin, CFA, has recently been promoted to junior portfolio manager for a large equity portfolio at Davidson-Sherman (DS), a large multinational investment-banking firm. He is specifically responsible for the development of a new investment strategy that DS wants all equity portfolio managers to implement. Upper management at DS has instructed its portfolio managers to begin overlaying option strategies on all equity portfolios. The relatively poor performance of many of their equity portfolios has been the main factor behind this decision. Prior to this new mandate, DS portfolio managers had been allowed to use options at their own discretion, and the results were somewhat inconsistent. Some portfolio managers were not comfortable with the most basic concepts of option valuation and their expected return profiles, and simply did not utilize options at all. Upper management of DS wants Franklin to develop an option strategy that would be applicable to all DS portfolios regardless of their underlying investment composition. Management views this new implementation of option strategies as an opportunity to either add value or reduce the risk of the portfolio. Franklin gained experience with basic options strategies at his previous job. As an exercise, he decides to review the fundamentals of option valuation using a simple example. Franklin recognizes that the behavior of an option's value is dependent on many variables and decides to spend some time closely analyzing this behavior. His analysis has resulted in the information shown in Exhibit 1 and Exhibit 2 for European style options. Exhibit 1: Input for European Options Stock Price (S) 100 Strike Price (X) 100 Interest Rate (r) 0.07 Dividend Yield (q) 0.00 Time to Maturity (years) (t) 1.00 Volatility (Std. Dev.)(Sigma) 0.20 Black-Scholes Put Option Value $4.7809 Exhibit 2: European Option Sensitivities Sensitivity Call Put Delta 0.6736 –0.3264 Gamma 0.0180 0.0180 Theta –3.9797 2.5470 Vega 36.0527 36.0527 Rho 55.8230 –37.4164