Question #82

A long floor (floor buyer) has the same general expiration-date payoff diagram as that for long interest rate put position. (Module 31.6, LOS 31.j) Joel 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. The portfolio is subdivided into several smaller portfolios. In general, the portfolios are composed of U.S. based equities, ranging from medium to large-cap stocks. Currently, DS is not involved in any foreign markets. In his new position, he will now be responsible for the development of a new investment strategy that DS wants all of its equity portfolios to implement. The strategy involves overlaying option strategies on its equity portfolios. Recent performance of many of their equity portfolios has been poor relative to their peer group. The upper management at DS views the new option strategies as an opportunity to either add value or reduce risk. Franklin recognizes that the behavior of an option's value is dependent upon many variables and decides to spend some time closely analyzing this behavior. He took an options strategies class in graduate school a few years ago, and feels that he is fairly knowledgeable about the valuation of options using the Black-Scholes model. Franklin understands that the volatility of the underlying asset returns is one of the most important contributors to option value. Therefore, he would like to know when the volatility has the largest effect on option value. Upper management at DS has also requested that he further explore the concept of a delta neutral portfolio. He must determine how to create a delta neutral portfolio, and how it would be expected to perform under a variety of scenarios. Franklin is also examining the change in the call option's delta as the underlying equity value changes. He also wants to determine the minimum and maximum bounds on the call option delta. Franklin has been authorized to purchase calls or puts on the equities in the portfolio. He may not, however, establish any uncovered or "naked" option positions. 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 Time to Maturity (years) (t) 1 Volatility (Std. Dev.) (sigma) 0.2 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