HuskyGrad2010

Which of the following is least likely one of the assumptions of the Black-Scholes-Merton option pricing model?

A) There are no cash flows on the underlying asset.

B) The risk-free rate of interest is known and does not change over the term of the option.

C) Changes in volatility are known and predictable.

---

The BSM model assumes that volatility is known and constant. The term predictable would allow for non-constant changes in volatility.

HuskyGrad2010

Which of the following is NOT one of the assumptions of the Black-Scholes-Merton (BSM) option-pricing model?

A) Any dividends are paid at a continuously compounded rate.

B) There are no taxes.

C) Options valued are European style.

---

The BSM model assumes there are no cash flows on the underlying asset.

HuskyGrad2010

The value of a put option is positively related to all of the following EXCEPT:

A) time to maturity.

B) risk-free rate.

C) exercise price.

---

The value of a put option is negatively related to increases in the risk-free rate.

HuskyGrad2010

The value of a European call option on an asset with no cash flows is positively related to all of the following EXCEPT:

A) exercise price.

B) time to exercise.

C) risk-free rate.

---

The value of a call option decreases as the exercise price increases.

HuskyGrad2010

The value of a European call option on an asset with no cash flows is positively related to all of the following EXCEPT:

A) exercise price.

B) time to exercise.

C) risk-free rate.

---

The value of a call option decreases as the exercise price increases.

HuskyGrad2010

For a change in which of the following inputs into the Black-Scholes-Merton option pricing model will the direction of the change in a put’s value and the direction of the change in a call’s value be the same?

A) Exercise price.

B) Risk-free rate.

C) Volatility.

---

A decrease/increase in the volatility of the price of the underlying asset will decrease/increase both put values and call values. A change in the values of the other inputs will have opposite effects on the values of puts and calls.

HuskyGrad2010

John Fairfax is a recently retired executive from Reston Industries. Over the years he has accumulated $10 million worth of Reston stock and another $2 million in a cash savings account. He hires Richard Potter, CFA, a financial adviser from Stan Morgan, LLC, to help him develop investment strategies. Potter suggests a number of interesting investment strategies for Fairfax's portfolio. Many of the strategies include the use of various equity derivatives. Potter's first recommendation includes the use of a total return equity swap. Potter outlines the characteristics of the swap in Table 1. In addition to the equity swap, Potter explains to Fairfax that there are numerous options available for him to obtain almost any risk return profile he might need. Potter suggests that Fairfax consider options on both Reston stock and the S&P 500. Potter collects the information needed to evaluate options for each security. These results are presented in Table 2.

Table 1: Specification of Equity Swap

Term	3 years
Notional principal	$10 million
Settlement frequency	Annual, commencing at end of year 1
Fairfax pays to broker	Total return on Reston Industries stock
Broker pays to Fairfax	Total return on S&P 500 Stock Index

Table 2: Option Characteristics

	Reston	S&P 500
Stock price	$50.00	$1,400.00
Strike price	$50.00	$1,400.00
Interest rate	6.00%	6.00%
Dividend yield	0.00%	0.00%
Time to expiration (years)	0.5	0.5
Volatility	40.00%	17.00%
Beta Coefficient	1.23	1
Correlation	0.4

Potter presents Fairfax with the prices of various options as shown in Table 3. Table 3 details standard European calls and put options. Potter presents the option sensitivities in Tables 4 and 5.

Table 3: Regular and Options (Option Values)

	Reston	S&P 500
European call	$6.31	$6.31
European put	$4.83	$4.83
American call	$6.28	$6.28
American put	$4.96	$4.96

Table 4: Reston Stock Option Sensitivities

	Delta
European call	0.5977
European put	−0.4023
American call	0.5973
American put	−0.4258

Table 5: S&P 500 Option Sensitivities

	Delta
European call	0.622
European put	−0.378
American call	0.621
American put	−0.441

Given the information regarding the various Reston stock options, which option will increase the most relative to an increase in the underlying Reston stock price?

A) American put.

B) European call.

C) American call.

---

Using its delta in Table 4, if the Reston stock increases by a dollar the European call on the stock will increase by 0.5977. (Study Session 17, LOS 56.a)

---

Fairfax is very interested in the total return swap and asks Potter how much it would cost to enter into this transaction. Which of the following is the cost of the swap at inception?

A) $340,885.

B) $45,007.

C) $0.

---

Swaps are always priced so that their value at inception is zero. (Study Session 17, LOS 57.a)

---

Fairfax would like to consider neutralizing his Reston equity position from changes in the stock price of Reston. Using the information in Table 4 how many standard Reston European options would have to be either bought or sold in order to create a delta neutral portfolio?

A) Sell 334,616 put options.

B) Sell 334,616 call options.

C) Buy 300,703 put options.

---

Number of call options = (Reston Portfolio Value / Stock PriceReston)(1 / Deltacall).
Number of call options = ($10,000,000 / $50.00/sh)(1 / 0.5977) = 334,616. (Study Session 17, LOS 56.e)

---

Fairfax remembers Potter explaining something about how options are not like futures and swaps because their risk-return profiles are non-linear. Which of the following option sensitivity measures does Fairfax need to consider to completely hedge his equity position in Reston from changes in the price of Reston stock?

A) Delta and Vega.

B) Delta and Gamma.

C) Gamma and Theta.

---

Vega measures the sensitivity relative to changes in volatility. Theta measures sensitivity relative to changes in time to expiration. (Study Session 17, LOS 56.d)

---

Fairfax has heard people talking about "making a portfolio delta neutral." What does it mean to make a portfolio delta neutral? The portfolio:

A) is insensitive to stock price changes.

B) is insensitive to volatility changes in the returns on the underlying equity.

C) is insensitive to interest rate changes.

---

The delta of the option portfolio is the change in value of the portfolio if the stock price changes. A delta neutral option portfolio has a delta of zero. (Study Session 17, LOS 56.e)

---

After discussing the various equity swap options with Fairfax, Potter checks his e-mail and reads a message from Clark Ali, a client of Potter and the treasurer of a firm that issued floating rate debt denominated in euros at London Interbank Offered Rate (LIBOR) + 125 basis points. Now Ali is concerned that LIBOR will rise in the future and wants to convert this into synthetic fixed rate debt. Potter recommends that Ali:

A) enter into a pay-fixed swap.

B) take a short position in Eurodollar futures.

C) enter into a receive-fixed swap.

---

The floating-rate debt will be effectively converted into fixed rate debt if he entered into a pay-fixed swap. A short position in Eurodollar futures would create a hedge, but in the wrong currency. (Study Session 17, LOS 57.d, e)

HuskyGrad2010

As a portfolio manager for the Herron Investments, an analyst is interested in establishing a dynamic hedge for one of his clients, Lou Gier. Gier has 200,000 shares of a stock that he believes could take a dive in the near future. Suppose that a call option with an exercise price of $100 and a maturity of 90 days has a price of $7. Also assume that the current stock price is $95 and the risk free rate is 5%. Assuming that the delta value of call option is 0.70, how many call option contracts would be needed to create a delta neutral hedge?

A) 2,000 contracts.

B) 2,857 contracts.

C) 285,714 contracts.

---

Click for Answer and Explanation

The number of call options needed is 200,000 / 0.70 = 285,714 options or approximately 2,857 contracts. Since Gier is long the stock, he should short the calls.

---

When a delta neutral hedge has been established using call options, which of the following statements is most correct? As the price of the underlying stock:

A) changes, no changes are needed in the number of call options purchased.

B) increases, some option contracts would need to be repurchased in order to retain the delta neutral position.

C) increases, some option contracts would need to be sold in order to retain the delta neutral position.

---

As the stock price increases, the delta of the call option increases as well, requiring fewer option contracts to hedge against the underlying stock price movements. Therefore, some options contracts would need to be repurchased in order to maintain the hedge.

HuskyGrad2010

The price of a June call option with an exercise price of $50 falls by $0.50 when the underlying stock price falls by $2.00. The delta of a June put option with an exercise price of $50 is closest to:

A) –0.75.

B) –0.25.

C) 0.25.

---

The call option delta is:

The put option delta is 0.25 – 1 = –0.75.

HuskyGrad2010

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 Exhibits 1 and 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

Using the information in Exhibit 1, Franklin wants to compute the value of the corresponding European call option. Which of the following is the closest to Franklin's answer?

A) $5.55.

B) $4.78.

C) $11.54.

---

This result can be obtained using put-call parity in the following way:

Call Value = Put Value − Xe−rt + S = $4.78 − $100.00e(−0.07 × 1.0) + 100 = $11.54

The incorrect value of $4.78 does not discount the strike price in the put-call parity formula. (Study Session 17, LOS 56.i)

---

Franklin is interested in the sensitivity of the European call option to changes in the volatility of the underlying equity's returns. What happens to the value of the call option if the volatility of the underlying equity's returns decreases? The call option value:

A) decreases.

B) increases or decreases.

C) increases.

---

Due to the limited potential downside loss, changes in volatility directly effect option value. Vega measures the option’s sensitivity relative to volatility changes. (Study Session 17, LOS 56.d)

---

Franklin is interested in the sensitivity of the European put option to changes in the volatility of the underlying equity's returns. What happens to the value of the put option if the volatility of the underlying equity's returns increases? The put option value:

A) increases.

B) decreases.

C) increases or decreases.

---

Due to the limited potential downside loss, changes in volatility directly effect option value. Vega measures the option price sensitivity relative to the volatility of the underlying stock. (Study Session 17, LOS 56.d)

---

Franklin wants to know how the put option in Exhibit 1 behaves when all the parameters are held constant except the delta. Which of the following is the best estimate of the change in the put option's price when the underlying equity increases by $1?

A) −$0.33.

B) −$0.37.

C) −$3.61.

---

The correct value is simply the delta of the put option in Exhibit 2.
The incorrect value −$3.61 represents the change due to the volatility divided by 10 multiplied by −1.
The incorrect value −$0.37 calculates the change by dividing the short-term interest rate divided by 100. (Study Session 17, LOS 56.e)

---

Franklin computes the rate of change in the European put option delta value, given a $1 increase in the underlying equity. Using the information in Exhibits 1 and 2, which of the following is the closest to Franklin's answer?

A) 0.0180.

B) 0.6736.

C) −0.3264.

---

The correct value 0.0180 is referred to as the put option's Gamma.
The incorrect value −0.3264 is the delta of the put option.
The incorrect value 0.6736 is the call option's delta. (Study Session 17, LOS 56.e)

---

Franklin wants to know if the option sensitivities shown in Exhibit 2 have minimum or maximum bounds. Which of the following are the minimum and maximum bounds, respectively, for the put option delta?

A) −1 and 0.

B) There are no minimum or maximum bounds.

C) −1 and 1.

---

The lower bound is achieved when the put option is far in the money so that it moves exactly in the opposite direction as the stock price. When the put option is far out of the money, the option delta is zero. Thus, the option price does not move even if the stock price moves since there is almost no chance that the option is going to be worth something at expiration. (Study Session 17, LOS 56.e)