HuskyGrad2010

Mark Washington, CFA, is an analyst with BIC, a Bermuda-based investment company that does business primarily in the U.S. and Canada. BIC has approximately $200 million of assets under management, the bulk of which is invested in U.S. equities. BIC has outperformed its target benchmark for eight of the past ten years, and has consistently been in the top quartile of performance when compared with its peer investment companies. Washington is a part of the Liability Management group that is responsible for hedging the equity portfolios under management. The Liability Management group has been authorized to use calls or puts on the underlying equities in the portfolio when appropriate, in order to minimize their exposure to market volatility. They also may utilize an options strategy in order to generate additional returns. One year ago, BIC analysts predicted that the U.S. equity market would most likely experience a slight downturn due to inflationary pressures. The analysts forecast a decrease in equity values of between 3 to 5% over the upcoming year and one-half. Based upon that prediction, the Liability Management group was instructed to utilize calls and puts to construct a delta-neutral portfolio. Washington immediately established option positions that he believed would hedge the underlying portfolio against the impending market decline.
As predicted, the U.S. equity markets did indeed experience a downturn of approximately 4% over a twelve-month period. However, portfolio performance for BIC during those twelve months was disappointing. The performance of the BIC portfolio lagged that of its peer group by nearly 10%. Upper management believes that a major factor in the portfolio’s underperformance was the option strategy utilized by Washington and the Liability Management group. Management has decided that the Liability Management group did not properly execute a delta-neutral strategy. Washington and his group have been told to review their options strategy to determine why the hedged portfolio did not perform as expected. Washington has decided to undertake a review of the most basic option concepts, and explore such elementary topics as option valuation, an option’s delta, and the expected performance of options under varying scenarios. He is going to examine all facets of a delta-neutral portfolio: how to construct one, how to determine the expected results, and when to use one. Management has given Washington and his group one week to immerse themselves in options theory, review the basic concepts, and then to present their findings as to why the portfolio did not perform as expected. Which of the following best explains a delta-neutral portfolio? A delta-neutral portfolio is perfectly hedged against:

A) small price decreases in the underlying asset.

B) all price changes in the underlying asset.

C) small price changes in the underlying asset.

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A delta-neutral portfolio is perfectly hedged against small price changes in the underlying asset. This is true both for price increases and decreases. That is, the portfolio value will not change significantly if the asset price changes by a small amount. However, large changes in the underlying will cause the hedge to become imperfect. This means that overall portfolio value can change by a significant amount if the price change in the underlying asset is large. (Study Session 17, LOS 56.e)

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After discussing the concept of a delta-neutral portfolio, Washington determines that he needs to further explain the concept of delta. Washington draws the payoff diagram for an option as a function of the underlying stock price. Using this diagram, how is delta interpreted? Delta is the:

A) slope in the option price diagram.

B) curvature of the option price graph.

C) level in the option price diagram.

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Delta is the change in the option price for a given instantaneous change in the stock price. The change is equal to the slope of the option price diagram. (Study Session 17, LOS 56.e)

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Washington considers a put option that has a delta of −0.65. If the price of the underlying asset decreases by $6, then which of the following is the best estimate of the change in option price?

A) −$6.50.

B) −$3.90.

C) +$3.90.

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The estimated change in the price of the option is:
Change in asset price × delta = −$6 × (−0.65) = $3.90
(Study Session 17, LOS 56.e)

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Washington is trying to determine the value of a call option. When the slope of the at expiration curve is close to zero, the call option is:

A) in-the-money.

B) out-of-the-money.

C) at-the-money.

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When a call option is deep out-of-the-money, the slope of the at expiration curve is close to zero, which means the delta will be close to zero. (Study Session 17, LOS 56.e)

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BIC owns 51,750 shares of Smith & Oates. The shares are currently priced at $69. A call option on Smith & Oates with a strike price of $70 is selling at $3.50, and has a delta of 0.69 What is the number of call options necessary to create a delta-neutral hedge?

A) 75,000.

B) 14,785.

C) 0.

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The number of call options necessary to delta hedge is = 51,750 / 0.69 = 75,000 options or 750 option contracts, each covering 100 shares. Since these are call options, the options should be sold short. (Study Session 17, LOS 56.e)

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Which of the following statements regarding the goal of a delta-neutral portfolio is most accurate? One example of a delta-neutral portfolio is to combine a:

A) long position in a stock with a short position in a call option so that the value of the portfolio changes with changes in the value of the stock.

B) long position in a stock with a short position in call options so that the value of the portfolio does not change with changes in the value of the stock.

C) long position in a stock with a long position in call options so that the value of the portfolio does not change with changes in the value of the stock.

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A delta-neutral portfolio can be created with any of the following combinations: long stock and short calls, long stock and long puts, short stock and long calls, and short stock and short puts. (Study Session 17, LOS 56.e)

HuskyGrad2010

In order to form a dynamic hedge using stock and calls with a delta of 0.2, an investor could buy 10,000 shares of stock and:

A) write 50,000 calls.

B) write 2,000 calls.

C) buy 50,000 calls.

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Each call will increase in price by $0.20 for each $1 increase in the stock price. The hedge ratio is –1/delta or –5. A short position of 50,000 calls will offset the risk of 10,000 shares of stock over the next instant.

HuskyGrad2010

The delta of an option is equal to the:

A) dollar change in the stock price divided by the dollar change in the option price.

B) dollar change in the option price divided by the dollar change in the stock price.

C) percentage change in option price divided by the percentage change in the asset price.

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The delta of an option is the dollar change in option price per $1 change in the price of the underlying asset.

HuskyGrad2010

John Williamson 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 Frank Potter, CFA, a financial adviser from Star Financial, LLC, to help him with his investment strategies. Potter has a number of interesting investment strategies for Williamson'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 Williamson that there are numerous options available for him to obtain almost any risk return profile he might need. Potter suggest that Williamson 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

Table 3: Regular and Exotic 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

Williamson would like to consider neutralizing his Reston equity position from changes in the stock price of Reston. Using the information in Tables 3 and 4 how many standard Reston European options would have to be bought/sold in order to create a delta neutral portfolio?

A) Sell 497,141 put options.

B) Sell 370,300 call options.

C) Buy 497,141 put options.

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Number of put options = (Reston Portfolio Value / Stock PriceReston) / −DeltaPut
Number of put options = ($10,000,000 / $50.00) / −0.4023 = −497,141 meaning buy 497,141 put options.Selling put options does not deliver any downside protection, but it aggravates the losses when the stock decreases in value.

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Williamson is very interested in the total return swap. He 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) $0.

B) $340,885.

C) $45,007.

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Swaps are priced so that their value at inception is zero.

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Williamson likes the characteristics of the swap arrangement in Table 1 but would like to consider the options in Table 3 before making an investment decision. Given Williamson's current situation which of the following option trades makes the most sense in the short-term (all options are on Reston stock)?

A) Buy out of the money call options.

B) Sell at the money call options.

C) Buy at the money put options.

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Buying at the money put options greatly reduces Williamson's downside risk. Selling call options yields an option premium to the seller but does not deliver any downside protection and limits the upside potential of the portfolio.

HuskyGrad2010

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 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
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

What does it mean to make an options portfolio delta neutral?  The option portfolio:

A) moves exactly in line with the stock price.

B) moves exactly in the opposite direction with the stock price.

C) is insensitive to price changes in the underlying security.

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

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Which of the following most accurately describes the sensitivity of the call option's delta to changes in the underlying asset’s price? The sensitivity to changes in the price of the underlying is the greatest when the call option is:

A) at the money.

B) in the money.

C) it depends on the other inputs.

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When the option is at the money, delta is most sensitive to changes in the underlying asset’s price. (Study Session 17, LOS 56.f)

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Which of the following most accurately describes when the call option delta reaches its minimum bound? The call option reaches its minimum bound when call option is:

A) at the money.

B) far out of the money.

C) the option's delta has no minimum bound.

When a call option is far out of the money its value is insensitive to changes in value of the underlying. This is because the chances that it is going to end up in the money at expiration are very small. (Study Session 17, LOS 56.e)

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If the portfolio has 10,000 shares of the underlying stock and he wants to completely hedge the price risk using options, what kind of options should Franklin buy?

A) Call and put options.

B) Put options.

C) Call options.

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Buying put options will allow Franklin to completely hedge the stock price risk. (Study Session 17, LOS 56.e)

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Compute the number of shares of stock necessary to create a delta neutral portfolio consisting of 100 long put options in Exhibit 2 and the stock.

A) 32.64.

B) 67.36.

C) −32.64.

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This is simply −100 times the put option delta. Since each share has a delta of 1, we only need 32.64 shares (long) to create a delta neutral portfolio. (Study Session 17, LOS 56.e)

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Compute the number of shares of stock necessary to create a delta neutral portfolio consisting of 100 long call options in Exhibit 2 and the stock.

A) −32.64.

B) 67.36.

C) −67.36.

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This is simply −100 times the call option delta. Since each share has a delta of 1, we only need −67.36 (short) shares to create a delta neutral portfolio. (Study Session 17, LOS 56.e)

HuskyGrad2010

Which of the following is the best approximation of the gamma of an option if its delta is equal to 0.6 when the price of the underlying security is 100 and 0.7 when the price of the underlying security is 110?

A) 0.01.

B) 0.10.

C) 1.00.

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The gamma of an option is computed as follows:
Gamma = change in delta/change in the price of the underlying = (0.7 – 0.6)/(110 – 100) = 0.01

HuskyGrad2010

Which of the following is the best approximation of the gamma of an option if its delta is equal to 0.6 when the price of the underlying security is 100 and 0.7 when the price of the underlying security is 110?

A) 0.01.

B) 0.10.

C) 1.00.

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The gamma of an option is computed as follows:
Gamma = change in delta/change in the price of the underlying = (0.7 – 0.6)/(110 – 100) = 0.01

HuskyGrad2010

When an option’s gamma is higher:

A) delta will be higher.

B) a delta hedge will perform more poorly over time.

C) a delta hedge will be more effective.

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Gamma measures the rate of change of delta (a high gamma could mean that delta will be higher or lower) as the asset price changes and, graphically, is the curvature of the option price as a function of the stock price. Delta measures the slope of the function at a point. The greater gamma is (the more delta changes as the asset price changes), the worse a delta hedge will perform over time.

HuskyGrad2010

Gamma is the greatest when an option:

A) is deep in the money.

B) is deep out of the money.

C) is at the money.

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Gamma, the curvature of the option-price/asset-price function, is greatest when the asset is at the money.

HuskyGrad2010

Two call options have the same delta but option A has a higher gamma than option B. When the price of the underlying asset increases, the number of option A calls necessary to hedge the price risk in 100 shares of stock, compared to the number of option B calls, is a:

A) larger positive number.

B) smaller (negative) number.

C) larger (negative) number.

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For call options larger gamma means that as the asset price increases, the delta of option A increases more than the delta of option B. Since the hedge ratio for calls is – 1/delta, the number of calls necessary for the hedge is a smaller (negative) number for option A than for option B.