Chapter 24 Integrating Derivative Assets and Portfolio Management

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Chapter 24Integrating Derivative Assets and
Portfolio Management

• Business 4179

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Key Points

• Index calls can increase the yield of a
  portfolio, and they are used for that purpose
  here.
• Both market and company specific risk are
  reduced.
• It is possible to minimize the cash outlay in a
  risk management application by proper selection
  of the puts and calls (and possibly futures)
  used.
• Simultaneous equations can be solved to get a
  desired position delta at minimum cost.
• Options can also be used with the fixed income
  portfolio, and the chapter briefly discusses the
  use of T-bill options.

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Question 24 - 1

• Writing index calls does not influence the value
  of the stock portfolio itself in any way.
  However, writing calls can result in a financial
  liability if they close in-the-money.
• Calls become in-the-money when the stock market
  rises, so presumably the stock portfolio rose as
  well if the index calls became valuable. It is
  likely that the loss on the calls is largely
  offset by a gain on the stock, so in practice the
  price appreciation of the total portfolio is
  limited.

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Question 24 - 2

• The lower the striking price the higher the
  premium income, but the greater the likelihood of
  exercise. Logically, high striking prices yield
  little income, but are seldom exercised. High
  striking prices also have low deltas, which means
  they provide only a modest adjustment to position
  delta. In-the-money options, which have high
  deltas, are powerful tools in altering the
  portfolio risk.

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Question 24 - 3

• You could also write index or equity puts.

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Question 24 - 4

• Individual equity options are useful in hedging
  company-specific risk. They are also useful for
  generating income in small portfolios that are
  not sufficiently valuable to provide the
  necessary collateral for option writing.

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Question 24 - 5

• There is disagreement over which is riskier,
  writing individual calls or index calls. A good
  argument can be made that writing individual
  equity calls is riskier, as a single security
  sometimes has a spectacular one-day gain, rising
  by perhaps 50 because of takeover news. The
  stock market has never experienced a gain of this
  size. Option writers are hurt by rapidly rising
  prices, and because equity options can rise
  faster than index options, a good argument can be
  made that the margin requirements should be
  stiffer on individual options.

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Question 24 - 6

• First, figure out the market value and beta of
  the portfolio to be hedged. Then select a
  striking price for the put depending on the level
  of protection desired. Next, calculate the delta
  of the desired option. (This may require
  calculating implied volatility first.) Finally,
  calculate the hedge ratio as shown on page 547.

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Question 24 - 7

• At-the-money futures puts and calls sell for the
  same price.

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Question 24 - 8

• Writing calls is a bearish strategy when done in
  isolation. From the writers perspective, gains
  accrue when the value of the underlying asset
  declines. Combining this strategy with a long
  position in the underlying asset declines.
  Combining this strategy with a long position in
  the underlying asset reduces the market exposure
  in the underlying asset, because the short option
  will offset some gains that might be experienced
  without the options.

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Question 24 - 9

• Option prices are not a linear function of the
  underlying stock price. The 0.5 decline results
  in the option falling in vlaue by 0.93, while a
  0.5 rise results in an option price rise of only
  0.50. This difference is primarily because the
  option was not initially at-the-money.

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Problem 24 - 2

• The income shortfall in the example beginning on
  page 536 is 16,624. The AUG 315 calls have a
  premium of 1.75. The number of contracts is
  therefore

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Problem 24 - 3

• As shown in the example, the market value of the
  stock portfolio is equal to about 36 OEX
  contracts. If fewer than 36 contracts were
  written, the maximum value of the stock portfolio
  would be theoretically unlimited. Writing 36 or
  more contracts puts a limit on the portfolio
  price appreciation, with the limit occurring at
  the option striking price.
• The index can rise from 298.96 to 315.00 ( a rise
  of 5.36) before the options become in-the-money.
  Therefore, the maximum value of the equity
  portfolio is approximately

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Problem 24 - 3 ...

• The index can rise from 298.96 to 315.00 ( a rise
  of 5.36) before the options become in-the-money.
  Therefore, the maximum value of the equity
  portfolio is approximately
• This assumes the option premium income was spent
  and that the stock portfolio tracks the OEX index
  perfectly.

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Problem 24 - 4

• A. 10 rise
• stock 996,975 0.10 1.08 107,673 gain
• calls 100 56 (3.40 - 20.68) 96,768 loss
• net 10,905 gain
• 996,975 10,905 3,025 1,010,905
• B. 10 decline
• stock 996,975 - 0.10 1.08 107,673 loss
• calls 100 56 (3.40 - 0) 19,040 gain
• net 88,633 loss
• 996,975 - 88,633 3,025 911,367

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Problem 24 - 9

• At-the-money futures puts and calls should sell
  for the same price. Therefore, the put should
  also sell for 2.

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Problem 24 - 10

• With a striking price of 99, an underlying asset
  price of 100, a riskfree interest rate of 5, a
  call premium of 2, and one-twelfth of a year
  until expiration, use the futures put-call parity
  relationship

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Problem 24 - 11

• CFA Guideline Answer
• A. The problem here is to sell equities and
  reinvest the proceeds with the skilled
  fixed-income manager, without changing the split
  between the existing allocations to the two asset
  classes. The solution is to turn to derivative
  financial instruments as the means to the end
  selling enough of the fixed-income exposure and
  brining in enough of the equity exposure to get
  the desired mix result.
• The following are distinct derivatives
  strategies that the board could use to increase
  the Funds allocation to the fixed-income

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Problem 24 - 11 ...

• CFA Guideline Answer
• A. ... manager without changing the present
  fixed-income index/equity proportions.
• Strategy 1. Use futures. One strategy would be
  to sell futures on a fixed-income index and buy
  futures on an equity index. Selling the futures
  eliminates the fixed-income index return and
  risk, while keeping the skilled fixed-income
  managers extra return. By being long the equity
  index, the portfolio obtains the index return and
  risk, keeping its exposure to the equity market.

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Problem 24 - 11 ...

• CFA Guideline Answer
• A. ...
• Strategy 2. Use swaps. A second strategy would
  be to use over-the-counter swaps.
• BI would swap a fixed-income index return for an
  equity index return in a notional amount large
  enough to keep the skilled managers extra return
  while eliminating the fixed-income market return
  and replacing it with the equity market return.

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Problem 24 - 11 ...

• CFA Guideline Answer
• A. ...
• Strategy 3. Use option combinations. A third
  strategy would use put and call options to create
  futures-like securities.
• Buying put options and selling call options on a
  fixed-income index, while selling put options and
  buying call options on a stock index, would
  achieve the same result as the appropriate
  futures position.

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Problem 24 - 11 ...

• CFA Guideline Answer
• B. The following are advantages and disadvantages
  of each strategy identified and explained in Part
  A
• Strategy 1. Use futures.
• Advantages
• 1. Futures contracts are liquid instruments.
• 2. Transaction costs are low.
• 3. Credit risk is negligible because the
  securities are marked to market daily.

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Problem 24 - 11 ...

• CFA Guideline Answer
• Strategy 1. Use futures.
• Disadvantages
• 1. If the holding period is long, rollover
  (transaction) costs are incurred.
• 2. Standard contract forms are limited, so
  contracts may not exist on the index or
  instrument needed.

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Problem 24 - 11 ...

• CFA Guideline Answer
• B. The following are advantages and disadvantages
  of each strategy identified and explained in Part
  A
• Strategy 2. Use swaps.
• Advantages
• 1. Swaps can be tailored to fit the desired
  investment horizon, eliminating (or reducing)
  rollover costs.
• 2. Swaps can be contracted for a specific index
  (like the performance benchmark) even if there is
  no futures contract on it.
• 3. The desired adjustment goal can be
  accomplished through a single transaction.

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Problem 24 - 11 ...

• CFA Guideline Answer
• B. The following are advantages and disadvantages
  of each strategy identified and explained in Part
  A
• Strategy 2. Use swaps.
• Disadvantages
• 1. A counterparty credit risk is created that can
  be much larger than with other types of
  instruments.
• 2. Swap agreements are illiquid instruments, and
  disposals can be both difficult and expensive.
• 3. Transaction costs are large because of typical
  tailoring of a given swap.

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Problem 24 - 11 ...

• CFA Guideline Answer
• B. The following are advantages and disadvantages
  of each strategy identified and explained in Part
  A
• Strategy 3. Use option combinations.
• Advantages
• 1. Transaction costs are low
• 2. Credit risks are small.
• Disadvantages
• 1. Rollover(s) may be necessary
• 2. The right option may not be available when
  needed or at all.
• 3. Holders may exercise the put option and end
  the hedge.

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Problem 24 - 11 ...

• CFA Guideline Answer
• B. The following are advantages and disadvantages
  of each strategy identified and explained in Part
  A
• A generic disadvantage of any strategy is that
  returns are automatically eroded by the costs of
  establishing and maintaining the strategies, of
  meeting margin requirements, if any, and of
  unwinding them, if necessary.