We discussed the payoffs of individual options in Reading 59. Options can be combined with the underlying to shape the risk and return characteristics of the underlying.

Covered Call: Stock plus a Short Call

In covered call transactions, a trader is generally assumed to already own a stock and writes a call option on the underlying stock. The term "covered" means that the potential obligation in selling the call (that is, to deliver the underlying) is covered by the underlying. When the call is exercised, the underlying is immediately available to be delivered to the buyer of the call.

The value at expiration of the covered call equals the value of the underlying plus the value of the short call:

Value of covered call = value of underlying + value of short call
= S_T - MAX(0, S_T - X)
= S_T if S_T <= X, or X if S_T > X

This strategy is generally undertaken as an income-enhancement technique, and the intention is to keep the premium without surrendering the stock through exercise. However, the writer of the covered call is actually exchanging the change of large gains on the stock position in favor of income from selling the option.

Example

• Tom buys a share of stock for $20, and simultaneously sells a call option on that stock for $5. Therefore, he pays a total of $15 for the portfolio.
• The exercise price of the call (X) is $30, and the call will expire in 3 months.
• Determine the expiration-day profits/loss of Tom's covered call position if the stock price finishes at $18, $32, or $40 respectively.

Solution

If the stock price finishes at:

• $0, the value of the covered call position will be $0, and the profit will be $0 + 5 - 20 = -$15. This is the potential maximum loss.
• $15, the value of the covered call position will be $15, and the profit will be $15 + 5 - 20 = $0. This price ($15) is called the breakeven price of the covered call.
• $18: the value of his position will be $18 (the value of the stock) + $5 (the option premium) = $23.
• $32: the value of his position will be $35 (the call option will be exercised by the buyer).
• $40: the value of this position will be also $35.

Protective Put: Stock plus a Long Put

A portfolio of stock has a potentially wide range of gains and losses. If all the stocks in the portfolio lost all of their value, the value of the portfolio would also lose all of its value. In other words, it would be possible to lose everything that had been invested. On the other hand, as the stocks in the portfolio increase in value, the value of the portfolio increases. Since the value of a share of stock has (theoretically) no upper limit, the value of a portfolio has no upper limit.

A protective put (portfolio insurance) is an investment management technique designed to protect a stock portfolio from severe drops in value. It involves holding a stock portfolio and buying a put option on the portfolio. Because the price of a put is always positive, it is clear that an insured portfolio costs more than the uninsured stock portfolio alone. At expiration, the value of the insured portfolio is: S_T + P_T + S_T + MAX {0, X - S_T}. As you can see, the strategy offers protection against large drops in value.

This strategy is like a long position in a call. A trader can buy a call and invest the extra proceeds in a bond in order to replicate a position in an insured portfolio.

Portfolio insurance limits the amount of loss on a portfolio by balancing that loss with the gain from a LONG put option. It also reduces the potential gain on a portfolio as a result of the premium paid for the put option. The "insurance" part of portfolio insurance, then, is the limitation of potential loss. The insurance is not free, however. The cost of the insurance is the put option premium.

Practice Question 1

In the option market, a covered writer would have which of the following portfolios?

A. Writer of an option
B. Writer of a put option, and short stock
C. Writer of a call option, and long stock

Correct Answer: C

Covered writer: A writer of an option who owns that stock on which the option is written. If the stock is not owned, the writer is deemed naked.

Practice Question 2

An investor purchases stock for $38/share and sells call options on that stock with an exercise price of $40 for a premium of $3/share. Ignoring dividends and transactions costs, what maximum profit can the investor earn if the position is held to expiration?

A. $2
B. $3
C. $5

Correct Answer: C

The maximum gain is the appreciation to the exercise price + the option premium: ($40 - $38) + $3 = $5

Practice Question 3

An at-the-money protective put position (comprised of owning the stock and the put) ______.

I. protects against loss at any stock price below the strike price of the put
II. has limited profit potential when the stock price rises
III. returns any increase in the stock's value, dollar for dollar, less the cost of the put
IV. provides a pattern of returns similar to a stop-loss order at the current stock price

Correct Answer: I and III

Practice Question 4

An investor would likely write a covered call under which of the following conditions?

A. The investor is concerned about downward price movement in the stock.
B. The investor wishes to leverage an anticipated rise in the stock price.
C. The investor does not anticipate a significant change in stock price in the near term.
D. The investor wishes to profit from an anticipated fall in the stock price.

Correct Answer: C

An investor would likely write a covered call if he or she does not anticipate a significant change in stock price in the near term.

Practice Question 5

An investor owns 100 shares of General Motors stock. She sells one stock call option. The investor's position is now a covered call with the following characteristics:

Stock position: LONG 100 shares of General Motors
Stock purchase price: $62.00 per share
Option position: SHORT 1 call option General Motors stock
Underlying asset: 100 shares of General Motors
Exercise price: $80.00 per share
Premium: $0.13 per share
Expiration date: October

The expiration-day price of General Motors stock is ST = $70.00 per share. The expiration-day profit/loss for the covered call is ______.

A. + $8.00 + $10.00 + $0.13 = $18.13
B. + $8.00 - $10.00 + $0.13 = -$1.87
C. + $8.00 - $0.00 + $0.13 = $8.13

Correct Answer: C

(S_T - S_t) - MAX (0, S_T - X) + C_t = (70.00 - 62.00) - MAX (0, 70.00 - 80.00) + .13 = 8.00 - MAX (0, -10) + .13 = 8.00 - 0 + .13 = 8.13

Practice Question 6

An exporter in the U.S. is expecting a payment of BP 5 million in three months. He is planning to hedge the position using options. He should ______.

A. buy call options
B. buy put options
C. write put options

Correct Answer: B

Practice Question 7

A portfolio insurance strategy consists of ______.

A. LONG stock portfolio and SHORT stock index put
B. LONG stock portfolio and LONG stock index put
C. SHORT stock portfolio and LONG stock index put

Correct Answer: B

Practice Question 8

An investor would likely buy a protective put under which of the following conditions?

A. The investor is concerned about downward price movement in the stock.
B. The investor wishes to leverage an anticipated rise in the stock price.
C. The investor does not anticipate a significant change in stock price in the near term.

Correct Answer: A

An investor would likely buy a protective put (portfolio insurance) if he/she were concerned about a downward price movement in the stock.

Practice Question 9

An investor owns a stock portfolio that closely follows the Standard & Poor's 500 Index (S&P 500). He purchases one S&P 500 stock index put option. The investor's position now has portfolio insurance with the following characteristics:

Portfolio position: LONG S&P 500
Portfolio purchase price: $1427.21
Option position: LONG 1 put option
Underlying asset: S&P 500 Index
Exercise price: $1225
Premium: $3
Expiration date: November 30

The expiration-day price of the S&P 500 is ST = $1500. The expiration-day profit/loss for the portfolio insurance is ______.

A. + 72.79 + 0 - 3 = $69.79
B. + 72.79 + 0 + 3 = $75.79
C. - 72.79 + 275 - 3 = $199.21

Correct Answer: A

(S_T - S_t) + MAX (0, X - S_T) - P_t = (1500 - 1427.21) + MAX (0, 1225 - 1500) - 3.00 = 72.79 + MAX (0, -275) - 3.00 = 72.79 + 0 - 3.00 = $69.79

Practice Question 10

Consider a stock call option with the following characteristics:

Type of option: call option on stock
Underlying asset: 100 shares of Anheuser Busch
Exercise price: ______
Premium: $0.63 per share
Expiration date: October

The expiration-day price of Anheuser Busch stock is ST = $45.63 per share. This stock price is known to be the breakeven stock price for the call option. What is the exercise price of the option?

A. $45.63
B. $46.26
C. $45.00

Correct Answer: C

X = S_T - C_t = 45.63 - .63 = 45.00

Practice Question 11

Suppose the return distribution of a stock is a bell shaped curve. Buying a put options does which of the following?

A. Truncates the left side of the curve and moves the whole bell curve to the right.
B. Truncates the left side of the curve and moves the whole bell curve to the left.
C. Truncates the right side of the curve and moves the whole bell curve to the right.
D. Truncates the right side of the curve and moves the whole bell curve to the left.

Correct Answer: B

Practice Question 12

An investor owns 100 shares of General Motors stock. She sells one stock call option. The investor's position is now a covered call with the following characteristics:

Stock position: LONG 100 shares of General Motors
Stock purchase price: $62.00 per share
Option position: SHORT 1 call option General Motors stock
Underlying asset: 100 shares of General Motors
Exercise price: $80.00 per share
Premium: $0.13 per share
Expiration date: October

If the expiration-day price of General Motors stock were $82.00 per share, then the expiration-day profit/loss for the covered call would be ______.

A. + $20.00 - $2.00 + $0.13 = $18.13
B. + $20.00 - $0.00 + $0.13 = $20.13
C. + $20.00 - $0.00 - $0.13 = $19.87

Correct Answer: A

(S_T - S_t) - MAX(0, S_T - X) + Ct = (82.00 - 62.00) - MAX (0, 82.00 - 80.00) + .13 = 20.00 - MAX (0, 2.00) + .13 = 20.00 - 2.00 + .13 = 18.13

Practice Question 13

An investor buys 100 baskets of the Standard and Poor's 500 stock index for $1,400 each. She insures the portfolio by buying put options. What is the effect of the put options?

A. The upside risk of the insured portfolio is truncated and the downside risk is reduced relative to the uninsured portfolio.
B. The downside risk of the insured portfolio is truncated and the upside return of the insured portfolio is lower relative to the uninsured portfolio.
C. The insured portfolio does better than the uninsured portfolio whenever the market declines.

Correct Answer: B

Practice Question 14

The profits and losses from an equity portfolio insured using puts would have the same profit and loss characteristics as ______.

A. being long a call option
B. writing covered puts
C. writing covered calls

Correct Answer: A

Being long a call has limited downside risk, as does portfolio insurance.

Practice Question 15

An investor buys shares of ABC Corp. at $30 and immediately writes a call on them. If the call carries a premium of $2.5 and its exercise price is $30, at what price of ABC shares will this investor break-even?

A. $27.50
B. $32.50
C. Call options cannot have a negative value, therefore, there is no break-even point.

Correct Answer: A

A call is at the money when its exercise price is equal to the current price of the asset. In this case, both the exercise price and the asset price is $30.

A covered call writer refers to an investor who owns the underlying asset and simultaneously sells (or writes) a call option. If the investor is writing the call, he will receive a premium of $2.50.

Should the asset price close above $30 before expiration, the writer of the call will have to deliver his stock. He loses the stock, but walks away with the premium he made.

On the other hand, if the stock price closes below $30, the writer will not be called upon to deliver the stock. However, the dropping stock price implies that he is losing value on the stock. If the stock price drops to $27.50, he has lost $2.50 on his stock, but since he made $2.50 selling the call in the beginning, he breaks even. Should the stock price drop below $27.50, his losses will offset any money he made selling the call. Hence, $27.50 is the break-even point.

Practice Question 16

Your research department has just made a sound presentation arguing that the equity markets are due for a severe correction in the short term. Which of the following strategies would be most suitable to safeguard the portfolio that you manage?

A. Long futures contacts on an equity index
B. Buy put options on an equity index
C. Buy call options on an equity index

Correct Answer: B

If you expect stock prices to decline, then you'll want to enter into an agreement that will allow you to sell shares at a pre-determined price. This way, you are effectively locking in the future value of the shares. There are only two strategies that will enable you to carry out this transaction. First, buying a put will give you the "right" to deliver these shares at a pre-determined price. Second, selling stock index futures will "obligate" you to deliver these shares at a pre-determined price.

Practice Question 17

Which of the following strategies would you advise against the most if you were expecting stock prices to appreciate significantly?

A. Writing a put while owning the underlying asset
B. Writing a put without actually owning the underlying asset
C. Writing calls without actually owning the underlying asset

Correct Answer: C

If stock prices are expected to increase, it would be very risky to sell securities that appreciate in value due to a market appreciation. Writing a call option would do exactly that. Uncovered call writing simply refers to the practice of selling a call when the underlying stock is not owned by the investor.

Practice Question 18

Which of the following statements is (are) true with respect to insuring a portfolio by way of protective strategy?

I. The strategy requires the sale of put options while owning the underlying asset.
II. If the price of the underlying asset increases dramatically, then an insured portfolio will perform much better than an uninsured portfolio.
III. The cost of portfolio insurance will rise as the volatility of the underlying asset increases.
IV. The upside potential for an insured portfolio is unlimited.

A. I and IV
B. III only
C. III and IV

Correct Answer: C

I is incorrect because this strategy requires the purchase of put options while owning the underlying asset.

II is incorrect because if the price of the underlying asset increases dramatically, then an insured portfolio will under-perform an uninsured portfolio. The cause of this under-performance is that fact that an insured portfolio always lags behind an uninsured portfolio by the amount of the premium.

Practice Question 19

A market participant has a view regarding the potential movement of a stock. He sells a customized over-the-counter put option on the stock when the stock is trading at $38. The put has an exercise price of $36 and the put seller receives $2.25 in premium. The price of the stock is $35 at expiration. The profit or loss for the put seller at expiration is ______.

A. -$2.15
B. $1.25
C. $2.25

Correct Answer: B

Profit = max (0, -value of put at expiration + premium) = max (0, -(X-S) +premium) = -1+2.25 = $1.25

Practice Question 20

An investor purchases a stock at $60 and at the same time sells a 3-month call on the stock. The short call has a strike price of $65 and a premium of $3.60. The risk-free rate is 4 percent. The breakeven underlying stock price at expiration is closest to ______.

A. $56.40
B. $58.2
C. $60.4

Correct Answer: A

A covered call breakeven price equals the price paid for the stock less the premium received for the call. Breakeven = (S-c) = (60-3.60) = $56.40