Subject 3. Covered Calls

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.

Motivations:

  • Income generation. This is the primary motivation. The intention is to keep the premium without surrendering the stock through exercise. However, the writer of the covered call is actually exchanging the chance of large gains on the stock position for income from selling the option.
  • Improving on the market to capture the time value.
  • Target price realization.

Profit and Loss at Expiration

At expiration:

  • Maximum profit is the appreciation to the exercise price + the option premium: X - S0 + c0
  • Maximum loss = S0 - c0
  • Breakeven point = S0 - c0
  • Expiration value = the value of a covered call = ST - Max(0, ST - X) = ST if ST <= X, or X if ST > X
  • Profit at expiration = the covered call value + the option premium - the original price of the stock: (ST - Max[(ST - X), 0] + c0 - S0

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.

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 the covered call position will be $18, and the profit will be $18 + 5 - 20 = $3.
  • $32, the value will be $30, and the profit will be $30 + 5 - 20 = $15.
  • $50, the value will be $30, and the profit will be $30 + 5 - 20 = $15.

Clearly, no matter how much the stock price rises, the maximum profit for Tom will be $15.

This strategy is like a cash-secured put, which refers to writing a put and simultaneously setting aside enough cash to buy the stock. The goal is also to acquire shares at a target price.

Practice Question 1

The most common motivation for writing covered calls is ______.

A. income generation
B. improving on the market
C. target price realization
Correct Answer: A

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 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 is the value of the covered call position if the position is held to expiration and the stock price becomes $45?

A. $40
B. $43
C. $45
Correct Answer: A

The value is the smaller of ST (45) or X (40). Note that the profit is $40 + $3 - $38 = $5.

Practice Question 4

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 is the breakeven price of the covered call?

A. $35
B. $37
C. $38
Correct Answer: A

35 + 3 - 38 = 0

Practice Question 5

If you own a stock and write calls with an exercise price below the current price of the stock, you are most likely trying to ______ by entering this covered call position.

A. generate income
B. improve on the market
C. realize your target price for the stock
Correct Answer: B

Practice Question 6

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 the 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 7

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 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

(ST - S0) - MAX (0, ST - X) + c0 = (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 8

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 31

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 = ST - c0 = 45.63 - .63 = 45.00

Practice Question 9

Barry has 1000 shares of Apple, Inc. The Apple shares are trading at $115 right now. To ______ he is going to write 10 call options with a strike price of $115 and a month to expire. One call option contract covers 100 shares.

A. generate income
B. improve on the market
C. realize his target price for Apple stock
Correct Answer: C

The target price realization strategy involves writing calls with an exercise price near the target price for the stock.

Practice Question 10

Suppose an investor buys one share of stock and a put option on the stock and simultaneously sells a call option on the stock with the same exercise price. What will be the value of his investment on the final exercise date?

A. Above the exercise price if the stock price rises and below the exercise price if it falls.
B. Equal to the exercise price regardless of the stock price.
C. Equal to zero regardless of the stock price.
Correct Answer: B

Practice Question 11

A long covered call position is similar to ______.

A. a long stock/short forward position
B. writing a cash-secured put
C. a long forward/short stock position
Correct Answer: B

Note that the long stock/short forward position has a similar delta as an at-the-money covered call or an at-the-money protective put. This question does not specify that the covered call is at-the-money, however.

Practice Question 12

Suppose the current price for stock A is $15. You can write either a Sept 15 call or Sept 15 put for $1. Assume there is no borrowing, lending or transaction costs. One option contract covers one share of stock A. You can establish a covered call or a cash-secured put position. Which position has a larger maximum profit?

A. Covered call
B. Cash-secured put
C. They will have the same "maximum profit."
Correct Answer: C

The maximum profit is $1 (the option premium) in both cases, as the strike price is equal to the current stock price.

Practice Question 13

Assume that in August 2016 Connor owned 100 shares of Amazon.com. The spot stock price was around $800. He wrote one Sept 700 call (one option contract covers 100 shares) at $120. The motivation for writing such an option was likely to be ______.

A. income generation
B. improving on the market
C. target price realization
Correct Answer: B

Since the exercise price of $700 is below the current spot price of $800, he is trying to improve on the market by capturing the time value.

Practice Question 14

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 was $82.00 per share, then the 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

(ST - S0) - MAX(0, ST - X) + c0 = (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 15

An investor buys shares of ABC Corp. at $30 and immediately writes a call on them. If the call carries a premium of $2.50 and its exercise price is $30, at what price will this investor break even?

A. $27.50
B. $32.50
C. Call options cannot have a negative value. Therefore, there is no breakeven 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 the stock is losing value. 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 breakeven point.

Practice Question 16

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 17

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. $58.20
C. $60.40
Correct Answer: A

A covered call breakeven price equals the price paid for the stock less the premium received for the call. Breakeven = (S0 - c0) = (60 - 3.60) = $56.40

Practice Question 18

The biggest risk for a cash-secured put writer is if the stock price ______.

A. falls to zero
B. remains unchanged
C. rises significantly
Correct Answer: A

In that case the trader will have to pay the strike price for a stock that is worth nothing.