# Reading 62: Risk Management Applications of Option Strategies

## Inhaltsverzeichnis

### Merke

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{*LOSnr38*}

Determine the value at expiration, the profit, maximum profit, maximum loss, breakeven underlying price at expiration, and general shape of the graph of the strategies of buying and selling calls and puts, and indicate the market outlook of investors using these strategies.

## Video: Reading 62: Risk Management Applications of Option Strategies

### Beispiel

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Example 1:

Assume the call option costs \$5. This means the buyer pays \$5 to the writer. So, at expiration when the price of the stock is equal to or less than the \$50 strike price (the option has zero value), the buyer of the option is out \$5 and the writer of the option is ahead \$5. As the stock’s price exceeds \$50 the buyer of the option starts to gain (breakeven will come at \$55, when the value of the stock equals the strike price and the option premium). However, as the price of the stock moves upward, the seller of the option starts to lose (negative figures will start at \$55, when the value of the stock equals the strike price and the option premium). The profit chart for the buyer and seller of a call option at expiration are presented below:

### Beispiel

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Example 2:

Assume the put option costs \$5. This means the buyer pays \$5 to the writer. So, when the price of the stock is equal to or more than the \$50 strike price (the put has zero value), the buyer of the option is out \$5 and the writer of the option is ahead \$5. As the stock’s price falls below \$50, the buyer of the put option starts to gain (breakeven will come at \$45, when the value of the stock equals the strike price less the option premium). However, as the price of the stock moves downward, the seller of the option starts to lose (negative profits will start at \$45, when the value of the stock equals the strike price less the option premium). The profit chart for the buyer and seller of a put option are:

### Beispiel

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Example 3:

Jimmy Casteel pays a premium of \$1.60 to buy a put option with a strike price of \$145. If the stock price at expiration is \$128, calculate Casteel’s profit or loss from the options position. ⇒The put option will be exercised and has a value of \$145-\$128 = \$17 [MAX (0, X-S)]. Therefore, Casteel receives \$17 minus the \$1.60 paid to buy the option. Therefore, the profit is \$15.40 (\$17 less \$1.60). ### Beispiel Hier klicken zum Ausklappen Example 4: A stock is trading at \$18 per share. An investor believes that the stock will move either up or down. He buys a call option on the stock with an exercise price of \$20. He also buys two put options on the same stock each with an exercise price of \$25. The call option costs \$2 and the put options cost \$9 each. The stock falls to \$17 per share at the expiration date and the investor closes his entire position. The investor’s net gain or loss is: A)$4 gain

B) $3 loss C)$4 loss

⇒The answer is C. The total cost of the options is \$2 + (\$9 × 2) = \$20 At expiration, the call is worth Max [0, 17-20] = 0. Each put is worth Max [0, 25-17] = \$8. The investor made \$16 on the puts but spent \$20 to buy the three options, for a net loss of \$4. ### Merke Hier klicken zum Ausklappen {*LOSnr39*} Determine the value at expiration, profit, maximum profit, maximum loss, breakeven underlying price at expiration, and general shape of the graph of a covered call strategy and a protective put strategy, and explain the risk management application of each strategy. ## Covered Call and Protective Put Covered call: • The term covered means that the stock covers the inherent obligation assumed in writing the call. • Why would you write a covered call? You feel the stock's price will not go up any time soon, and you want to increase your income by collecting some call option premiums. • This strategy for enhancing income is not without risk. The call writer trades the stock's upside potential, above the strike price, for the call premium. ### Methode Hier klicken zum Ausklappen A covered call is the combination of a long stock and a short call: Covered call=S－C The term covered means that the stock covers the inherent obligation assumed in writing the call. You want to increase your income by collecting some call option premiums. To add some insurance that the stock won’t get called away, the call writer can write out-of-the money calls. The call writer is trading the stock’s upside potential for the call premium. The graph below demonstrates the profit of the stock and the covered call as of the expiration date of the option. When the call was written, the stock’s price was \$50. The call’s strike price was \$55, and the call premium (C) was \$4. This was an out-of-the-money covered call. This graph shows that at expiration:

• If the stock closes below \$50, the option will expire, and the option writer’s loss is offset by the premium income of \$4.

• If the stock closes between \$50 and \$55, the option will expire worthless. Since this option was an out-of-the-money call, the option writer will get any stock appreciation above the original stock price and the strike price. So the gain (premium plus stock appreciation) will be between \$4 and \$9.

• If stock closes above \$55, the strike price, the writer will get nothing more. The maximum gain is \$9 on the covered out-of-the-money call.

### Beispiel

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Example:

The potential profits from writing a covered call position on a stock are:

B. limited to the premium plus stock appreciation up to the exercise price.

C. greater than the potential profits from owning the stock.

The answer is B. You should know that this strategy for enhancing one’s income is not without risk. The call writer is trading the stock’s upside potential for the call premium. The desirability of writing a covered call to enhance income depends upon the chance that the stock price will exceed the exercise price at which the trader writes the call. The owner of a stock has the rights to all upside potential. The profits for a short call are limited to the premium.

## Video: Reading 62: Risk Management Applications of Option Strategies

Protective put:

• A protective put is an investment management technique designed to protect a stock from a decline in value.

• If the stock price is above the strike price, you make money on the stock's appreciation, but the gain is reduced by the put premium paid.

• If the stock price decreases, the loss on the stock is offset by the gain on the put. The loss on the position is the put premium and any amount that the strike price is below the original stock price.

### Methode

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A protective put is constructed by buying a stock and a put option on that stock

Protective Put=S+P

### Beispiel

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Example:

An investor buys a share of stock at \$33 and simultaneously writes a 35 call for a premium of \$3. What is the maximum gain and loss?

The maximum gain on the stock itself is \$2 (\$35 - \$33). At stock prices above the exercise price, the stock will be called away from the investor. The gain from writing the call is \$3 so the total maximum gain is \$5. If the stock ends up worthless, the call writer still has the call premium of \$3 to offset the \$33 loss on the stock so the total maximum loss is \$30.