After completing this reading, you should be able to:

- Explain the motivation to initiate a covered call or a protective put strategy.
- Describe the use and calculate the payoffs of various spread strategies.
- Describe the use and explain the payoff functions of combination strategies.

## Covered Call

A **covered call** describes a trading strategy where the seller (writer) of a call option also owns the underlying stock. The writer sells call options for the same amount (or less) of stock. If the option is not exercised, the writer gets to keep the premium. If the option is exercised, the writer simply hands the option buyer their shares.

A covered call is the opposite of a **naked call**. In the latter, the writer of the call option does not own the underlying stock. In the event that the option is exercised, the writer is obligated to buy the shares at the market price and deliver them to the option buyer. A naked call, therefore, has unlimited risk because the market price can rise unpredictably.

The holder of a covered call can only profit on the stock **up to** the strike price of the options contract. The maximum profit is capped at:

$$ (Strike\quad Price-Stock\quad Entry\quad Price)+Option\quad Premium\quad Received $$

For example, let’s say you’ve bought a stock at \($10\), received a \($0.50\) option premium from selling a \($12\) strike price call. You’d maintain your stock position as long as the stock price stays below \($12\) at expiration. If the stock rises to \($13\), you will only profit up to \($12\), so your total profit will be \($2.5\left( =$12-$10+$0.50 \right) \). You’d be forced to give up the extra \($0.5\).

The maximum loss a covered call holder can incur is equal to:

$$ (Stock\quad Entry\quad Price-$0)+Option\quad Premium\quad Received $$

That could happen when the stock drops to $0.

For these reasons, a covered position is taken up to generate cash on a stock that is not expected to increase above the exercise price over the life of the option.

## Protective Put Strategy

A **protective put**, also called a put hedge, is a hedging strategy where the holder of a security buys a put to protect themselves against a drop in the stock price of that security.

A protective put has unlimited profit potential. A profit is achieved when the price of the underlying stock exceeds its purchase price plus the premium paid for the option. The maximum loss, on the other hand, is limited and is equal to the premium paid for buying the put option.

- Max profit = Unlimited
- Max loss = Premium Paid + Purchase Price of Underlying – Put Strike + Commissions Paid

A protective put is taken by bullish investors worried about near-term uncertainties on a stock.

## Payoffs of various Spread Strategies

Spread strategies include:

**Bull Spread:**A bull spread is a bullish options strategy designed to take advantage of a moderate rise in the price of the underlying in the near term. In a**bull call spread**, the bullish trader buys a call with a lower strike price and simultaneously sells a call with a higher strike price. The premium received from the sale of the higher strike call subsidizes the premium paid for the purchase of the lower strike call.Being bullish, the buyer of a bull call spread expects the price of the underlying stock to rise but remain below the strike of the short call.

Example of a bull call spread:

$$

\begin{array}{|l|c|}

\hline

Buy \quad 1 \quad ABC \quad 100 \quad call \quad at & \left( $5.50 \right) \\ \hline

Sell \quad 1 \quad ABC \quad 105 \quad call \quad at & $2.0 \\ \hline

Net \quad cost & \left( $3.50 \right) \\ \hline

\end{array}

$$The premium paid for the lower strike is higher than the premium received for the higher strike because the lower strike has higher chances of being attained in the near term.

In a

**bull put spread**, the bullish trader buys a put with a lower strike and simultaneously sells a put with a higher strike. The premium received from the sale of the higher strike put is higher than the premium paid for the lower strike put. As such, the two positions generate a positive net income.Example of a bull put spread:

$$

\begin{array}{|l|c|}

\hline

Sell \quad 1 \quad ABC \quad 100 \quad call \quad at & $3.50 \\ \hline

Buy \quad 1 \quad ABC \quad 95 \quad call \quad at & \left( $1.8 \right) \\ \hline

Net \quad cost & $1.7 \\ \hline

\end{array}

$$The maximum gain is capped by the difference between the strike prices minus the premium received.The most this spread can lose, on the other hand, is limited to the net premium.

Note: In both call and put spreads, the expiration date, as well as the underlying asset, must be

**the same**for both positions.**Bear Spreads:**A**bull spread**is a bearish options strategy designed to take advantage of a moderate decline in the price of the underlying in the near term. A**bull call**spread consists of one long call with a lower strike price and one short call with a higher strike price. On the other hand, a**bear put spread**consists of one long put with a higher strike price and one short put with a lower strike price.**Butterfly spreads:**A butterfly spread is a neutral, limited risk strategy that involves a combination of various bull spreads and bear spreads. The holder combines four option contracts having the same expiry date at three strike price points. Two option contracts are bought – one at a higher strike price and one at a lower strike price – and two option contracts are sold at a strike price in between. A butterfly trader has reason to believe the underlying asset will not move too far away from the current price.**Calendar spreads:**A calendar spread is a trading strategy set up by simultaneously entering a long and a short position on the same underlying asset and at the same strike price, but with different months to expiration. It’s a low-risk strategy that’s directionally neutral. The holder profits from the passage of time or increase in the underlying’s implied volatility. As in a butterfly spread, the holder also believes the stock will have a narrow range.We have several categories of calendar spreads;**A neutral calendar**– when the strike price is close to the current stock price**A bullish calendar spread**– has a strike price above the current stock price**A bearish calendar spread**has a strike price below the current stock price**A reverse calendar spread**– opposite of a calendar spread

**Diagonal spreads:**A diagonal spread works much like a calendar spread, but with a little difference; the options in a diagonal spread can have different strike prices in addition to different expirations.

## Payoff Functions of Combination Strategies

**Straddle:**A straddle involves two transactions on the same security, with positions that offset one another. A**long straddle**is created by purchasing a call and a put with the same strike price and expiration. A**short straddle**is created by selling a call and a put with the same strike price and expiration. Straddles work much like butterfly and calendar spreads, albeit the losses can be unlimited for short straddles. Long straddles can be appropriate when an investor expects significant movement in the stock price.**Strangle:**Similar to the straddle, a long strangle consists of**a long call**and**a long put option**on the same underlying asset and with the same expiration date. In a strangle, however, the two options have**different exercise prices**.**Strips:**A strip involves the purchase of two puts and one call with the same strike price and expiration. An investor enters into a long strip position when he expects a large move in a stock and considers a decrease in the stock price more likely than an increase.**Straps:**A long strap is a mirror image of a strip strategy. It consists of a**long position in two calls**and**one put**with the same exercise price and expiration date. An investor enters into a long strap position when he expects large moves in a stock but considers an increase in the stock price more likely than a decrease.**Collar:**A collar is a combination of a protective put and a covered call.

## Interest Rate Caps and Floors

An **interest rate cap** is a type of interest rate derivative in which the buyer receives payments at the end of each period in which the interest rate exceeds the agreed strike price. The strike rate is also called the cap rate. For example, the buyer could receive payments when the rate exceeds LIBOR + 200bps.

An **interest rate floor**, on the other hand, is a derivative contract in which the buyer receives payments at the end of periods in which the interest rate is below the agreed strike price. For example, the buyer could be entitled to a payment whenever the rate is below LIBOR + 50 bps.

Interest rate caps and floors **provide protection** against fluctuating interest rates.

## Question

Which of the following options trading strategies exposes the party to unlimited losses?

- Bull spread
- Covered call
- Butterfly spread
- Long straddle

The correct answer is **B**.

Options strategies that expose the party to unlimited losses include:

- Covered call
- Short straddle
- Short strangle
- etc.