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.