Covered call and protective put strategies

Covered call strategy: The covered call strategy is the combination of long underlying and short call option. It is a conservative strategy that reduces the risk of the long underlying position. Though it also reduces the return as well as there is a limit to the upside and not that much to the downside.

The value at the expiration will be simply the addition of the value of long underlying position and value of short call position. The short call position is taken at an exercise price that is generally higher than the spot price of the underlying when the position is initiated.

V_T = S_T - Max(0, S_T - X)

If S_T >X, then V_T = S_T - S_T + X = X

If S_T ≤X, then V_T = S_T - 0 = S_T

Profit from the strategy at expiration = Value at expiration - Payment made for the initiation of the trade = V_T - (S₀ - c₀) (Because we pay the amount for buying the underlying and receive the premium on selling the call option)

Profit when S_T>X = X - (S₀ - c₀) = X - S₀ + c₀

Profit when S_T ≤X = S_T - (S₀ - c₀) = S_T - S₀ + c₀

Since the X is always greater than S₀, the maximum profit possible from the position = X - S₀ + c₀ (this profit will occur when the stock price ends up at a value greater than or equal to the strike price)

The maximum loss will be when the underlying falls to zero. The maximum loss = S₀ - c₀ (because if the underlying falls to zero then our stock position will be worthless and we will lose all the money paid for it, and the call option will expire worthlessly and we will gain all the premium)

Since we receive some premium for selling the call option, the breakeven price will be the price when that premium is equal to the loss in the underlying position. If the underlying falls by an amount equal to the premium received for selling the call option, that price will be the breakeven price.

Therefore, breakeven price = S₀ - c₀

Please note that the breakeven price and the maximum loss are identical. As the stock starts falling beyond the breakeven price, we will start incurring the loss in the covered call position and the loss will maximize when it falls to the zero.

Risk management by covered call position: The short call position is very risky if it is seen separately. However, with the combination of the underlying, it reduces the risk.  Thus, any investor who holds a stock cannot be called too conservative when he is selling the call option on the stock.

The strategy not only reduces the risk but also reduces the expected return as compared with the standalone long position in the underlying. The investor can miss a lot of upside potential in the bull markets. However, the investor stands to gain premiums in the bear markets as the losses on the underlying will be reduced by that premium amount.

It looks like that the strategy has lots of opportunity loss with a very small amount to be gained as a premium. But we are missing the probabilities here. The probability that we end up earning the premium during a given period is much higher than the probability of taking a large opportunity loss. That's where the shrewd investors or portfolio managers can take advantage of this strategy and can earn an excess return on their portfolio. The strategy works best when the market is not expected to be bullish and it is expected to have a low volatility.

Graphical interpretation: The covered call position is S₀ - c₀. From the put-call parity equation, we know that

S₀ - c₀ = X(1+r)^-T - p₀

But since the factor X(1+r)^-T will remain the constant regardless of the underlying movement, we can say that graphically S₀ - c₀ is equivalent to a short position in the put option. So, its graph will be identical to the graph of the short put position.

Graph:

Protective put strategy: This strategy also provides protection in the underlying position. However, it is totally opposite of the covered call position as in this strategy; the upside potential is unlimited and downside potential is limited.

This strategy is the combination of a long underlying position with the long put position. The put option is bought at a strike lower than the spot price at the initiation of the strategy. In this strategy, we pay for the both - the stock position and the long put position. If the stock falls below the exercise price at maturity, then the payoff will be equal to the exercise price of the option because whatever we are going to lose is the long underlying position will be covered by the long put position. So, it can be viewed as a kind of insurance contract where we pay a premium amount to get rid of the risk.

The value of the strategy at the expiration is equal to the value of long stock position plus the value of long put position.

 V_T = S_T + Max(0, X - S_T)

If S_T ≥X, then V_T = S_T + 0 = S_T

If S_T <X, then V_T = S_T + X - S_T = X

The profit from the strategy at the expiration will be equal to the value of the strategy at the expiration minus the amount paid for the strategy at the initiation of the contract (spot price at time 0 and put premium paid at time 0, S₀ + p₀)

Profit when S_T ≥X, then ∏ = S_T - S₀ - p₀

Profit when S_T <X, then ∏ = X - S₀ - p₀

The maximum profit of the strategy will occur when the underlying reaches infinity. Hence, the maximum profit is unlimited.

The maximum loss of the strategy will occur when the underlying falls to any level at or below the exercise price of the put option. In that scenario, the final payoff will be equal to X and the maximum loss will be equal to S₀ + p₀ - X.

The breakeven price will be the price where we would be able to recover the put premium paid for the put position. So, the underlying price should increase by the premium paid for the put option for the breakeven. Therefore, the breakeven price = S₀ + p₀.

Risk management by protective put position: This strategy acts as an insurance against the fall in the underlying price during the contract period.

Just like insurance costs a premium amount, this strategy also costs a premium. So, we need to pay some premium to get the downside protection and to keep the upside potential. So, it decreases the upside potential by the premium amount paid. So, the strategy generally works best when there is a lot of volatility expected in the underlying due to some event such as election result, corporate result or FED rate announcement meetings. Otherwise, most of the times, the investors will end up losing the premium amount and that will reduce his overall return.

Graphical interpretation: The protective put position is S₀ + p₀. From the put-call parity equation, we know that

c₀ + X(1+r)^-T = S₀ + p₀

But since the factor X(1+r)^-T will remain the constant regardless of the underlying movement, we can say that graphically S₀ + p₀  is equivalent to a long position in the call option. So, its payoff graph will be identical to the payoff graph of a long call position.

Graph:

Check your concepts:

(59.5) What is the profit of a covered call position at expiration if the spot price at expiration is $32.00? The position was initiated at a spot price of $30.50. The call option sold had a premium of $1.30 and an exercise price of $32.50.

(a) $0.80
(b) $1.80
(c) $2.80

(59.6) The breakeven price for a covered call position is $97. The call premium received for the selling the call option is $3. The exercise price of the call position is $105. What is the total profit/loss in the position if the stock price falls to $89 at expiration?

(a) Loss of $5
(b) Loss of $8
(c) Loss of $13

(59.7) James bought a stock for $25 and a put option for the exercise price of $22 at a price of $1. The stock price at the expiration moves to $29. What is the breakeven price of the protective put position?

(a) $24
(b) $26
(c) $28

(59.8) The graph of a protective put position is identical to the graph of a:

(a) Short position in underlying
(b) Short position in call option
(c) Long position in call option

Solutions:

(59.5) Correct Answer is C: The covered call position is a combination of two positions - long underlying and short call option. We can calculate the separate profit for each position and then add those up to get the profit of the covered call position. Profit in the long underlying position = 32.00 - 30.50 = $1.50. The profit in the short call position = $1.30 (because the option expired worthless at the expiry). Therefore, total profit = 1.50 + 1.30 = $2.80

(59.6) Correct Answer is B: The breakeven price for a covered call position equals the spot price at the initiation minus the call premium. Therefore, the spot price at the initiation = Breakeven price + Call premium = 97 + 3 = $100. Now, the loss in the underlying = 100 - 89 =$11. Profit in the short call option position = $3 (as the option expired worthless at expiration). Therefore, total loss = 11 - 3 = $8.

(59.7) Correct Answer is B: The breakeven price for a protective put position is equal to the underlying price at the initiation of the contract plus the put premium. Therefore, breakeven price = 25 + 1 =$26.

(59.8) Correct Answer is C: The graph of the protective put position is identical to the graph of a long call position. We can deduce this result from the put-call parity equation.

Previous LOS: Call option and put option strategies

Risk Management Applications of Option Strategies: Chapter Test