Covered Call

Covered call is one of the simplest and most popular option strategies. It is used to enhance returns from holding an asset (such as a stock) and provide income by writing call options on that asset. This page explains its payoff and risk profile, exposures to different factors like underlying price and volatility, which are measured by the Greeks, and practical trading considerations such as selecting strike and expiration.

Setup

Covered call position has two legs, but only one of them involves options:

Covered vs. Uncovered

The word covered in covered call refers to the fact that the long position in the underlying asset protects against potential losses from the short call position.

A standalone short call (uncovered or naked call) has unlimited potential loss, as there is no theoretical limit on how high underlying price can go.

With a covered call, these potentially infinite losses would be offset with an increase in the underlying position’s value. If the option gets exercised and we (as the writer) get assigned, we can deliver the underlying without having to buy it in the market for the (now high) price.

Covered Call vs. Buy-Write

You may sometimes encounter the term buy-write for this strategy. That can be considered a subtype of covered call.

There are two kinds of covered call strategies:

In the first type, you hold the underlying asset (e.g. a stock) for the long term, perhaps with positive expectations about the long-term prospects of the company. But you may think that in the short term, the stock price is unlikely to increase much, for whatever reason. You don’t expect it to fall and don’t want to sell the stock, but you see the short-term growth potential as limited. You choose to sell (write) a call option to get additional income from the underlying position.

In the second type, sometimes called buy-write, you don’t own the underlying asset first. You only choose to buy it at the same time as selling the call option, as part of the covered call position. In this case, holding the underlying asset is primarily as part of the covered call position, while in the former case the primary motivation is the long-term investment, and selling covered calls is just a byproduct to enhance returns.

That said, there is no need to worry too much about terminology. Just remember that buy-write is the same strategy as covered call, only its specific case when both the underlying and the short call positions are opened at the same time.

Covered Call Payoff

The objective with a covered call position is for the underlying price to stay the same or grow moderately. It should not fall, but we don’t expect it to increase too much either. There are three possible scenarios at the call option expiration:

  1. Underlying price exactly at call strike
  2. Underlying price above call strike
  3. Underlying price below call strike

Scenario 1: Our primary target with a covered call is for the underlying to end up exactly at the short call strike price at expiration. When this happens, the call option expires worthless (we are short, so that is good for us – we don’t get assigned) and the underlying asset (which we are still holding) is worth the strike price. This is the best case and maximum profit from a covered call position.

Scenario 2: If (contrary to our expectations) the underlying does indeed increase a lot and ends up above the call strike, we still make the same, maximum profit. Only this time the call option is in the money, we get assigned and have to deliver the underlying to the call option owner who exercised it. We no longer own the underlying, but receive the strike price amount for it.

Financially, scenarios 1 and 2 are equal. Maximum possible profit from a covered call is:

Max profit = call strike – initial underlying price + call premium received

Scenario 3 is where we can lose money. If underlying ends up below the call strike, the call option expires worthless. We still keep the premium collected when we sold the call. On the call option, we have gained. But we are long the underlying asset, whose price has decreased. Total outcome can be either still profit (if the decrease in underlying price is smaller than the call premium received) or a loss (if it’s bigger).

If underlying ends up below the call strike, profit or loss from the covered call is:

P/L = underlying price at expiration – initial underlying price + call premium received

The worst case scenario and maximum possible loss is when underlying price goes to zero:

Maximum loss = call premium received – initial underlying price

Break-Even Point

The break-even point is the underlying price where our loss from the long underlying position equals the call premium received, so total P/L is zero:

Underlying loss = call premium received

Initial underlying price – B/E underlying price at expiration = call premium received

B/E = initial underlying price – call premium received

Notice two things:

  1. The break-even underlying price is numerically the same as maximum possible loss (just opposite sign if we write loss with minus sign). This makes sense, as maximum loss occurs when underlying price drops to zero.
  2. Unlike many other option strategies, covered call break-even formula does not directly include strike price. Strike selection does affect it, but only indirectly – via the call premium received.

Strike Selection

Which strike you select for the short call will affect both the downside (break-even point and maximum possible loss) and the upside (maximum profit).

The higher strike you select, the smaller the collected premium will be (because higher strike calls are cheaper). Therefore, the break-even point will be higher (when underlying falls, you will start losing money sooner) and maximum possible loss will be greater (because premium received reduces maximum loss). Higher strike means more risk – bad for the downside.

However, higher strike also means higher potential profit. Because covered call maximum profit is:

Max profit = call strike – initial underlying price + call premium received

As you choose higher strikes, the “call strike” part of the maximum profit formula grows, while the “call premium received” decreases. But the decrease in premium received for higher strikes is slower, so the combined maximum profit grows (the difference between premiums of two otherwise identical options with different strikes can’t be greater than the strike difference, otherwise there would be an arbitrage opportunity; therefore the decrease in premium is slower than the increase in strike).

In sum, higher strike means higher break-even point (bad), greater maximum loss (bad) and greater maximum profit (good).

But so far we have only looked at the extremes. Out base scenario with a covered call is that the underlying price remains more or less unchanged. Which strike gets the best result in that case?

The answer is the strike closest to our expected underlying price at expiration. With that, we collect the maximum premium, reducing our break-even point and maximum risk the most, but the option still expires worthless and we keep the entire premium at expiration.

In practice, our strike selection should start from our expected underlying price at the call option’s expiration.

If it is very important to avoid being assigned and avoid possibly losing the long underlying position (which can also be for tax reasons, in some cases), we may want to choose a strike slightly higher for a greater margin of safety.

Expiration Selection

Besides strike, the other decision to make is which expiration to use for the short call.

Because option time value decays fastest (at least for options near the money) in the last days before expiration, if we base our decision solely on maximizing income (premium collected per unit of time), it is best to choose short expiration. In this case, the premium received for each written call will be lower (because it is closer to expiration), but we will write calls more frequently, making total premium income per year higher.

However, the above assumes that the market remains favorable to our position (underlying price stays more or less unchanged – doesn’t fall and doesn’t increase above the call strike).

If underlying price jumps above the call strike and the options expire in the money, we will have to deliver the underlying and can’t write any more covered calls. In such case, it would have been better to write a longer dated call and collect higher premium in the beginning.

Longer expiration not only makes the premium collected for one option write higher, but it also shifts our break-even point lower and reduces downside risk. If underlying price falls sharply, with a longer dated covered call we have collected more premium to offset any losses on the long underlying position. At a new lower underlying price, we won’t be able to write calls at the original strike for the same amount of premium – we will have to either choose a lower strike or accept lower premium.

In sum, there is a trade-off. Shorter expirations make total premium collected per time higher, if all goes well. Longer expirations are more conservative and provide greater margin of safety.

In practice, we must also consider liquidity – the longer the expiration, the less liquid the options usually are. On less liquid underlyings, expirations beyond 3 months are not really a reasonable choice for this reason.

Greeks

Even when you don’t intend to manage or adjust the covered call position before expiration, it is useful to understand how the position reacts to changes in different factors – particularly underlying price, volatility, and passage of time. Sensitivity to these is measured by the Greeks.

Delta

A covered call position always has positive delta. The long underlying position has delta of +1, which is constant. A call option can have delta from 0 to +1, but we are short, so delta of the short call leg is between -1 and 0. Therefore, combined delta (long underlying + short call) is between 0 and +1.

When the call option is deep in the money (underlying price above strike), its delta is close to +1, so short call delta is close to -1, and total covered call delta is close to 0.

When the call option is far out of the money (underlying price below strike), its delta is close to 0 (a small positive number), so short call delta is a small negative number, and total covered call delta is only slightly below +1.

When underlying price is near the call strike, the delta is near the middle of the range: about +0.5. This means that with every $1 increase in underlying price, the long underlying position is worth $1 more, but about half of that is offset by the increase in value of the short call. Value of the combined covered call position increases by 50 cents.

Selection of strike (and expiration) affects initial delta of the position:

Choosing a higher strike means total delta is closer to +1 (the position is more like long underlying, because the delta of the short call is close to zero).

Choosing a lower strike means total delta is closer to zero and the position is less directional, as the high delta of the short call offsets almost all of the underlying delta.

Choosing an at-the-money call makes total delta close to +0.5.

Time to expiration pushes the delta either closer to +0.5 (longer expiration) or away from it and closer to either 0 or +1 (shorted expiration). For example, covered call with out-of-the-money strike expiring in 1 months can have delta +0.9 (because the call delta is very small), while the same strike covered call expiring in 3 months can have delta +0.6 (because the call has more time value and bigger delta). Volatility has a similar effect – higher volatility pushes option delta closer to 0.5.

Gamma, Theta, Vega

All other Greeks are zero for the long underlying position. Therefore, total covered call gamma, theta, and vega are driven solely by the short call part.

Covered call gamma is negative (delta becomes worse for us as underlying price moves in either direction), vega is also negative (higher volatility makes the short call more valuable and our position less so), while theta is positive (as the short call decays with passing time).

Generally, closer to the money, longer time to expiration, or higher volatility increases option time value and makes gamma, vega, and theta more significant. That said, for at-the-money strikes theta can actually increase (time decay accelerates) as the option gets closer to expiration.

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