Delta of a Covered Call and Protective Put Position

Investors frequently seek to modify their investment positions for various reasons, such as securing profits, generating income, or taking advantage of potential stock price declines. As time progresses, investment strategies tend to become more dynamic. Monitoring overall risk exposure can be achieved by utilizing option and portfolio delta to assess the impact of changes in stock prices on the overall portfolio.

Option Delta

Options delta represents the expected change in the option’s price for a $1.00 move in the underlying stock.

• Call options have a positive delta ranging from 0 to 1, indicating that their prices increase in value as the underlying stock price rises.
• Put options have a negative delta between 0 and -1, indicating an inverse relationship with the underlying stock price.

This means call prices gain in value, up to a pace of dollar for dollar, as the underlying stock position increases. Puts, on the other hand, have an inverse relationship to price. The price of the put decreases as the underlying stock price increases. Position delta can be summarized as follows:

$$ \textbf{Delta} =\frac {\text{Change in Price of Option}}{\text{Change in Price of Stock}} $$

Portfolio Deltas

Based on our observations, the delta of put and call options can range from -1 to +1. Notably, options with strike prices matching the current stock price generally exhibit deltas around 0.5. This means a call option would increase by $0.5 for every $1.00 increase in the stock price. On the other hand, a put option would decrease by the same amount for an equal change in the stock price.

Finally, we can also assign delta values to the underlying positions themselves. We can calculate the total portfolio or position delta by determining the underlying delta and combining it with the delta of the options positions. Long stock has a delta of 1.00, meaning it moves in sync with itself. On the other hand, short stock has a negative delta of 1.00, indicating it moves in the opposite direction of the underlying stock. A forward or futures contract will have the same delta as the underlying positions if it covers the same number of shares as the option contract. For instance, since most options are sold in round lots of 100 shares, the position will have a delta of 100. An investor could short 50 shares of futures contracts to minimize delta exposure without eliminating it. By offsetting the 100 and 50, the total position delta becomes 50.

The Bottom Line

Portfolios with the same delta share the same risk exposure to price direction. To illustrate, consider an investor with a stock position carrying a delta of 100 and a protective put with a delta of -50. This risk exposure is equivalent to an investor who bought a call option with a delta 50. Given that delta is positive, both positions indicate a bullish stance.

$$ (100 \text{ shares} \times 1.0 \text{ Delta}) – 50 \text{ put option delta} = 50 \text{ call option delta} $$

These two positions will both $0.50 for every $1.00 stock appreciation.

Question

An investor who has a position being short 100 shares of Tresla Motors Corporation and wants to hedge risk exposure in half would most likely?

1. Buy a call with a delta of 50.
2. Sell a call with a delta of 50.
3. Buy 100 shares of Tresla in the open market.

Solution

The correct answer is A.

To hedge a short position, an investor can use a put option. The current portfolio delta of the short Tresla shares is -100 because short shares have a negative delta. To reduce half of the risk exposure, the investor would need to increase the position delta by +50. This can be achieved by buying a put option with a delta of 50. Buying the put would result in a new position delta of -100 + 50 = -50, effectively hedging half of the risk exposure.

B is incorrect: Selling a call would reduce the position delta to-100 + -(50) = -150.

C is incorrect: Buying 100 shares would reduce the position’s delta to 0, implying that it will be completely hedged.

Derivatives and Risk Management: Learning Module 1: Options Strategies; Los 1(d) Compare the delta of covered call and protective put positions with the position of being long an asset and short a forward on the underlying asset