Understanding Delta: a key guide for Investors and Traders - part 2 Understanding Delta: a key guide for Investors and Traders - part 2 Understanding Delta: a key guide for Investors and Traders - part 2

Understanding Delta: a key guide for Investors and Traders - part 2

Equities 10 minutes to read
Koen Hoorelbeke

Options Strategist

Summary:  Explore the advanced applications, real-world examples, and limitations of Delta in the final part of the comprehensive Delta guide, equipping investors and traders with the insights needed to navigate the complex world of options trading.

Understanding Delta: a key guide for Investors and Traders - part 2

Thank you for joining us in the second part of our "Understanding Delta: a key guide for Investors and Traders". Here, we'll continue our exploration of the multifaceted applications and nuances of this essential concept in options trading.

In the first part we discussed the very essence of Delta: it's definition (chapter 1), the ranges (chapter 2), it's moneyness (chapter 3) and relation to probability (chapter 4).

In this second part we'll be focusing on more advanced topics.


Chapter 5: Delta Hedging

Delta hedging is a strategy used by traders to reduce the risk associated with the price movements of an underlying asset. By creating a portfolio that is 'delta neutral', traders can attempt to offset the impact of price changes in the underlying asset on the overall value of the portfolio.

The basic idea behind delta hedging is to create a portfolio where the combined delta of the assets is zero. This is achieved by taking a position in the underlying asset that is opposite to the delta of the options. For example, if you have a long call option with a delta of 0.6, you could hedge this position by shorting 60 shares of the underlying stock. This would create a delta neutral position, as the delta of the short stock position (-0.6) would offset the delta of the long call option (+0.6).

Delta hedging is often used by options market makers and institutional traders to manage risk. But also advanced retail options traders/investors use this technique/strategy, to keep a neutral balance in their portfolio. However, it's important to note that maintaining a delta neutral position requires frequent rebalancing of the portfolio, as the delta of an option changes with the price and volatility of the underlying asset, as well as with time.

In the next chapter, we'll explore how delta can be used in portfolio management, including how to calculate the overall delta of a portfolio of options and the underlying asset.

Chapter 6: Delta and Portfolio Management

Delta is not only useful for individual option contracts but also plays a crucial role in managing a portfolio of options and underlying assets. By understanding the concept of delta, investors and traders can gauge the overall risk exposure of their portfolio to movements in the underlying asset's price.

Let's consider an example. Suppose you own 100 shares of a stock, which means you have a position of +100 delta because each share of stock has a delta of +1. Now, let's say you also own 2 put options on the same stock, each with a delta of -0.5. However, remember that each option contract represents 100 shares. So, the total delta for the options is -100 (because -0.5 * 2 * 100 = -100).

When you add the delta of the stock position (+100) to the delta of the option position (-100), the overall portfolio delta is 0. This means that for every $1 increase in the stock's price, the value of the portfolio would remain unchanged, because the gain in the stock position would be offset by the loss in the option position.

This is a simplified example, but it illustrates how delta can be used to manage risk and create a balanced portfolio. By adjusting the number and type of option contracts in a portfolio, an investor or trader can manipulate the portfolio's overall delta to achieve a desired level of exposure to the underlying asset's price movements.

Chapter 7: Delta Neutral Strategies

Delta neutral strategies are a type of options trading strategy that aims to achieve a total delta of zero. This is done by combining positions with positive and negative deltas so that the overall delta of the assets in question totals zero.

In a delta neutral strategy, the trader creates a scenario in which the delta of the options and the underlying assets offset each other. This results in a position where small changes in the underlying asset's price do not affect the overall value of the position.

For example, let's say a trader owns 100 shares of a certain stock. The delta of this position is +100, as owning a stock has a delta of 1 per share. Now, the trader could open a position in options contracts with a total delta of -100. This could be achieved by buying 2 put options contracts with a delta of -0.5 each (remember, each options contract represents 100 shares).

By doing this, the trader has created a delta neutral position. This means that if the price of the underlying stock increases or decreases by a small amount, the change in value of the stock position will be offset by the change in value of the options position.

Delta neutral strategies are often used in hedging, where the aim is to reduce risk, rather than to achieve high returns. However, they are also used in premium selling strategies. In this case, a trader might sell options to collect the premium (the price of the option) and then hedge the delta risk by taking positions in the underlying asset to achieve a delta neutral portfolio. This way, the trader is not betting on the direction of the market, but rather on the time decay of the options. As options approach their expiration date, they lose value - a phenomenon known as time decay, or theta decay. This decay can provide profits for the premium seller, as long as the underlying asset's price doesn't move in an unfavorable direction too much, hence the need for delta neutrality.

These strategies can be complex and require a good understanding of options and their greeks, but they can provide a way to manage risk effectively in volatile markets.

Chapter 8: Delta and Time

As an option approaches its expiration date, its delta can change significantly. This is due to the effect of time decay, or theta, which is another of the "Greeks" used in options pricing. As time passes, the value of an option decreases, which can cause a change in delta.

For out-of-the-money options (options where the strike price is not favorable compared to the current price of the underlying asset), the delta will approach zero as the option nears expiration. This is because the probability of the option becoming in-the-money (profitable) is decreasing.

Conversely, for in-the-money options (where the strike price is favorable compared to the current price of the underlying asset), the delta will approach 1 for call options and -1 for put options as expiration nears. This is because the likelihood of the option remaining in-the-money is increasing.

At-the-money options (where the strike price is very close to the current price of the underlying asset) have deltas close to 0.5 for calls and -0.5 for puts. As expiration approaches, the delta of an at-the-money call option will either increase towards 1 or decrease towards 0, and the delta of an at-the-money put option will either decrease towards -1 or increase towards 0, depending on the movement of the underlying asset's price.

It's important to note that while delta can give an indication of an option's likelihood of ending up in-the-money at expiration, it's not a definitive probability measure. Other factors, such as implied volatility, can also impact an option's price and the likelihood of it being profitable at expiration.

In summary, time has a significant impact on delta. As an option's expiration date approaches, the delta can change rapidly, especially for at-the-money options. This is an important consideration for options traders, particularly those who hold positions over a longer period of time.

Chapter 9: Real World Examples

Let's look at some real-world examples to better understand how delta is used in options trading.

Example 1: Delta in Options Buying

Suppose an investor is bullish on stock Ahold (AD:xams), which is currently trading at €30.70. The investor decides to buy a call option with a strike price of €31 that expires in approx. 1 month. He can buy the option for €0.58 (bullet 1 in screenshot below) The delta of this call option is 0.41 (bullet 2 in screenshot below).

This means that if stock AD:xams increases by €1 to €31.70, the price of the call option will increase by approximately 41% of that €1, or €0.41. So, if the option was initially worth €0.58 (bullet 1 in screenshot above), it will now be worth approximately €0.99 (0.58 + 0.41).

Example 2: Delta in Options Selling

Now, let's consider a trader who believes that the AEX-index is not going to move much in price. The trader decides to sell a put option on AEX with a strike price of $769 (1) for €0.64 (2) and a delta of -0.33 (3).
If the trader is correct and the stock price remains stable, the put option will decrease in value due to time decay, allowing the trader to buy it back at a lower price for a profit. However, if the stock price does decrease by $1, the value of the put option will increase by approximately 33% of that €1, or €0.33. This would result in a loss for the trader, as this would mean that the price of the option will go from €0.64 to €0.97. Which would mean the trader would need to buy the option back at a higher price than he sold it.

Example 3: Delta in Delta-Neutral Strategies

Consider a hedge fund that has a large position in stock NVDA. To protect against downside risk, the fund buys put options on NVDA. The fund chooses the number of options to purchase based on the delta of the options and the number of shares it owns in order to create a delta-neutral position.

For instance, if the fund owns 10135 shares of NVDA as in the example below (1) and the delta of the put options is -0.4938 (2), the fund would need to buy 205 (3) put options (representing 20,500 shares) to hedge its position. Why 205 contracts? Divide 10135 by 0.4938 and you'll get at 20524.50. Divide this by 100 (the number of shares per options-contract for NVDA) and the number of contracts is 205. This way, if the stock price decreases with $1, the loss on the stock position would be offset by the gain on the options position. Since the put option has a delta of -0.4938, multiplied by 205 (contracts) * 100 (shares per contract), would result in a profit of $10122.9.

1 dollar loss on the shares, would result in a loss of $10135,- but would be (almost) negated by the profit of $10122.9 on the put options.
These examples illustrate how understanding and using delta can be beneficial in various trading scenarios. Whether you're buying options, selling options, or hedging a position, delta is a crucial concept to understand in options trading.

Chapter 10: Limitations of Delta

While delta is a powerful tool in the options trader's arsenal, it's important to understand its limitations. Here are a few key points to keep in mind:

1. Delta is a Theoretical Estimate: Delta is derived from an options pricing model, such as the Black-Scholes model. These models make certain assumptions, such as a constant volatility and a lognormal distribution of stock prices, which may not hold true in the real world. Therefore, the actual change in an option's price may not always match the change predicted by delta.

2. Delta Changes with the Underlying Price: Delta is not a static value. It changes as the price of the underlying asset changes, a phenomenon known as "gamma." This means that the delta of an option can become more or less sensitive to changes in the price of the underlying asset as the asset's price changes.

3. Delta Assumes Small Price Changes: Delta measures the expected change in an option's price for a small change in the price of the underlying asset. For larger price changes, the relationship between the option's price and the underlying asset's price may not be linear. This non-linearity can make delta less accurate for predicting an option's price change.

4. Delta Does Not Account for Time Decay: While delta measures how an option's price changes with the price of the underlying asset, it does not account for the effect of time decay (theta). As an option approaches its expiration date, its time value decreases, which can affect the option's price regardless of changes in the underlying asset's price.

5. Delta Does Not Account for Changes in Volatility: Delta does not factor in changes in the volatility of the underlying asset. An increase in volatility can increase the price of an option, while a decrease in volatility can decrease the price of an option, regardless of changes in the price of the underlying asset. This effect is captured by another Greek, vega.

In conclusion, while delta is a useful tool for options traders, it should be used in conjunction with other tools and metrics to make informed trading decisions. Understanding the limitations of delta can help traders use it more effectively and avoid potential pitfalls.

Summary and Conclusion

In this guide, we explored the concept of Delta, one of the key "Greeks" in options trading. Delta measures the sensitivity of an option's price to changes in the price of the underlying asset. It is a crucial tool for options traders as it helps them understand and quantify their exposure to price changes in the underlying asset.

Understanding Delta is fundamental for any options trader. It provides valuable insights into how an option's price will change with movements in the underlying asset's price, enabling traders to manage risk and make informed decisions. However, like any tool, it should be used wisely and in the context of a well-planned trading strategy.

Options are complex, high-risk products and require knowledge, investment experience and, in many applications, high risk acceptance. We recommend that before you invest in options, you inform yourself well about the operation and risks. In Saxo Bank's Terms of Use you will find more information on this in the Important Information Options, Futures, Margin and Deficit Procedure. You can also consult the Essential Information Document of the option you want to invest in on Saxo Bank's website.

Quarterly Outlook 2024 Q3

Sandcastle economics

01 / 05

  • Macro: Sandcastle economics

    Invest wisely in Q3 2024: Discover SaxoStrats' insights on navigating a stable yet fragile global economy.

    Read article
  • Bonds: What to do until inflation stabilises

    Discover strategies for managing bonds as US and European yields remain rangebound due to uncertain inflation and evolving monetary policies.

    Read article
  • Equities: Are we blowing bubbles again

    Explore key trends and opportunities in European equities and electrification theme as market dynamics echo 2021's rally.

    Read article
  • FX: Risk-on currencies to surge against havens

    Explore the outlook for USD, AUD, NZD, and EM carry trades as risk-on currencies are set to outperform in Q3 2024.

    Read article
  • Commodities: Energy and grains in focus as metals pause

    Energy and grains to shine as metals pause. Discover key trends and market drivers for commodities in Q3 2024.

    Read article


The Saxo Bank Group entities each provide execution-only service and access to Analysis permitting a person to view and/or use content available on or via the website. This content is not intended to and does not change or expand on the execution-only service. Such access and use are at all times subject to (i) The Terms of Use; (ii) Full Disclaimer; (iii) The Risk Warning; (iv) the Rules of Engagement and (v) Notices applying to Saxo News & Research and/or its content in addition (where relevant) to the terms governing the use of hyperlinks on the website of a member of the Saxo Bank Group by which access to Saxo News & Research is gained. Such content is therefore provided as no more than information. In particular no advice is intended to be provided or to be relied on as provided nor endorsed by any Saxo Bank Group entity; nor is it to be construed as solicitation or an incentive provided to subscribe for or sell or purchase any financial instrument. All trading or investments you make must be pursuant to your own unprompted and informed self-directed decision. As such no Saxo Bank Group entity will have or be liable for any losses that you may sustain as a result of any investment decision made in reliance on information which is available on Saxo News & Research or as a result of the use of the Saxo News & Research. Orders given and trades effected are deemed intended to be given or effected for the account of the customer with the Saxo Bank Group entity operating in the jurisdiction in which the customer resides and/or with whom the customer opened and maintains his/her trading account. Saxo News & Research does not contain (and should not be construed as containing) financial, investment, tax or trading advice or advice of any sort offered, recommended or endorsed by Saxo Bank Group and should not be construed as a record of our trading prices, or as an offer, incentive or solicitation for the subscription, sale or purchase in any financial instrument. To the extent that any content is construed as investment research, you must note and accept that the content was not intended to and has not been prepared in accordance with legal requirements designed to promote the independence of investment research and as such, would be considered as a marketing communication under relevant laws.

Please read our disclaimers:
- Notification on Non-Independent Investment Research (https://www.home.saxo/legal/niird/notification)
- Full disclaimer (https://www.home.saxo/en-gb/legal/disclaimer/saxo-disclaimer)

40 Bank Street, 26th floor
E14 5DA
United Kingdom

Contact Saxo

Select region

United Kingdom
United Kingdom

Trade Responsibly
All trading carries risk. To help you understand the risks involved we have put together a series of Key Information Documents (KIDs) highlighting the risks and rewards related to each product. Read more
Additional Key Information Documents are available in our trading platform.

Saxo is a registered Trading Name of Saxo Capital Markets UK Ltd (‘Saxo’). Saxo is authorised and regulated by the Financial Conduct Authority, Firm Reference Number 551422. Registered address: 26th Floor, 40 Bank Street, Canary Wharf, London E14 5DA. Company number 7413871. Registered in England & Wales.

This website, including the information and materials contained in it, are not directed at, or intended for distribution to or use by, any person or entity who is a citizen or resident of or located in the United States, Belgium or any other jurisdiction where such distribution, publication, availability or use would be contrary to applicable law or regulation.

It is important that you understand that with investments, your capital is at risk. Past performance is not a guide to future performance. It is your responsibility to ensure that you make an informed decision about whether or not to invest with us. If you are still unsure if investing is right for you, please seek independent advice. Saxo assumes no liability for any loss sustained from trading in accordance with a recommendation.

Apple, iPad and iPhone are trademarks of Apple Inc., registered in the U.S. and other countries. App Store is a service mark of Apple Inc. Android is a trademark of Google Inc.

©   since 1992