In this post, I’ll be going over how to use Lambda when determining hedges for your positions.
Introduction to Lambda Hedging with Options
Why do we care about Hedging?
Every investor’s strategy should include a plan for how to manage risk. Often this term is called hedging and includes various financial tools to set up. One common means of setting up a portfolio hedge is to use option contracts and with them come many questions. Greek values are utilized to help understand how option price may react to various events in the market but still leave many investors lost and confused.
This is where Lambda comes into play to make our lives a bit easier. Lambda is a lesser known Greek value that most exchanges will not display but is very important when determining leverage. If this seems unfamiliar to you, don’t worry as I’ve previously covered this topic on another post with an introduction to the concept and some example calculations:
How does Lambda help when Hedging?
Lambda gives us what is sometimes referred to as the elasticity factor of a stock option. It tells us for each percent gain observed in the underlying stock, what percent gain we should observe in the given options contract. For example, if a call option for XYZ stock had a Lambda value of 2, and XYZ market price went up 5%, then the call option with Lambda of 2 should have risen 10%.
When picking options, Lambda should be one of the main things we consider as it helps explicitly describe the price-movement relationship between option contract and underlying stock. If I do not wish to buy stock directly, I may choose to undergo a stock substitution strategy and use long term LEAP call options instead with Lambda values greater than 1 to achieve greater capital efficiency. Lambda, when used with the other Greek values, helps clear up some of the mystery surrounding options.
Option Exposure and Leverage Risks
Most stock replacement strategies have you buy long term LEAP options as a replacement for (or in addition to) the underlying to help leverage your returns. Because the Lambda value is greater than 1, your market exposure to the movements in the underlying stock is greater than just owning the stock outright. This is good when the stock price increases, but may lead to trouble if the price falls. In addition to price movements, stock options are affected additionally by both time and volatility as well so these factors must also be taken into account. Given all these risks and variables, it is easy to see why people will tend to avoid options and call them too risky.
Setting up your Lambda Hedge with Puts
We will be taking a deeper look into how we can use them to reduce instead of compounding risk. In our case we will not be averaging down on our call options if price falls but instead will be applying protective puts as hedges.
Our long LEAP Calls:
The Put used as our hedge:
As you can see, the contracts being selected are both several months out in expiration. They will therefore cost more money since there’s more time value left, but the impact of theta and time decay is minimized giving ample time to manage your plays.
Calculations
Lambda
The Call option strike is chosen deep in the money with a higher delta value of: 0.7513 since we are using them as stock replacements. The put is chosen with a slightly in the money strike with a -0.5014 delta value. The Call options cost $64.13 per contract while the Put options cost $17.74. The underlying stock SPY costs $346.21 per share.
This gives the Call options a lambda value of:
0.7513 * $346.21 / $64.13 = 4.056
and the Put options a lambda value of:
-0.5014 * $346.21 / $17.74 = -9.785
Delta Notional
Now that we have the lambda values of these contracts, we can calculate the delta notional values by multiplying by the 100 times the contract price to see the dollar exposure given by each contract.
For the call options we see a delta notional value of:
4.056 * $64.13 * 100 = $26,011.13
For the put options we see a delta notional value of:
-9.785 * $17.74 * 100 = -$17,358.59
Explanation
This means that for each call option we buy for $6413 gives us a dollar exposure equivalent of $26,011.13 while each put purchased for $1774 provides a dollar exposure equivalent of -$17,358.59. When building our positions, we can use these numbers to gain the appropriate amount of exposure desired by either adding exposure through call options or by reducing it through put options. We can fully control how bullish or bearish we want to be using ratios of the two different assets as well as other strikes and expirations. In times of uncertainty, both can be applied evenly to give a delta neutral position that stays relatively constant in value regardless of price direction.
Conclusion
Lambda when used with the other greeks gives insight into how much leverage or hedge one is being exposed to when buying an options contract. Using Lambda to calculate your delta notional can give an exact exposure amount to let you know how bullish or bearish your positions are and provides a means to balance out risk by neutralizing said value. When investing, make sure you have taken things like Lambda and Delta notional into account to make sure you are not taking on more risk than you can handle. When used properly, these techniques will help safeguard you against potential losses. As always feel free to reach out with questions.
