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para
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Joined: August 19th, 2022, 3:12 am

Which is more Appropriate to calculate Leverage with Options ?

August 19th, 2022, 3:20 am

Below are 2 Methods for calculating the Leverage of a Option Contract with examples. The first method is the standard method i have seen. the second method is what intuitively i would use in calcuating leverage.

Method 1

It seems like the more referred way online to calculate Leverage for a Option Contract is to use the formula below,

Leverage = (Delta x Underlying Stock Price) / Option Premium Price

Example : Stock Price = $ 10 per share

Strike Price = $ 10 per share

Delta = 0.6

Now the following is using standard leverage formula,

Assuming the same details, lets add that the Delta = 0.6,

Leverage = (Delta x Underlying Stock Price) / Option Premium Price

Leverage = ( 0.6 x 10pershare)/ 1 option premium price

Leverage = 6 Leverage = 6 to 1

The conlusion is that this option contract provides a 6 to 1 Leverage.

Method 2

The way I would intuitively calculate the leverage of the option contract is like the formula below,

Leverage = (Notional Value of Option Contract - Premium Price Cost) / Option Premium Price Cost Paid

For the same scenario,

Notional Value = 5000WorthofUnderlyingStockShares( 10 per share x 500 Shares)

Option Premium Cost Paid = 500( 1 per option contract x 500 Shares )

Leverage = ( 5,000− 500) / 500 Leverage = 9 Leverage = 9 to 1

In this method of calculating the leverage, it is actually showing you the amount that you are being leveraged, because it places the Notional Value of the Option Contract($ 5,000) in the numerator in the formula. The Notional Value of the Option Contract, is the value of the Stocks Shares you control with the option with the option contract. This Notional Value of Stock shares is much more Bigger in value than the premium you paid. In other words, just for easy words sake, i will pu tit like htis, The Notional Value is the amount your being lent or how much your borrowing, so to speak. This is the total value your being leveraged. to get the exact leverage, the premium cost is subtracted from the Notional Value.

Now my questions :

1.) As explained in Method 1, i do not see the reason of using the theoritical underyling potential profit gain from underlying stock that does not control same amount of shares as an option contract. refer to method 1 for my reasoning. Why is it being used, when it underestimates levereage by great amounts ?

2.) Delta can change during the option contract timeframe, so when you enter in the contract, if you used the Leverage formula that uses Delta, could your Leverage Value that you calculated when you entered the contract be inaccurate because your detla value could be totally different at later time frame in the Option Contract ?

3.) For Method 2, the method i used with Notional Value to calculate leverage, is this way of calcuating leverage only approriate if youre assuming you will hold option contract until expiration ?

4.) Which method is more accurate, Method 1 calcualting Leverage with Delta, or Method 2 Calculating Leverage with Notional Value and Premium Cost ?

5.) I plan on creating and using synthetic option strategies that would hold the option contracts near or at expiration dates. Which Method is more accurate for Calcualting Leverage before entering and buying an Option Contract ?
 
Mercadian
Posts: 39
Joined: July 24th, 2020, 4:22 pm

Re: Which is more Appropriate to calculate Leverage with Options ?

August 19th, 2022, 2:00 pm

Hey Para,

I think here you need to consider the fact that this is a contingent claim/contract i.e. there is uncertainty involved, so based on that you could compute the Leverage in both ways... however I will slightly challenge your option 2 approach.

option 1. is a Leverage value which is Probability Adjusted i.e. how likely it is to be actually materialized
option 2. is a Leverage value which represents the max leverage or boundary attainable by the position**

** I think there might be a slight error in your logic here, as I see you are substracting the Paid Premium Value (500) from the Option Notional (5000) in your numerator, keep in mind that the 500 does not go towards the final purchase of the stock (does not reduce the amount to be paid) hence if anything you should not substract but rather keep it or actually add it on top of the notional.

You need to consider also if you're using the Strike Price or the Market Spot price for the underlying, in your case I think you might be more interested in the Strike.

Another way to compute this would be as a gearing ratio = derivative price / underlying price which in your example is 1/10.

Rgds,
M
 
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bearish
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Joined: February 3rd, 2011, 2:19 pm

Re: Which is more Appropriate to calculate Leverage with Options ?

August 19th, 2022, 4:09 pm

If you put up $x and borrow $y to purchase $(x+y) worth of stock, I think we will say that your leverage on this position is (x+y)/x. Likewise, if you put up $p to pay the premium on a call with a delta of d on a stock with a current market price of $s, then your exposure will locally be the same, and so it makes sense to define your leverage as d*s/p. In both cases you can mark your leverage to market.
 
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para
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Joined: August 19th, 2022, 3:12 am

Re: Which is more Appropriate to calculate Leverage with Options ?

August 20th, 2022, 4:58 pm

Mercadian, 

Thanks, yes i see that 500 should not be there. the 500 is the cost of the Premium Paid for the option. I made the error there, the 500 should be subtracted when considering when closing the option position from a Profit/Loss. I would edit and delete that varible in the formula above, and take out the 500, but it will not let me edit the post here.

So essentially, if i was calculating the Leverage for a Option that had a more short term strategy and considering closing the position before expiration, Method 1- by calculating with Delta is more appropriate, but if considering more Long Term strategy and excercising the Option near or at Expiration, Method 2 - by calculating with the Notional Value is more appropriate. Do you agree with this notion ?
 
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para
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Joined: August 19th, 2022, 3:12 am

Re: Which is more Appropriate to calculate Leverage with Options ?

August 20th, 2022, 5:00 pm

Bearish, 

What do you mean by the "Exposure will be Locally the Same" ?
 
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bearish
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Joined: February 3rd, 2011, 2:19 pm

Re: Which is more Appropriate to calculate Leverage with Options ?

August 20th, 2022, 10:42 pm

I mean that your P/L from a small stock price move relative to the net value of your position will be the same in the two cases.
 
Mercadian
Posts: 39
Joined: July 24th, 2020, 4:22 pm

Re: Which is more Appropriate to calculate Leverage with Options ?

August 25th, 2022, 2:32 am

Para,

For me there is no right or wrong answer, its a matter of appetite in terms of risk management and capital efficiency.

You can go with option 1 and have a leaner capital structure (less leverage = less capital aside) or you can go with option 2 and have a heavier capital structure (more leverage = more capital aside). 

For a sell-side institution it might be ok to consider the max loss for a certain segment of clients thus using option 2 because they really don't have access to many other pricing sources while use option 1 for the more sophisticated ones, of course it can be much more nuanced than this but just as an example of how they can both co-exist.

Rgds,
M