Question about calculating ratio of Relative Difference

[Aston08]

I was hoping someone might be able to help sort out where I am going wrong in my calculation of the ratio of relative difference.

Value1= .0759
Value2= .0544

SqRt(.0759 / .0544) = 1.181195


The above calculation seems to work, but in a situation like below where the values are reversed the calculation is missing something.

SqRt(.0544/ .0759 ) = 0.846600



The reason I say this is if I utilize the ratio to split $5,000 there is an overage

$5,000 / 2 = $2,500
$2,500 * 1.181195 = $2,952.98

&

$5,000 / 2 = $2,500
$2,500 * 0.846600 = $2,116.50

$2,952.98 + $2,116.50 = $5,069.48 ... $69.48 too much



Any idea where I messed things up ?

 

[mathman]

1.181195 + 0.846600 = 2.027795, not 2.

I am not sure what you intend by using the square root of the ratio. However it doesn't seem to make sense in what you are doing.

 

[Aston08]

Haha yea I have something wrong... I just am not quite sure where.

I am trying to calculate a delta neutral position. Most of the time the size of these positions are based on a number of shares someone is trying to hedge and the cost is whatever it ends up being to create the hedge. I am trying to calculate it the other way around, assuming I want to buy $5k worth of calls and puts based on the delta and price of each, how many do I need to purchase to stay delta neutral and as close to $5k as possible.

Basic Delta Neutral Calculation
0.5 (call option delta) - 0.5 (put option delta) = 0 Delta


Assuming I was buying a $5k combination of the following:

Call Contract
Price - $.59 each
Delta - .0759

Put Contract
Price - $.60 each
Delta - .0544

..Contracts are in multiples of 100

My thought process was that if I could determine the relative difference between the 2 delta's I could determine how much of the $5k needed to be allocated to each. But I am missing something it seems. I can get things to balance out with the first set of values, but, when I put in a second set of values like below things didn't balance as effectively.


2nd Set of Values
Call Contract
Price - $.85 each
Delta - .1207

Put Contract
Price - $1.30 each
Delta - .1419

I have attached a copy of my basic worksheet

 

[mathman]

It looks like you are trying to have no. calls x call delta as close as possible to no. puts x put delta.

Therefore the ratio call/put should be approximately = delta put / delta call.
Your other equation is no. puts x put price + no. calls x call price = money available.

 

[CellCoree]

First of all, it is important to clarify that the ratio of relative difference is typically calculated as the absolute difference between two values divided by the average of those two values. It is not clear from your question if this is the method you are using.

Assuming that you are using the correct method, it appears that the issue lies in your understanding of how the ratio of relative difference should be applied in your calculation. In your example, you are using the calculated ratio as a multiplier for the individual values, but this is not the correct way to use the ratio of relative difference.

Instead, the ratio of relative difference should be used to adjust the overall amount being split. For example, in your first calculation, the ratio of relative difference is 1.181195, which means that the total amount should be divided by 1.181195 before being split into two equal parts. This would result in each part being $2,500 / 1.181195 = $2,118.79, which is closer to the expected value of $2,116.50.

In summary, it seems that your calculation method is correct, but you are not applying the ratio of relative difference correctly in your example. I would suggest reviewing the concept and ensuring that you are using it in the correct context in your calculations.