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.