Hedge Ratio

[dailygrind]

Im having trouble wrapping this around my head. Example…given a current stock price (not call or put price), how do you figure out whether you need to be in a short or long position in call options and the underlying stock?
This is referring to CFAI EOC Reading 50 question 3 and 4.
Please help, thanks guys.

 

[cleverCFA]

Just think of it in terms of delta, I think it makes this concept easier to understand.
The delta of a stock is always 1. The delta of a call is always positive, the delta of a put is always negative.
Now, you will probably be given your delta value for the call/put options, say it’s 0.6 delta for the call option, and -0.3 for the put.
Having a hedged portfolio (delta only) means that you are delta neutral (i.e. you have no delta exposore, your delta position sums to 0).
Now just add up you deltas and solve for what you are trying to solve for (i.e. how many calls or how many puts or how many underlying)
So as an example
1) if you are given that you are long 100 calls, how many underlying do you need to hedge porfolio:
simply solve this equation 100 * 0.6 + x * 1 = 0
this is the 100 calls times their delta plus x amount of stock with a 1 delta equal to zero delta (i.e. delta neutral).
2) If you are short 100 puts
-100 * -0.3 + x * 1 = 0
again, just solve for x
3) you are long 100 shares, how many calls do you need to hedge
x * 0.6 + 100 * 1 = 0
again solve for x to tell you how many calls
4) you are long 100 calls, how many puts do you need to hedge
100 * 0.6 + x * -0.3 = 0
sove for x to figure out how many puts you need

 

[kc123]

The delta for call is positive, so to hedge one exposure you have to do the opposite with the hedging instrument i.e. if you are long on call, you will need to short stock to be delta neutral and vice versa. For puts, the delta is -ve so the stock and put together make a natural hedging instrument. Hope that helps..

 

[mpearc4]

The above explanations are correct. But it’s really simpler than that. Just think about what exactly a call/put does and your position in the underlying and you’re fine. You know that a person long a call will benefit when the underlying increases in value. So if you’re already long the underlying (meaning you benefit when it increases in value), you need something that benefits you when the underlying LOSES value. So short the call. Similarly, you could go long a put.
For hedging purposes, if you’re long the stock, you’ll always need to short a call or long a put to offset your exposure.

 

[dailygrind]

Thanks guys

 

[kjames05]

if it helps you in any way, I just remember that whatever position I have in the call I need the opposite position in the stock, or if I have a put I need the same position in the stock.

 

[kobi]

kjames05 wrote:
if it helps you in any way, I just remember that whatever position I have in the call I need the opposite position in the stock, or if I have a put I need the same position in the stock.

this one works best!

 

[S2000magician]

kjames05 wrote:if it helps you in any way, I just remember that whatever position I have in the call I need the opposite position in the stock, or if I have a put I need the same position in the stock.

A long position in a call is like a long position in the underlying (without the downside).
A long position in a put is like a short position in the underlying (without the downside).
You hedge a long position in the underlying with a short position in the underlying, and vice-versa.