# hedge portfolio for puts, why two different formulas?

This really irritated me… Between R49 EOC #3c and EOC#5b they calculate the hedge ratio differently for puts… Im confused about which one to use and when/why??

n=p-(-)p+/S+(-)S-

n=p+(-)p-/S+(-)S-

I think the issue here is the difference between replicating a loan and a risk free hedge… can someone spell this out?

with calls is its always c+ (-) c-?

Tickersu, I don’t understand this part of your answer. I was thinking that the numerator is (P-) - (P+) because puts increase in value when stock prices decline, so I need to subtract P+, otherwise I’d have a negative hedge ratio… What do you mean by having a negative hede ratio and buy both or sell both?

BTW, thanks for taking the time to reply to so many of our questions, particulary regarding Quant. You’ve been a tremendous help to all of us.

What I think he is saying is a stock prices go up, calls go up, but puts go down. Therefore inversely related. what confuse me is why this is called an arbitrage opportunity because there is no way we can lock values of the stock in. A new ceo can come in tomorrow and the stock could perform completely different than expected

if you refer to the actual solution to EOC 5b and EOC 3c you will see what the discrepency is

the formulas are not mathematically equivalent in the case that both p(down) and p(up) have a value different from zero

I just looked at the solutions that you mentioned, and I’m still seeing this: the absolute value of the answer will be the same, irrespective of whether p(down) and p(up) are non-zero.

Assume that

S(u) = 20 S(d)=5 , so our denominator is 15

if we say p(down) - p (up) divided by 15, we get the same magnitude answer as p(up) - p (down) divided by 15…

It’s no different than saying 3-8= -5 or 8 - 3 = +5… the magnitude is identical, it doesn’t matter if one or both are non-zero values

I’m saying that the value of a put is inversely related to movements in the underlying’s price (the stock).

The call value is positively related to movements in the stock’s price.