Hedge ratio: H = nS - c, Rdg 62, EOC 4

Hi, EOC 4 b) says to find the n (hedge ratio) for a stock value (S) of 65, c+ value of 20.86, c- value of 2.68, c value of 12.85, S+ of 78, and S- of 53.95. if you do that math for n with the n formula: n = (20.86 - 2.68)/(78 - 53.95) = .7559 and I have no problem up to now. my issue comes when I try to use the H = nS - c formula. I feel like if you’ve correctly calculated n, you should get an H value of 0, but maybe this is an incorrect assumption. in any case, for this problem; H = nS - c = .7559(65) - 12.85 = 36.84 Again; I was under the impression that the H value should be 0 in a perfectly hedged portfolio, so my question is, if that’s not the case, what does 36.84 represent in this scenario? Is $36.84 just the value of being long .7559 of a share, and being short one option? is it not “supposed” to be something in a perfectly hedged portfolio?

From what I understand, you’re looking for dynamic delta hedging. I don’t have the question in front of me, but here’s my shot at it from the info in your question. 1. Find delta: Cu-Cd / Su-Sd 20.86-2.68 / 78-53.95 = .7559 = delta 2. Find number of calls to short to delta hedge (objective is to get 1:1 value change): 1/.7559 = 1.3229 calls shorted for every share long. The formula you’re presented seems like a method of figuring out how much the total position will cost you per call shorted.

To get to your rationale, it should be change in s and C in the formula.