help with Market making problem...

[MusaAli]

u knw that formula for return on portfolio?

1/2 * S^2 * (volatality)^2 * (1-x^2)h

yeah, so how do u calculate x?

here's a problem:

"Consider the Black‐Scholes framework. A market‐maker, who delta‐hedges, observes the behavior of a hedged portfolio over the course of one week. Last Friday, the market‐maker sold 600 call options, and the following data are available about the stock and the options:
(i) Last Friday, at market close, when the call options were sold, the stock
price was $55.
(ii) The annual volatility of the stock is 25%
(iii) Gamma for the options is 0.019
(iv) This Friday, at market close, the stock price was $53
(v) There are 52 weeks in the year
What was the market maker’s profit or loss on the hedged portfolio?"

solution:

"Here, Γ = ‐11.4 (because the market maker is short 600 options), and since a single standard deviation of movement would be S0*σ*h0.5 = $1.9068, xi = ‐$2/$1.9068 = ‐1.0489. Thus, the return on the portfolio is ½*‐11.4*3025*0.0625*(1/52)*(‐1.04892‐1) = ‐$2.08"

so now where did the $2 come from in calculation of x?

thanks in advance!

[StevieB]

xi is the change in the stock price

[MusaAli]

yeah, figured it out on my own but thanks anyway =)