Question

a common stock will have a price of either $75 or $25 in two months. a two month call option on the stock has a strike price of $65. create a riskless portdolio. sell 100 call options, how many shares should you buy?

Answer 1

Strike price =		65
Upside value =		75
Downside value =		25
VC at upper = Upper value - Strike price (subject to 0)
75 - 65 =	10
VC at down
25 - 65 = 0 (it cannot be negative)
Hedge ratio = (V.C. at Upper value -V.C. at Down value) / (Upper Value - Down value)
	(10-0) /(75 - 25)
	0.2
Hedge ratio is 0.2. It means if one share is long then 0.20 call should be short.
Formula for no. of shares buy = no. of call options/Hedge ratio
so no.of shares buy should be = 100/0.20
500
So, 500 shares should be bought to create riskless portfolio.