Question

a) Explain how to calculate the delta of a portfolio of options (see 17.4 of Hull).

b) Suppose you are long 50 shares of Tesla stock that you bought at 798. You are also short 100 puts (=one contract) with a strike of 800 and 100 calls (one contract) with a strike of 850 that expire on June 19^th. You are given the following information on the deltas of these instruments:

	Position	Quantity	Delta/share
	TSLA	50	1
	850 Call	-100	-0.4719
	800 Put	-100	0.3954

What is the delta of your overall Tesla position? Show the calculations by providing a screenshot from Excel, or your work below.

Answer 1

Calls have Positive Delta and Puts have Negative Delta.

Therefore, If we are Long on Options, Delta of Call will be Positive and Delta of Put will be Negative.

In this case, we are Short on Options, therefore, Delta of Call will be Negative and Delta of Put will be Positive.

Net Delta of Overall Position = Delta of Stock Position + Delta of Put Position - Delta of Call Position = (50*1) + (100*0.3954) - (100*0.4719) = 50 + 39.54 - 47.19 = 42.35

Therefore, If Stock Price will Increase by $1, there will be a profit of $42.35 and vice versa.