Question

Gold is currently trading for about 1,650 per ounce. You are considering 3 ways of taking a short position on gold: (i) sell 100 ounces of gold short, (ii) take a short position in 1000 gold futures (October 2020), (iii) buy a futures put options on 1000 gold futures at K=1650 (October 2020).

(a) If you enter the above positions when gold equals 1,650, compare the dollars in profit from the three ways of betting against the price of gold if gold ends up at the following prices at time t: 1400, 1450, 1500, 1550, 1600, 1650, 1700, 1750, 1800, 1850 (Note: you should assume the price of one futures put option is $10).

(b) Draw a diagram showing the profits for each position for each price of gold.

(c) Which option has the lowest risk? Explain

could you please the detail step in excel. thansk! please!

Answer 1

	Current Price of Gold =1650 per ounce
	1. Sell 100 ounce of gold short
	Price at expiry=St
	Payoff =(1650-St)*100
	2.Short position in 1000 gold futures
	Payoff =(1650-St)*1000
	3. Buy 1000 Put Option atK=1650
	Payoff =1000*(Max.((1650-St),0)
	Cost =1000*10=10000
	Profit/Loss=Payoff-10000
		St	A	B	C	D=C-10000
		Price at expiration	Sell 100 Ounce short(Gain/Loss)	Short positionin 1000 futures(Gain/(loss)	Buy 1000 Put Option K=1650(Payoff)	Buy 1000 Put Option K=1650(PROFIT/(Loss))
		1400	25,000	250,000	250,000	240,000
		1450	20,000	200,000	200,000	190,000
		1500	15,000	150,000	150,000	140,000
		1550	10,000	100,000	100,000	90,000
		1600	5,000	50,000	50,000	40,000
		1650	0	0	0	(10,000)
		1700	(5,000)	(50,000)	0	(10,000)
		1750	(10,000)	(100,000)	0	(10,000)
		1800	(15,000)	(150,000)	0	(10,000)
		1850	(20,000)	(200,000)	0	(10,000)
	PUT OPTION has the lowest risk
	Because, loss is limited to 10000
	Potential of gain is unlimited