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