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US Silver mines silver at a total cost of $9 per ounce. To hedge their sale pric

ID: 2761983 • Letter: U

Question

US Silver mines silver at a total cost of $9 per ounce. To hedge their sale price, US Silver uses a collar strategy by buying Puts with strike $9.75 and selling Calls with strike $10.25. The respective premia are P = 0.246 and C = 0.374. Assume that these premia are already in T-dollars (i.e this is their future value). Plot the net per-ounce profit of US Silver as a function of silver price St at date T. What is the minimum/maximum profit US Silver might record? (Assume that silver prices will be for sure between $2 and $20 dollars in the future) Find the exact net per-ounce profit of US Silver if Silver price ends up at (i) S_t = 9.6; (ii) at S_T = 10.1.

Explanation / Answer

Net per ounce profit

Minimum profit = $0.76 per ounce,  Maximum profit = $1.26 per ounce

b)

I) if price ends up to 9.7

Profit = Put exercised - Cost + Net premia received = 9.75 - 9 + 0.01 = $0.76 per ounce

II) if price ends up at 10.2

Profit = Market price - Cost + Net premia received = 10.2 - 9 + 0.01 = $1.21 per ounce

Price 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Put 9.75 9.75 9.75 9.75 9.75 9.75 9.75 9.75 - - - - - - - - - - - Call - - - - - - - - - 10.25 10.25 10.25 10.25 10.25 10.25 10.25 10.25 10.25 10.25 Market - - - - - - - - 10 - - - - - - - - - - P (0.264) (0.264) (0.264) (0.264) (0.264) (0.264) (0.264) (0.264) (0.264) (0.264) (0.264) (0.264) (0.264) (0.264) (0.264) (0.264) (0.264) (0.264) (0.264) C 0.274 0.274 0.274 0.274 0.274 0.274 0.274 0.274 0.274 0.274 0.274 0.274 0.274 0.274 0.274 0.274 0.274 0.274 0.274 Cost 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 Profit 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 1.01 1.26 1.26 1.26 1.26 1.26 1.26 1.26 1.26 1.26 1.26