Question

Again, suppose silver is currently selling at $4.23 per ounce in the spot market. Assume as well that the current risk-free rate (implied repo rate) is 3.75% and that silver contracts involve 5000 ounces each. Also, now assume that carrying costs (storage and insurance) for silver are accessed at .31% (0.0031) per ounce price.

a. Including carrying costs, what should the 6 month (180 days) silver futures contract be selling for according to the cost-of-carry model?

b. If the 6 month (180 day) futures contract for silver is selling for $4.18 per ounce, what should you, as an investor, do?

c. What arbitrage profit will you realize if you decide to work with two (2) silver contracts?

These are the correct answers, how do I get to them?

a. $21,600 (at a price of $4.32/oz.)

b. reverse cash-and-carry arbitrage needed

c. $1293.13

Answer 1

a) according to cost of carry model, future price is spot rate * e^(r*t), where r is risk free rate of interest and t is time period in years

given to us

spot rate = $4.23

r = 3.75% or 0.0375

t = 6 months or 0.5 years

using the formula,

future price = 4.23 * e^(0.0375*0.5)

using exponential table or scientific calculator e^0.01875 = 1.019

thus future price is $4.3103 per ounce

now carrying cost being 0.0031

future price = future price ( 1+ carrying cost)

= 4.3103 * 1.0031 = 4.323

for 5000 ounces future price is 5000*4.32 = $21600

b) if future price is $4.18 per ounce which is less than the expected future price, combination of short position in cash and long position in underlying future to initiate trade at discount this is called reverse cash and carry arbitrage

c) arbitrage profit = expected future price - (actual future price * carrying cost)

4.323 - (4.18 * 1.0031)  = $0.13 per ounce

profit for 1 silver contract = 0.13 * 5000 = 650

arbitrage profit for 2 silver contracts $650 *2 = $1300