Here is an example of cash and carry arbitrage:
The following data is available on stock A as on Jan 1st, 2017
Cash market price: Rs.1500
May Futures: Rs.1520
Contract Multiplier: 100 shares
Assume an implied cost of carry of 8% p.a. i.e 0.75% per month.
Fair price is measured by the formula: F = S*exp(rT)
where S = Spot price, r = carrying cost(in %) and T = Time to expiration(in years)
Here,
F = 1504.69 (= 1500 * exp(0.0075*5/12))
This shows that May Futures on the stock is overvalued.
To take advantage of this mis-pricing, an arbitrageur may buy 100 shares of stock A and sell 1 futures contract on that at given prices.
This would result in an arbitrage profit of Rs.1531.
Case I: Stock rises to Rs. 1550
Profit on underlying = (1550 – 1500) x 100 = Rs. 5000
Loss on futures = (1550 - 1520) x 100 = Rs. 3000
Gain on Arbitrage = Rs. 2,000
Cost of Arbitrage in terms of financing (Rs. 4.69 for 100 shares) = Rs. 469
Net gain out of arbitrage = (2000 – 469)= Rs 1531
Case II: Stock falls to Rs.1480
Loss on underlying = (1500- 1480) x 100 = Rs. 2000
Profit on futures = (1520-1480) x 100 = Rs. 4000
Gain on Arbitrage = Rs. 2000
Cost of Arbitrage in terms of financing (Rs. 4.69 for 100 shares) = Rs. 469
Net gain out of arbitrage = (2000 – 469) = Rs. 1531