Question

2)The current spot price of Priceline’s stock is $1,578 and pays no dividends for the next 6 months. The current 6-month future price on Priceline is $1,617.50. The current 6-month risk-free rate is 5% per annum with continuous compounding. If there is a $20 transaction fee for the combination of all transactions made, paid today, can you make an arbitrage profit? If there is an arbitrage, how much would you make using 50 shares of Priceline? Otherwise prove an arbitrage isnot possible

Answer 1

Current spot price: $1,578

Current 6-month futures price is $1,617.50

6-month risk-free rate (per annum) = 5%

PV of the future price at continuously discounting of 5% =

which is below the current price of $1,578, hence arbitrage opportunity exists, where one should short the share at current spot price and lend it at the risk-free rate and purchase the futures contract on the stock, after six months buy the share at the predetermined future price and deliver it.

50shares scenario:

Return from lending (assuming continuous compounding):

Using $1,617.5 to purchase it at futures contract price gives a profit of $0.44726 (1617.94726-1617.50) per share

for 50 shares profit = 50*$0.44726 =$22.363

the transaction cost of $20 is to be considered

Total risk-free profit of $2.363 (22.363-20) on 50 shares