Question

Suppose that the bid price of Google stock is $498 per share and the asking price is $500 per share. Google does not pay any dividends. Short selling the stock is feasible at zero cost. You can borrow at an annual rate of 6.0 and lend at 4.8% (simple compounding). What is the lowest forward price that will not allow arbitrage? Please round to two decimal places.

The answer is 521.9. Please explain

Answer 1

Price of futures = Minimum of [{bid rate*(1+lending rate),ask rate *(1+borrowing rate)}

Price of future=Minimum of{($498*(1+0.048),$500*(1+0.06)}

Price of futures= Min{$498*1.048,$500*1.06}

Price of futures=Min{$521.9,$530}

Price of futures= $521.9

Explanation- In order to prevent the arbitrage the future price must be such that

-a person who buy futures and short sells the stock to cover his position ,and invest (@4.8%) the amount obtained by short selling the stock (Bid price i.e. $498)

gets the benefit 0 or loss.

-Similarly a person who sells futures and buy a stock(ask price of $500) to cover his position,and borrows (@ 6%) to buy stock gets the benefit 0 or loss

Now the minimum of the 2 amounts will solve the purpose of eliminating the arbitrage.Hence the price of futures is minimum of the 2 amounts.

If you have any doubt,please ask.