Question

Suppose that the bid price of Google stock is $497 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 5.6 and lend at 4.8% (simple compounding). The commission of closing a forward position is $0.4 per share. The short sell cost is $3 payable when the borrowed stock is returned. What is the lowest forward price that will not allow arbitrage? Please round to two decimal places.

The answer is 517.46. Please explain

Answer 1

Bid rate - Ask rate = $497 - $500

Short Selling i.e borrowing the stock from dealer / broker to sell ( we don't own the share ) and repurchasing it on future date from market and returning back to Broker/ Dealer

Step 1:- Borrowing 1 stock from Dealer/ Broker

Step 2 :- Selling the stock at zero cost thus $497 received from selling the stock in market and entering forward contract to repurchase it after 1 year

Step 3:- Lending this money at 4.8% p.a ( considering 1 year forward contract it is)

Money received after 1 year = $497 + $ 23.86 = $ 520.86

Step 4:- Closing Forward Contract Let say at Price X

Commission paid $0.4 = Total outflow = X + $0.4

Step 5:- Returning the stock to Broker/ dealer and paying short sell cost of $3

Total outflow = X + $0.4 + $3

Step 6:-To be in zero or No Arbitrage position, Inflow should equal outflow

i.e Step 3 = Step 6

$520.86 = X + $0.4 + $3

X = $ 517.46