Question

The current spot price of Amazon stock is $1,823 the current 1-year forward price is $1,944. The current 1-year risk free rate is 6.5% per annum with semiannual compounding. If there is a $20 transaction fee for the combination of all transactions made, paid today, can you make an arbitrage profit with 100 shares? If there is an arbitrage how much would you make? Otherwise prove that there is not an arbitrage.

Answer 1

Current Spot Price of Amazon = $ 1823

Cost To trade = $20

Risk Free Rate 6.5 % P.A. compounded semi annually.

Our Annual Rate is 6.5, our semi annual rate will become 6.5 / 2 = 3.25 %

With Semi Annual Compounding the Effective Rate Will be.

(1+(R/100))ⁿ-1

Where R is our rate and n is no of times compounding is done.

Putting values in our formula

(1 + (3.25/100))²-1

(1.0325)²-1

1.06605 - 1

0.06605 or 6.60 %

Checking Arbitrage:

We will discount our forward rate with the Discount rate calculated above to get the current spot price and possible mismatching.

Forward rate / (1 +( R/100))

1944 / (1.06605)

=1823.54 Approx

Since amazon stock is currently trading at 1823, there is a mismatching in price hence arbitrage profit of 0.54 Per share, which is the difference between the present value of the forward contract and the current spot price.

For 100 Shares profit will be 0.54 * 100 = $54

Also, the current cost of Transaction is $20, so we will subtract the Cost from the profit, then our profit will become 54-20 = $34

$34 is the Present Value of Arbitrage Profits available on this trade.

We will get 34 * ( 1.0660)(Our Compounding rate) = 36.24 $ after One year.