Question

Suppose XYZ stock costs $100/share today and is expected to pay $1.25/share quarterly dividend with the first coming 3 months from today and the last just prior to the end of the year (from today). Price a one-year forward contract on the XYZ stock if you know that the annual continuously compounded risk-free rate is 10%. If the one –year forward contract on XYZ stock is listed at $108, do you see any arbitrage profit opportunity in this case? If yes, what strategy you will apply to reap that profit? Please explain your answer by detailing the cash flows today and at expiration to realize the arbitrage profit.

Answer 1

FIRST LET US CALCULATE THE PRICE OF THE STOCK MINUS THE PRESENT VALUE OF THE QUARTERLY DIVIDENDS . AS THE RISK FREE RATE IS CONTINUOUSLY COMPOUNDED THE VALUE OF THE STOCK MINUS THE PRESENT VALUE OF THE DIVIDENDS IS.

THE FIRST DIVIDEND AFTER 3 MONTHS : $1.25/ e^0.10*3/12 = 1.25/1.0253 = 1.2192

THE SECOND DIVIDEND AFTER 6 MONTHS IT'S PV IS = $1.25/e^0.10*6/12 =1,25/1.0513 = 1.1890

THE THIRD DIVIDEND AFTER 9 MONTHS PRESENT VALUE IS : 1.25/ e^0.10*9/12 = 1.25/1.0779 = 1.1597

THE FOURTH DIVIDEND AFTER 12 MONTHS PV IS : 1.25/ e^0.10 = 1.25/1.1052 = 1.1310

THEREFORE, THE VALUE OF THE STOCK MINUS THE PV OF ALL THE DIVIDENDS IS = 95.3

THE VALUE OF THE STOCK AFTER ONE YEAR IS 95.3 * e^0.10 = $105.3228

THE VALUE OF THE FORWARD CONTRACT AFTER ONE YEAR IS $108.

SO IF WE ENTER INTO A SHORT FORWARD CONTRACT WHERE WE DECIDE TO SELL THE STOCK AT $108 AFTER ONE YEAR. WE CAN BUY THE STOCK AT $105.3228 IN THE MARKET AND SELL IT AT $108 IN THE FORWARD CONTRACT AND EARN PROFIT OF $ 2.6772.