On Monday 18 November 2013, an investor takes a short position in a forward contract on Royal Dutch Shell shares with delivery on Tuesday 18 February 2014. The price of the shares at that time is $20.69. Shell intends to pay a dividend on Monday 16 December 2013. Assume that the dividend is $0.27 per share and that the risk-free interest rate is 0.5% (per annum, compounded continuously). You may use any sensible day-count convention (ignore this if you do not know what a day-count convention is).
(a) Find the forward price, assuming no arbitrage. Give your answer correct to four decimal places (e.g., $23.4567).
(b) Suppose that on the delivery date, 18 February 2014, a share costs $22.09. Is the investor better or worse off compared to somebody who did not enter into the forward contract, but just sold the stock on 18 February 2014? By how much?