Hi Friends, My doubt is w.r.t. dividend paying share in a forward contract price. In Sep 2014 Q.5 (ii), how is the Portfolio B taken as 1.05^-4 long in shares and short Cash. The question as per the Paper is this: "Assume that, at time zero, the share price is 500, and that the forward contract has maturity two years. The share pays a dividend of 5% of the share price every six months with the next dividend due in two months, and the continuously compounded risk-free rate is 3% p.a. Determine the forward price for this contract." Please help! Thanks & Regards Jhanani.M
Portfolio B is chosen in this way so that it replicates the payoff from Portfolio A. Portfolio A is a long forward contract, so results in purchasing 1 unit of the share at maturity. To replicate this outcome, we start out by buying less than 1 share in Portfolio B, and because the share pays dividends, we use the dividends paid to purchase more units of the share in order to reach 1 unit after the last dividend has been paid. Let's take the simpler situation where the share just pays one dividend of 5% of the shareholding at some point during the term of the contract (say, time t1). If we start out with 1.05^(-1) units of the share, then at time t1, we will still own 1.05^(-1) units of the share, as no dividends have yet been paid. This will be worth St1*1.05^(-1) (where St1 is the share price at time t1). The dividend is 5% of this value, which is worth 0.05*St1*1.05^(-1). So the value after the dividend is paid is St1*1.05^(-1) + 0.05*St1*1.05^(-1) = 1.05*St1*1.05^(-1) = St1, ie we own 1 share. Since no more dividends are paid (in this example), we'll then own exactly 1 share at maturity. Although it sounds awkward, the general result for the number of shares to hold at outset is 1 unit discounted using the dividend yield over the term of the contract. This gives 1.05^(-4) in the question you cite.
