Question

Emma and Robert are discussing an investment opportunity about the stock XYZ. The stock has a current price of €100 and the forward price for delivery of this stock in 1 year is €110. The annual effective risk-free interest rate is 5%. This stock currently pays no dividends. Read the following discussions about the contract. Do you support them or not? Justify your answers.

i. Emma argues that investing in XYZ stock versus investing in the forward contract does not provide a comparative advantage.

ii. Robert says that he has read about rumours of a dividend of 3.5 to be paid on this stock, 6 months from now. If true, he is arguing that it would be more beneficial to invest in the forward contract, rather than investing in the stock.

iii. Emma argues that investing in the forward contract would be more advantageous than investing in the stock only if the 5% interest rate is not annual effective but continuously compounded.

Answer 1

Forward Price, F = FV of stock Price - FV of any dividen

i. Emma argues that investing in XYZ stock versus investing in the forward contract does not provide a comparative advantage.

This statement is correct. Stock price today is nothing but present value of the forward price. In a risk neutral world without any arbitrage opportunity, Forward Price = Expected price of stock in future = S x e^{r_f x t} .

However, the real world is not a risk neutral world and hence deviation is seen in the market place.

ii. Robert says that he has read about rumours of a dividend of 3.5 to be paid on this stock, 6 months from now. If true, he is arguing that it would be more beneficial to invest in the forward contract, rather than investing in the stock.

S = current price = €100 and the forward price for delivery of this stock in t = 1 year is given by F = €110. The annual effective risk-free interest rate, r_f = 5%. This stock currently pays no dividends. Hence, d = 0

Under discreet compounding, expected forward price, F_exp = FV of stock - FV of dividend = S x (1 + r_f x t) - D x [1 + r_f x (t - 0.5)] = 100 x (1 + 5% x 1) - 3.5 x [1 + 5% x (1 - 0.5)] = €101.4125 < F = €110

It will indeed be more beneficial to invest in the forward contract, rather than investing in the stock. Hence, this statement is correct.

iii. Emma argues that investing in the forward contract would be more advantageous than investing in the stock only if the 5% interest rate is not annual effective but continuously compounded.

Under continuous compounding, expected forward price, F_exp = FV of stock - FV of dividend = S x e^r_ft - D x e^{r_f(t - 0.5)} = 100 x e^{5% x 1} - 3.5 x e^{5% x (1 - 0.5)} =  101.54 < F = €110

So, this argument is not correct. Under continuous compounding as well, It will indeed be more beneficial to invest in the forward contract, rather than investing in the stock.