Question

Consider a stock priced at $150, which will pay a dividend of $1.25 in one month, $1.25 in four months, another $1.25 in seven months, and another $1.25 in ten months. The continuous compounding risk-free rate is 5.25%. If you take a short position in an 8- month forward contract, what should be the forward price of a contract established today?

Answer 1

The forward price of the stock is calculated by discounting the dividend payments back to their present value using continuous compounding and then subtracting these from the current stock price.

Step-by-step explanation:

The question at hand involves calculating the forward price of a stock given its future dividend payments and the continuous compounding risk-free rate. To find the forward price for an 8-month contract, we need to discount the dividend payments back to the present value and then subtract these from the current stock price. The forward price can be calculated using the following formula.

Forward Price = Stock price - Present value of dividends

We will use the continuous compounding formula, PV = D * e^(-rt), to calculate the present value of each dividend, where PV is the present value, D is the dividend, e is the base of the natural logarithm, r is the continuous compounding risk-free rate, and t is the time in years. To answer the student's question, we would apply this formula to each dividend payment, discount them to their present values, and then adjust the stock price accordingly to find the forward price.