Question

You are considering taking a short position in one-year futures on a stock. The stock is expected to pay two dividends; each dividend is $4 per share; first dividend is to be paid in four months, and the second dividend is paid in ten months. The current stock price is $100, and the risk-free rate of interest is 10% for all maturities. What should be one-year futures price contract?

Answer 1

Future Price, F₀ = (S₀-I)e^rT

^{Here, S₀ = Spot price = $100}

^{r= risk free rate = 10%}

^{T= time period = 1 year}

^{Calculating I = Present value of dividends paid}

= 4/ (1+(10%/12))⁴ + 4/(1+(10%/12))¹⁰

=3.87+3.68

=7.55

Thus, F₀ = (100-7.55)*e^(0.10*1)

Future Price, F₀ = 102.17