Question

5. Suppose that the current value of the S&P 500 stock index is USD 2600. Assume that the per annum rates of interest in USD and GBP(British Pound) are respectively 3% and 2% on a continuously compounded basis, and that the S&P 500 index pays a continuous dividend rate of 2% per annum. Finally, the spot exchange rate is USD1.3 per GBP. a) Compute the forward price of the S&P 500 in USD for delivery in one year. for delivery in one year delivery in one year b) Compute the forward price (exchange rate) of USD in GBP c) Compute the forward price of the S&P 500 in GBP for

Answer 1

(a)

Forward price = spot price * e^((r-d)*t)

where r = continuously compounded risk free rate

d = dividend yield

t = time in years

Forward price = 2600 * e^((0.03 - 0.02)*1)

Forward price = 2600* e^0.01 ==> USD 2,626.13  

(b)

f = s * ((1 + I_d)/(1 + I_f))^n , where

f = forward exchange rate (in terms on number of units of domestic currency per unit of foreign currency)

s = spot exchange rate (in terms on number of units of domestic currency per unit of foreign currency)

I_d = domestic interest rate

I_f = foreign interest rate

n = number of time periods

f = 1.3 * ((1 + 0.03)/(1 + 0.02))^1

f = 1.3217

(c)

forward price of S&P 500 in GBP = forward price of S&P 500 in USD / forward exchange rate

forward price of S&P 500 in GBP = 2,626.13 / 1.3127 ==> GBP 2,000.49