Question

The S&R index level is 900 at t=0. The dividend yield is 3% p.a. continuously compounded and the risk-free rate is 5% continuously compounded.

(a) What is the theoretical forward price with a maturity of 1 year?

(b) Suppose you observe a forward price with a maturity of 1 year equal to 950. What position do you take in order to earn arbitrage profit?

A. Long stock and short forward

B. Long stock and long forward

C. Short stock and long forward

D. Short stock and short forward

(c) Suppose you observe a forward price with a maturity of 1 year equal to 950. What is your arbitrage profit at t=1?

Answer 1

a). Forward price F₀ = S₀e^(r-d)T

where S₀ = current price = 900

r = risk-free rate = 5%

d = dividend yield = 3%

T = duration = 1 year

F₀ = 900*(e^(5%-3%)*1)

= $918.18

b). If the observed forward price is $950 then long stock and short forward (option A)

c). Borrow $900 at 5% for one year. Amount payable after one year will be 900e^(5%*1) = $946.14

Short a forward contract to sell the stock after one year at $950.

After one year, net profit is 950 - 946.14 = $3.86