Question

Question 3 2017:

Suppose that the current one-year interest rate is at 2%, the two-year rate is at
3% and the three-year rate is at 4%. A trader quotes the one-year rate, one year
forward as 4.2%. Assume that there is no bid-ask spread (i.e., you can lend and
borrow at the same rate) and that no other trader is quoting in the forward
market.

a) What is the one-year forward rate for a contract that expires in one year?

b) How would you trade if the one-year forward rate quoted by the trader was 3%?

c) Calculate the one-year forward rate for a contract that expires in three years.

Answer 1

a) Let the one year forward rate be x

If there is no arbitrage opportunity investing in a two year rate will be same as investing investing in 1 year and again buying a forward contract after 1 year that expires in one year

Therefore, (1+3%)^2 = (1+2%)*(1+x)

x = 4%

b) One year forward rate quoted by the trader is less than the no arbitrage one year forward rate calculated in above solution

Hence we can borrow at 1 year forward rate from the trader pay 3% and invest this amount for 2 years in spot market at 3%

c)

Let the one year forward rate that expires in 3 years be y

If there is no arbitrage opportunity investing in a three year rate will be same as investing investing in 2 year rate and again buying a forward contract after 1 year that expires in third year

Therefore, (1+4%)^3 = (1+3%)^2*(1+y)

y = 6.02%