Question

Consider the following spot rate curve:

s1	s2	s3	s4	s5
0.050	0.055	0.061	0.067	0.075

(a) What is the forward interest rate that applies from period 3 to period 5? That is, what is the value of f_3,5? Assume annual compounding. (Keep your answer to 4 decimal places, e.g. 0.1234.)

(b) If the market forward rate from period 3 to period 5 is not equal to the value derived in (a), how can you create an arbitrage opportunity?

Answer 1

Answer a) In general term ,

(1+S_A)^A x (1+IFR_A,B-A)^B-A = (1+S_B)^B

As per question , the above equation will change as ,

(1+S₃)³ x (1+F_3,,5)² = (1+S₅)⁵

=> (1+F_3,,5)² = (1+0.075)⁵ / (1+0.061)³ =1.2019

=>F_3,5 = (1.2019)^0.5- 1= 0.09635.

Answer b) Difference in calculated forward rate and actual market rate always give an opportunity for risk free return as arbitrage opportunity. The actual difference in the rate may consider as return from the arrangement.

Investor can borrow from market for S3 and invest for S5 , to earn the differential amount without any amount of risk