Question

There are two assets, A and B. Asset A costs 1.25 today and pays off 3 in one year and 2 in two years. Asset B costs 1 and pays off 2 in one year and 2 in two years. What is the price of asset C which pays off 2 in one year and 1 in two years?

Answer 1

Let asset C is made up of a parts of A and b parts of B.

hence, C = aA + bB

Payoff from C in year 1 = 2 = resultant payoff of aA + bB at the end of year 1 = a x 3 + b x 2

Hence, 3a + 2b = 2 -------------------- equation (1)

Payoff from C in year 2 = 1 = resultant payoff of aA + bB at the end of year 2 = a x 2 + b x 2

Hence, 2a + 2b = 1 -------------------- equation (2)

Equation (1) - (2) gives:

a = 1; hence b = (1 - 2a) / 2 = (1 - 2 x 1) / 2 = - 1 / 2

Hence price of C = a x Price of A + b x Price of B = 1 x 1.25 - 1/ 2 x 1 = 0.75

Hence, the price of asset C which pays off 2 in one year and 1 in two years = 0.75