Question

Suppose that the risk-free interest rate is 10%. A bond with 8% yield is traded at a price. The current bond price is $100.

(a) Calculate the theoretical future price for the contract deliverable in six months.

(b) If the actual future price for this stock is $102, describe the arbitrage opportunity and calculate the profit that you can realize.

Answer 1

Solution:

a. As the stock has carrying a specific Yied, we have to use the following formula.

F = S0 x

Where,

F = Theoretical Future Price

S0 = Current spot price

r = Rate of interest

t = No. of years

y = Yield

Given that, S0 = 100,

r = 10% = 0.10,

y = 8% = 0.08,

t = 6 months = 0.5 year

Theoretical Future Price (F) = 100 x

                                                      = 100 x

                                                      =100 x

                                                     = $ 101

b. If the actual future price is $ 102, it means the stock is overvalued in future. The recommended action is Buy - Spot, Sell - Future. There by you can make a profit of $ 1.