Question

Suppose that the risk-free interest rate is 10% per annum with continuous compounding and that the dividend yield on a stock index is 3% per annum. The index is standing at 395, and the futures price for a contract deliverable in three months is 404.

What arbitrage opportunities does this create?

Answer 1

See Below

Step-by-step explanation:

We can use the future price formula here, which is:

`F=Pe^{(r_f-d_y)*(n)/(12)}`

Where

F is the theoretical future price

P is the present index standing

r_f is the risk free rate

d_y is the dividend yield

n is the number of months of the futures deliverable

Now,

given

P = 395

r_f = 0.1

d_y = 0.03

n = 3

Substituting, we get:

`F=Pe^{(r_f-d_y)*(n)/(12)}\\F=(395)e^{(0.1-0.03)*(3)/(12)}\\F=(395)e^(0.0175)\\F=401.97`

Actual future price is 404. The index future price is higher. So the strategy would be to sell the futures contracts. Long the shares underlying the index.