Question

ANSWER THIS : Calculate the implied annual risk-free rate if the actual market price of the equity futures contract in Problem 1a is 2,376. How would an investor construct a portfolio to earn this rate of return? (MAIN QUESTION)

PART THAT YOU NEED TO ANSWER ABOVE QUESTION IS BELOW.

Problem 1

Calculate the fair value of the following contracts with 50 trading days (t = 50/250 = 0.20 years) to expiration and a continuously compounded annual risk-free rate of 1.5%.

1. An equity index futures contract with the current index level of 2,364 and a continuously compounded annual dividend yield of 2.1%.

Answer 1

Problem 1

Current value of Index =S= 2364

Future value of Index =F = S*e^((r-d)*t)  

Where r is the continuously compounded risk free interest rate , d is the continuously compounded dividend yield and t is the time till maturity in years

F = 2364* e^((0.015-0.021)*0.2) = 2361.165

If the actual price of Equity futures is 2376 , the implied risk free rate (r) is

2376 = 2364* e^((r-0.021)*0.2)

=> (r-0.021)*0.2 = ln (2376/2364) = 0.005063

=> r-0.021 = 0.025317

=> r = 0.046317 or 4.6317%

One can buy the Index today (all the constituents in the proportion the index is composed) at 2364 and sell the equity index futures today at 2376 to realise the risk free rate of 4.6317% , as during the period , one will get the dividends as well as capital gains on selling the index futures , so overall gain will be 4.6317%