The portfolio of stock that comprises the ASX200 index is currently worth $5000. The continuously compounded interest rates on Australian government bonds is 1.5% per annum for each of the next five years. The forward price for delivery in five years' time of the stock comprising the ASX200 index is $5,150.

(a) What is the present value today of what the ASX200 index will be worth in five years' time?

(b) What is the present value of the next five years' worth of dividends on the stock in the ASX200 Index? $5,000 invested in Australian government securities will grow at the end of five years to $5,000×e0.015×5 = $5,389.42. Five-year European-style put options on the ASX 200 index withan exercise price of $5,389.42 are trading at $422.121. Investor Bank is advertising the following offer: If you invest $5,000 with us and pay our $450 management fee, then we guarantee that you will receive

• What you would have received in five years' time by investing in Australian government bonds, plus

• Any excess of the capital gain on a five-year investment of $5,000 in the ASX 200 index over and the accumulated interest on a five-year investment of $5,000 in Australian government bonds, plus

• All the dividends paid on the ASX200 index over the next five years.

(c) Draw a diagram which shows the promised payoff in five years' time as a function of the level of the ASX 200 index in five years' time to someone who today pays a total of $5,450 to Investor Bank.

(d) What trades in the portfolio of stock comprising the ASX200 index and a put option will allow Magic Money Inc to (i) hedge all its commitments to an investor who pays $5,450 to Investor Bank today

(e) Use put call parity to determine the value of a 5-year European-style call option on the ASX 200 index with an exercise price of $5,389.42.

(f) What amount of arbitrage profit will Investor Bank make each time someone is willing to pay a total of $5,450 to Investor Bank today?

Answer rating: 100% (QA)

ANSWER a The present value today of what the ASX200 index will be worth in five years time is calculated using the forward price and the interest rate Present Value Forward Price 1 interest raten wher... View the full answer