A stock index futures contract delivering in 3 months is priced at 1015 while th

Question

A stock index futures contract delivering in 3 months is priced at 1015 while the underlying stock index is at 1003. The risk-free rate is 3.5 per cent per annum and the dividend yield is 1.2 per cent per annum, both expressed with continuous compounding. (a) What is the basis? (b) By how much is the futures contract mispriced? (c) Detail the transactions (dates and trades etc.) that you would undertake earn a risk-free profit, and as much as you can, if your maximum exposure to any instrument is $1M.

Explanation / Answer

Future Price = $1015

Index Price = $1003

Risk free rate = 3.5%

Dividend yield = 1.2%

Time = 3 months = 3/12 years

a) Basis = Future price - spot price = $1015 - $1003 = 12

b) Expected Future Price = Spot Price * e ^ (( Risk Free rate - dividend yield) * time)

Expected Future Price = $1003 * e^((0.035 - .0.12)*(1/4))

Expected Future Price = $1008.8

So future contract is mispriced by = $1015 - $1008.8 = $6.2

c) Future price overpriced since future price is more than exepected future price, So we will sell the future contracts.

1. Borrow $1 million from market at risk free rate to but the stock index

Money borrowed = $1,000,000

Interest rate = 3.5%

Dividend yield = 1.2%

Amount needs to return after 3 month effective of dividend yield = $1,000,000 * e^((0.035-0.012)*0.25)

Amount needs to return after 3 month effective of dividend yield = $1,005,766.56

Short sell the forward contract at $1015, so after 3 months, you will get that money

Money receive after 3 months = $1015

Number of shares to be shorted = 1,000,000 / 1003 = 997

Total money = 997*1015 = $1,011,964

Money to be returned = $1,005,766.56

Profit = $1,011,964 - $1005,766.56 = $6197.43

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.