Question

You have \(\$ 100,000\) to invest today. You are bullish about the stock market and you think that the S\&P 500 index is going up. You want to leverage your investment by taking a long position in S\&P 500 index futures.

Micro E-mini S\&P 500 Futures contract

There is a new futures contract on the S\&P 500 index with a lower contract multiplier-only 5 times the index. You are using this contract to implement your strategy. You chose the contract expiring on March 19, \(2021 .\)

Spot level for S\&P 500 index \(\left(S_{0}\right)\) on November \(27,2020: 3,635\)

Futures price \(\left(F_{0}\right)\) on November \(27,2020: 3,624\)

Discount rate \(\left(r_{f}\right.\) annual): \(0.09 \%\)

Dividend rate ( \(d\) annual): \(1.08 \%\)

Time to expiration: \(0.307\) years

Initial margin: \(\$ 1,320\)

What should be the price of the futures contract?

Based on the current futures price of 3,624, is there an arbitrage opportunity? (You can ignore the decimals for this question.)

If the price of the futures was 3,610 instead of 3,624, which strategy would you use to exploit the arbitrage opportunity?

A. Take a long position in the futures, short the index, and invest the proceeds in the risk-free asset

B. Take a short position in the futures, borrow at the risk-free rate, and take a long position in the index.

When you enter the long position today, do you have to exchange money with the party that takes the short position?

Answer 1

(a) Qubavnage T T Price Mata عمل 0.301 opportunity discount dividend Faubon futuru, spot [1+ price 3635 [17:0009 -0.0108] 3635 X 09970. = 3624 Actual future price ů $36 24. also, Hunce there i mo aubitrage oppoutunity exist (b) If future price is 3610, then there is arbitrage opportunity since future price is undervalued we will long on cowrect option is (A), Take long position in future, shout the index and invest proueds in risk full go ) the future. asset. position when we go long, lou take long position), we have not to pay money to party that takes shout we will have to deposit money with our broken and party taking shout position will also deposit some money with his broken only, Hene Ansunen iu No. (d) Yes, we have to set other money aside. We have to deposit some money with broken. That money is called initial margin inicial margin (margin auount) (e) yes, party taking shout position also has to set up money (+) Yes, margen account will be adjusted on daily basis margin amount to recognise P&L, that houss is called marked to market [NTMI . aside in a

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