Why are futures prices and forward prices often different when, in principle, they have the same fair value calculation in principle?

Q1 Suppose you short 21 contracts of E-Mini S&P 500 futures at 4,486. The next day, their price goes to 4,512. What would be the profit or loss if you closed your short position at that price?

Q2 Suppose you bought 33 futures contracts of gold (contract size = 100 oz.) The current futures price is $1,791 per ounce. The initial margin is $9,900 per contract, the maintenance margin is $9,000/contract. At what price level would you receive a margin call?

Q3 The spot exchange rate for Britain and US is currently at 1.3845 ($ per pound). Britain’s continuously compounded risk-free rate is 1.50%. The U.S. continuously compounded risk-free is 0.50%. Calculate the 8-month forward exchange rate.

Q4 The S&P 500 Index is currently trading at 4,500. The continuously compounded risk-free rate is 0.25%. The dividend yield (continuous comp.) is 1.30%. Calculate the fair-value futures price expiring in 10 months.

Q5 An investor holds 20,000 shares of a certain stock. The stock is currently trading at $245.00 per share.

He is interested in hedging against short-term movements in the market and decides to use E-Mini S&P 500 futures to hedge his exposure. The Index is currently at 4,500. Contract size = $50 times index.

The Beta of the Stock is 1.2. Calculate how many E-Mini S&P 500 futures contracts are needed to hedge the investor’s holdings against downside price risk. What position (long or short) is required?

Q7 Explain how margins in futures markets are both a blessing and a curse. From a risk management perspective, what are the pros and cons of margin requirements in futures?

Q8 Why are futures prices and forward prices often different when, in principle, they have the same fair value calculation in principle?

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