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Chapter 5: Problem 11

Suppose the S\&P 500 index futures price is currently 1200. You wish to purchase four futures contracts on margin. a. What is the notional value of your position? b. Assuming a \(10 \%\) initial margin, what is the value of the initial margin?

Short Answer

Expert verified
The notional value of your position is \(1200 x 4 = \$4800\). The initial margin is \(4800 x 0.10 = \$480\).

Step by step solution

01

Calculation of Notional Value

The notional value of the position can be calculated by multiplying the futures price by the number of futures contracts. In this case, the futures price is 1200 and the number of futures contracts is 4. Therefore, notional value = futures price x number of contracts = \(1200 x 4\).
02

Calculation of Initial Margin

Once the notional value has been determined, the initial margin can be calculated as a percentage of the notional value. In this case, the percentage given for the initial margin is \(10\%\). Therefore, initial margin = notional value x margin percentage = \(Notional~Value~from~Step~1~x~10\% \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Notional Value
The notional value is a term often used in the context of futures contracts to represent the total value of the underlying assets involved in the contract. It's calculated by multiplying the price of a single futures contract by the number of contracts you intend to buy or sell. In the example of the S&P 500 index futures, where the price is 1200, and you plan to purchase four contracts, the notional value would be:
  • Notional Value = Futures Price x Number of Contracts
  • Notional Value = 1200 x 4
  • Notional Value = 4800
This value helps investors understand the size and risk of their positions without needing to own the actual asset.
Initial Margin
The initial margin is the amount of money that must be deposited in your account to open a position in futures trading. It's a percentage of the notional value that acts as a security to ensure both parties fulfill their obligations. In the context of the S&P 500 futures contract example:
  • Notional Value = 4800
  • Initial Margin Percentage = 10%
  • Initial Margin = Notional Value x Initial Margin Percentage
  • Initial Margin = 4800 x 0.10 = 480
This margin acts as a financial safeguard against potential losses during the life of the contract.
S&P 500 Index
The S&P 500 Index is one of the most widely followed equity indices in the world. It includes 500 of the largest companies listed on stock exchanges in the United States, representing a broad spectrum of the market. When trading futures contracts based on the S&P 500:
  • Investors are betting on the future value of this index.
  • The index serves as a benchmark for the performance of U.S. stocks.
  • S&P 500 futures allow investors to speculate or hedge against market movements.
Understanding how futures contracts are tied to indices like the S&P 500 helps in making informed trading and investment decisions.

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Most popular questions from this chapter

Suppose the stock price is \(\$ 35\) and the continuously compounded interest rate is \(5 \%\) a. What is the 6 -month forward price, assuming dividends are zero? b. If the 6 -month forward price is \(\$ 35.50\), what is the annualized forward premium? c. If the forward price is \(\$ 35.50,\) what is the annualized continuous dividend yield?

The S\&R index spot price is 1100 and the continuously compounded risk-free rate is \(5 \% .\) You observe a 9 -month forward price of 1129.257 a. What dividend yield is implied by this forward price? b. Suppose you believe the dividend yicld over the next 9 months will be only \(0.5 \%\). What arbitrage would you undertake? c. Suppose you believe the dividend yield will be \(3 \%\) over the next 9 months. What arbitrage would you undertake?

Suppose we wish to borrow \(\$ 10\) million for 91 days beginning next June, and that the quoted Eurodollar futures price is 93.23 a. What 3 -month LIBOR rate is implied by this price? b. How much will be needed to repay the loan?

Suppose the S\&P 500 currently has a level of 875 . The continuously compounded return on a 1-year T-bill is \(4.75 \%\). You wish to hedge an \(\$ 800,000\) portfolio that has a beta of 1.1 and a correlation of 1.0 with the \(S \& P 500\). a. What is the 1-year futures price for the S\&P 500 assuming no dividends? b. How many S\&P 500 futures contracts should you short to hedge your portfolio? What return do you expect on the hedged portfolio?

Suppose you are a market-maker in S\&ER index forward contracts. The S\&R index spot price is 1100 , the risk-free rate is \(5 \%\), and the dividend yield on the index is 0 a. What is the no-arbitrage forward price for delivery in 9 months? b. Suppose a customer wishes to enter a short index futures position. If you take the opposite position, demonstrate how you would hedge your resulting long position using the index and borrowing or lending. c. Suppose a customer wishes to enter a long index futures position. If you take the opposite position, demonstrate how you would hedge your resulting short position using the index and borrowing or lending.
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