Question

a futures contract on a non-dividend-paying stock index with current value $290 has a maturity of one year. if the t-bill rate is 3%, what should the futures price be?

Answer 1

The correct futures price for a non-dividend-paying stock index currently valued at $290 with a one-year maturity, assuming a 3% T-bill rate, would be $298.70. This is calculated using the formula Futures Price = Spot Price × (1 + Risk-Free Interest Rate)^Time to Maturity.

Step-by-step explanation:

The subject of the question is to determine the futures price for a non-dividend-paying stock index, assuming it matures in one year and the current risk-free interest rate (e.g., T-bill rate) is 3%. The futures price is the price at which you would agree today to buy or sell an asset in the future. Since the stock index does not pay dividends, and hence there are no cash flows during the holding period, the calculation of the futures price is straightforward.

To find the futures price, we would use the no-arbitrage principle and cost-of-carry model, which states:

Futures Price = Spot Price × (1 + Risk-Free Interest Rate)^Time to Maturity

Here's how the calculation works:

• Spot Price: $290 (the current value of the stock index)
• Risk-Free Interest Rate: 3% (the T-bill rate given in the problem)
• Time to Maturity: 1 year (the time until the futures contract expires)

Now, apply the formula:

Futures Price = $290 × (1 + 0.03)^1

Solving this,

Futures Price = $290 × 1.03

Futures Price = $298.70

Therefore, the correct futures price for the stock index given the parameters would be $298.70.

Answer 2

The futures price for a non-dividend-paying stock index with a current value of $290, a maturity of one year, and a T-bill rate of 3%, is calculated using the formula $F = S \times (1 + r)^t$, resulting in a futures price of $298.70.

Step-by-step explanation:

The student has asked about the determination of the futures price for a non-dividend-paying stock index with a given current value, a specific maturity, and a given risk-free rate. The calculation of the futures price of a non-dividend-paying stock index takes into account the current value of the index and adjusts it according to the risk-free rate available in the market, here represented by the T-bill rate.

To calculate the futures price, we can use the formula for the future value of a single sum of money, which is:
$$F = S \times (1 + r)^t$$

Where:

• F is the futures price
• S is the current value of the stock index
• r is the risk-free interest rate (T-bill rate)
• t is the time to maturity of the futures contract (in years)

Given:

• S = $290
• r = 3% or 0.03
• t = 1 year

we calculate the

futures price

as follows:
$$F = 290 \times (1 + 0.03)^1$$
$$F = 290 \times 1.03$$
$$F = $298.70

This means the correct futures price for the stock index should be $298.70, assuming that all other market conditions remain constant.