Suppose an investor enters into a futures contract on a stock index with a spot index level (S0) of 3,000, a dividend yield (y) of 2%, and a risk-free rate (r) of 4%. If the futures contract has a maturity of 3 months, calculate the theoretical futures price (F0(T)) using the cost-of-carry model
Question
Suppose an investor enters into a futures contract on a stock index with a spot index level (S0) of 3,000, a dividend yield (y) of 2%, and a risk-free rate (r) of 4%. If the futures contract has a maturity of 3 months, calculate the theoretical futures price (F0(T)) using the cost-of-carry model
Solution
To calculate the theoretical futures price (F0(T)) using the cost-of-carry model, we need to consider the spot index level (S0), the dividend yield (y), the risk-free rate (r), and the maturity of the futures contract (T).
Step 1: Calculate the cost of carry (C): C = (S0 * e^((r-y) * T))
Step 2: Calculate the theoretical futures price (F0(T)): F0(T) = S0 + C
In this case, the spot index level (S0) is given as 3,000, the dividend yield (y) is 2%, the risk-free rate (r) is 4%, and the maturity of the futures contract (T) is 3 months.
Step 1: Calculate the cost of carry (C): C = (3,000 * e^((0.04-0.02) * (3/12)))
Step 2: Calculate the theoretical futures price (F0(T)): F0(T) = 3,000 + C
By plugging in the values and performing the calculations, you can find the theoretical futures price (F0(T)).
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