Final answer:
The dividend yield implied by the futures contract can be calculated using the formula: Dividend Yield = (Dividend / Futures Price) * (1 / Time Period) * 100.
Step-by-step explanation:
The dividend yield implied by the futures contract can be calculated using the cost-of-carry model, which takes into account the interest rate and the difference between the futures price and the spot price.
The formula for the cost-of-carry model is:
\[F = S \times e^{(r - q) \times T}\]
Where:
\(F\) = Futures price
\(S\) = Spot price (current index value)
\(r\) = Interest rate
\(q\) = Dividend yield
\(T\) = Time to delivery in years
Given:
Spot price (\(S\)) = 13,500
Futures price (\(F\)) = 14,100
Interest rate (\(r\)) = 8% or 0.08
Time to delivery (\(T\)) = 9 months or 0.75 years (since 9 months is 3/4 of a year)
Rearranging the formula to solve for the dividend yield (\(q\)), we get:
\[q = r - \frac{{\ln\left(\frac{F}{S}\right)}}{T}\]
Let's plug in the values:
\[q = 0.08 - \frac{{\ln\left(\frac{14,100}{13,500}\right)}}{0.75}\]
First, calculate the natural logarithm:
\[\ln\left(\frac{14,100}{13,500}\right) ≈ \ln(1.044444) ≈ 0.043763\]
Now, substitute the values into the equation:
\[q ≈ 0.08 - \frac{0.043763}{0.75} ≈ 0.08 - 0.05835 ≈ 0.02165\]
So, the implied dividend yield by the futures contract is approximately 2.165%