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Answer:
Hey Ruben! No worries friend, for I will explain this to you:
First, we must calculate the theoretical futures price using the formula for the cost of carry, which is given by:
F = S * e^(r * t)
where:
F is the theoretical futures price
S is the spot price ($1,000)
e is the base of the natural logarithm (approximately 2.71828)
r is the risk-free interest rate (2.3% or 0.023)
t is the time to maturity (1 year)
Substituting the values, we get:
F = 1000 * e^(0.023 * 1)
Next, we need to calculate e^(0.023). Using the ancient method of logarithmic expansion, we approximate e^(0.023) as follows:
e^(0.023) ≈ 1 + 0.023 + (0.023^2)/2 + (0.023^3)/6
Calculating each term, we get:
0.023^2 = 0.000529
0.023^3 = 0.000012167
Therefore:
e^(0.023) ≈ 1 + 0.023 + 0.0002645 + 0.000002027833 ≈ 1.023266527833
Now, we multiply this by the spot price:
F = 1000 * 1.023266527833 ≈ 1023.27
The theoretical futures price is approximately $1,023.27. However, the actual futures price is $1,025. To find the potential arbitrage profit, we need to compare the actual futures price with the theoretical futures price.
The potential arbitrage profit can be calculated as:
Arbitrage Profit = Actual Futures Price - Theoretical Futures Price
Substituting the values, we get:
Arbitrage Profit = 1025 - 1023.27 = 1.73
Therefore, the potential arbitrage profit is 1.73$