The Pairagain mutual fund has entered into an equity swap with SingleSol, LLC, with a notional principal of $50 million. Pairagain has agreed to pay the quarterly return on the NASDAQ 100 in exchange for a fixed rate of 7.0%. The initial price of the NASDAQ 100 was 1825, and the value at the end of the first quarter, 91 days later, was 1755. The swap uses a 365-day year convention. What is the net payment to be made at the end of the first quarter?
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A. B. C.A
To calculate the net payment to be made at the end of the first quarter, we need to determine the difference between the quarterly return on the NASDAQ 100 and the fixed rate of 7.0% and then apply that difference to the notional principal of $50 million.
First, let's calculate the quarterly return on the NASDAQ 100. The initial price of the NASDAQ 100 was 1825, and the value at the end of the first quarter, 91 days later, was 1755.
To calculate the quarterly return, we use the formula:
Quarterly Return = (Ending Value - Beginning Value) / Beginning Value
Quarterly Return = (1755 - 1825) / 1825 = -0.0384 or -3.84%
Next, we need to calculate the net payment by multiplying the quarterly return by the notional principal of $50 million and subtracting the fixed rate payment.
Net Payment = (Quarterly Return × Notional Principal) - Fixed Rate Payment
Fixed Rate Payment = (Fixed Rate × Notional Principal) × (Quarter Length / Year Length)
Fixed Rate Payment = (0.07 × $50,000,000) × (91 / 365) = $875,342.47
Net Payment = (-0.0384 × $50,000,000) - $875,342.47
Net Payment = -$1,920,000 - $875,342.47
Net Payment = -$2,795,342.47
Since the value is negative, it means that SingleSol pays the amount to Pairagain. However, the options provided in the question are positive amounts, so there might be an error in the options.
Based on the calculations, the correct net payment to be made at the end of the first quarter should be:
Net Payment = -$2,795,342.47
Therefore, none of the provided answer options (A, B, or C) is correct.