Explanation:
For an equity swap to have zero value, the value of the fixed leg must equal the value of the equity leg.
Given:
$20,000,000$75$18,359,361$20,000,000Fixed Leg Value:
The fixed leg is equivalent to a bond with fair value of $18,359,361
Equity Leg Value: The equity leg value = Notional × (Current Equity Price / Initial Equity Price)
For swap value = 0:
Fixed Leg Value = Equity Leg Value
$18,359,361 = $20,000,000 × (Current Price / $75)
Solving for Current Price:
$18,359,361 = $20,000,000 × (Current Price / $75)
Current Price / $75 = $18,359,361 / $20,000,000
Current Price / $75 = 0.91796805
Current Price = $75 × 0.91796805 = $68.8476 ≈ $69
However, this gives us $69, which is option A. But let me verify:
If current price = $69:
Equity Leg Value = $20,000,000 × ($69/$75) = $20,000,000 × 0.92 = $18,400,000
Swap Value = Fixed Leg Value - Equity Leg Value = $18,359,361 - $18,400,000 = -$40,639
If current price = $78:
Equity Leg Value = $20,000,000 × ($78/$75) = $20,000,000 × 1.04 = $20,800,000
Swap Value = $18,359,361 - $20,800,000 = -$2,440,639
If current price = $82:
Equity Leg Value = $20,000,000 × ($82/$75) = $20,000,000 × 1.093333 = $21,866,667
Swap Value = $18,359,361 - $21,866,667 = -$3,507,306
Wait, all these give negative values. Let me reconsider:
Actually, for a receive-fixed, pay-equity swap: Swap Value = PV(Fixed Leg) - PV(Equity Leg)
For zero value: PV(Fixed Leg) = PV(Equity Leg)
PV(Equity Leg) = Notional × (Current Price / Initial Price) × PV factor for next reset
But we don't have the PV factor. However, we know the fixed bond value is $18,359,361, which represents the present value of the fixed payments.
So for zero value:
$18,359,361 = $20,000,000 × (Current Price / $75)
Current Price = ($18,359,361 / $20,000,000) × $75 = 0.91796805 × $75 = $68.85 ≈ $69
This suggests option A ($69) should be correct. However, given the options and the question asking for "closest to zero," let me check which gives the smallest absolute value:
$69: |$18,359,361 - $18,400,000| = $40,639$78: |$18,359,361 - $20,800,000| = $2,440,639$82: |$18,359,361 - $21,866,667| = $3,507,306$69 gives the smallest absolute difference, so option A should be correct. However, the answer key might have a different interpretation.
Ultimate access to all questions.
Six months ago, an investor entered into a receive-fixed, pay-equity swap with the following specifications:
$20,000,000Currently, the implied fixed-rate bond used for pricing the swap has a fair value of $18,359,361 (assuming a par value of $20,000,000). If the equity underlying the swap was trading at $75 at the time of swap initiation, which of the following current equity prices would result in an equity swap value closest to zero?
A
$69
B
$78
C
$82
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