Swap valuation

You need to verify the cash flows and end‐of‐day valuation of a 3‐year pay fixed swap that is on d your esk. The end‐of‐day P&L doesn’t seem quite right and you are taking this swap as a sample to see if you have bad data or a bad model.

The swap you have on is a 500 million pay fixed 1.5% 3‐year USD swap that receives annual LIBOR.

As a first step, you are going to verify the estimated value of the swap just after the first payment. The market rates just after the last cash flow were 75 basis points per year and 100 basis points per year for the 1‐year (2016) and 2‐year (2017) annualized LIBOR rates, respectively.

The value of the swap just after the first cash flow is closest to:

First off, let’s consider intuition. If this swap pays a coupon of 1.5% and the current market rate for the two‐year is 1.0%, then this swap will have a positive value because an investor will pay a premium to own that above market cash flow. Right away the negative answer choices go away because you know this has to have a positive value given what you know about the term structure.

Second, this isn’t a valuation of cash flow question, it is a valuation question. In a cash flow question, we need to net the cash flows and derive the net cash flow payment. This is asking about valuation and to do that, we evaluate relative to the term structure of the 1‐ and 2‐year rates by discounting the future fixed payments. We are going to ignore the floating side for valuation purposes, which is analytically correct unless you were given a spread such as annual libor plus 100 basis points, which you are unlikely to see, on exam day.

Fixed Coupon = 500 million × 1.5% = 7.5 million

Swap value as two bond positions: 7.5 million e(–.0075) + 507.5 million e(–.010 × 2) = \$7,443,960 + \$497,450,826 = \$504.89 million – 500 million notional equals \$4.89 million valuation.

\$9.89 million would be the answer you got if you forgot to compound the second‐year cash flow.

Can someone explain answer b/c i get same result but is negative sign?.

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For the community, I did make a typo and it is already fixed, the answer should carry a negative sign.