- CFA Exams
- CFA Level I Exam
- Study Session 14. Derivatives
- Reading 37. Pricing and Valuation of Forward Commitments
- Subject 8. Interest Rate Swap Contracts

###
**CFA Practice Question**

Suppose we have entered into a one-year swap with quarterly payments on days 90, 180, 270, and 360. The fixed rate we pay is 3.68% (annualized). The underlying is 90-day LIBOR. The notional principal is $1,000,000. On day 0 the 90-day LIBOR was 3.45%. Suppose we have now moved 60 days into the life of the swap. At day 60, we face a new term structure of LIBORs, which is given as follows:

L

_{60}(30) = 0.0425 L_{60}(120) = 0.0432 L_{60}(210) = 0.0437 L_{60}(300) = 0.0444What is the value of the swap?

A. $7,900

B. $5,300

C. $4,700

**Explanation:**The new set of discount factors is:

PV

_{60}(90) = 1 / (1 + 0.0425 x 30/360) = 0.9965

PV

_{60}(180) = 1 / (1 + 0.0432 x 120/360) = 0.9858

PV

_{60}(270) = 1 / (1 + 0.0437 x 210/360) = 0.9751

PV

_{60}(360) = 1 / (1 + 0.0444 x 300/360) = 0.9643

The present value of the remaining fixed payments of 0.0092 (0.0368/4), including the hypothetical notional principal, is 0.0092 x (0.9965 + 0.9858 + 0.9751 + 0.9643) + 1 x 0.9643 = 1.0004.

As the market value of the remaining payments on day 90, including the hypothetical final notional principal, is 1.0, we discount 1.00 + 0.0086 (which is 0.0345/4) = 1.0086 back 30 days to obtain 1.0086 x 0.9965 = 1.0051.

Therefore, the value of the swap is (1.0051 - 1.0004) x 1,000,000 = $4,700.

###
**User Contributed Comments**
3

User |
Comment |
---|---|

carst |
How do we get to the 0.0092 for the PV value of remaining fixed payments? |

ljamieson |
0.0368/4 = 0.0092 |

Paulvw |
$4665 if you don't round (or write out each step) as you go - then be brave and pick the nearest answer. Shows how important significant digits are. |