CFA Practice Question

There are 227 practice questions for this study session.

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:

L60(30) = 0.0425 L60(120) = 0.0432 L60(210) = 0.0437 L60(300) = 0.0444

What is the value of the swap?
A. $7,900
B. $5,300
C. $4,700
Explanation: The new set of discount factors is:
PV60(90) = 1 / (1 + 0.0425 x 30/360) = 0.9965
PV60(180) = 1 / (1 + 0.0432 x 120/360) = 0.9858
PV60(270) = 1 / (1 + 0.0437 x 210/360) = 0.9751
PV60(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.
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