# Collar expiration

Hi

Could someone explain to me the answer?

Why does the first collar expiration occur on February 1 for payment on August 1?

Why is there no collar payment on the first February 1?

Thank you.

Qn:

On August 1, a bank enters a 2-year, zero-cost collar for a \$20 million portfolio of floating-rate loans by buying the floor and selling the cap. The floor strike is 2.5%, the cap strike is 4.7%, and the reference rate is LIBOR. The interest payments on the loan assets are LIBOR plus 240 basis points. The collar’s semiannual settlement dates exactly match the dates when the floating-rate payments are made: August 1 and February 1 over the next two years. Payments made August 1 cover 181 days and payments made February 1 cover 184 days. Current LIBOR is 4.1%. The values of LIBOR on the next three settlement dates are 2.4%, 5%, and 5%. Calculate the actual interest rate payments (to the bank), settlements, and effective interest payments.

Ans:

The first collar expiration will occur on February 1 for payment on August 1.

There will be no collar payment on the first February 1. The payoffs on the derivatives are:

Floorlets:

Year 1 payoff on Feb. 1 = N/A

payoff on Aug. 1 = \$10,056 = \$20,000,000[max(0, 0.025 − 0.024)(181 / 360)] Year 2 payoff on Feb. 1 = \$0 = \$20,000,000[max(0, 0.025 − 0.050)(184 / 360)]

payoff on Aug. 1 = \$0 = \$20,000,000[max(0, 0.025 − 0.050)(181 / 360)]

Caplets:

Year 1 payoff on Feb. 1 = N/A

payoff on Aug. 1 = \$0 = \$20,000,000[max(0, 0.024 − 0.047)(181 / 360)] Year 2 payoff on Feb. 1 = \$30,667 = \$20,000,000[max(0, 0.050 − 0.047)(184 / 360)] payoff on Aug. 1 = \$30,167 = \$20,000,000[max(0, 0.050 − 0.047)(181 / 360)] The interest payments are:

pmt. on Feb. 1 = \$664,444 = \$20,000,000(0.041 + 0.024)(184 / 360) pmt. on Aug. 1 = \$482,667 = \$20,000,000(0.024 + 0.024)(181 / 360) pmt. on Feb. 1 = \$756,444 = \$20,000,000(0.050 + 0.024)(184 / 360) pmt. on Aug. 1 = \$744,111 = \$20,000,000(0.050 + 0.024)(181 / 360)

The expiration is the date on which the LIBOR rate is set (and the payoff amount is determined). The amount is determined in advance (at the beginning of the 6-month period) and paid in arrears (at the end of the 6-month period). In that respect, it’s similar to a plain vanilla interest rate swap, or a floating-rate bond or note.