FRA Question

My issue with the question below is that I cannot figure out what time we are in right now and what we are valuing. Even after reading the answer, I don’t get why they’re going ahead to day 150 while supposedely at day 60. Can someone help to illustrate just what the timeline here looks like? 30 days ago, J. Klein took a short position in a \$10 million 90-day forward rate agreement (FRA) based on the 90-day London Interbank Offered Rate (LIBOR) and priced at 5%. The current LIBOR curve is: 30-day = 4.8% 60-day = 5.0% 90-day = 5.1% 120-day = 5.2% 150-day = 5.4% The current value of the FRA, to the short, is closest to: A) −\$15,495. B) −\$15,280. C) −\$15,154. Your answer: C was correct! FRAs are entered in to hedge against interest rate risk. A person would buy a FRA anticipating an increase in interest rates. If interest rates increase more than the rate agreed upon in the FRA (5% in this case) then the long position is owed a payment from the short position. Step 1: Find the forward 90-day LIBOR 60-days from now. [(1 + 0.054(150 / 360)) / (1 + 0.05(60 / 360)) − 1](360 / 90) = 0.056198. Since projected interest rates at the end of the FRA have increased to approximately 5.6%, which is above the contracted rate of 5%, the short position currently owes the long position. Step 2: Find the interest differential between a loan at the projected forward rate and a loan at the forward contract rate. (0.056198 − 0.05) × (90 / 360) = 0.0015495 × 10,000,000 = \$15,495 Step 3: Find the present value of this amount ‘payable’ 90 days after contract expiration (or 60 + 90 = 150 days from now) and note once again that the short (who must ‘deliver’ the loan at the forward contract rate) loses because the forward 90-day LIBOR of 5.6198% is greater than the contract rate of 5%. [15,495 / (1 + 0.054(150 / 360))] = \$15,154.03 This is the negative value to the short.

-30…0…60…150 30 days ago took a 90 day forward agreement on 90 day LIBOR so it was a 3 x 6 FRA taken 30 days ago. if it had been time zero today 0…90…180