Question #20

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 MRR 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 MRR 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.