Hedging: Suppose you have a bond portfolio with face value PortF and DV01 of DVport and wish to hedge interest rate risk by selling short another security with DV01 of DVhedge. You will sell the following face amount of the hedging security to be duration hedged: PortF DVport + X DVhedge = 0 = PortF DVport = X DVhedge = X = PortF DVport DVhedge

(a) A portfolio manager purchases B million face of a JNJ bond and wishes to hedge it with (3) the current 20-year on-the-run Treasury bond. You determine B by adding the last 2 digits of your UIN to 150 (example: last 2 digits is 26, so B is 176 million). Specification Maturity Coupon Payment Frequency Yield Settlement Date Day Count Convention JNJ Bond 05/15/2041 4.85% semi-annual 2.66% 06/30/2021 30/360 20-Year Treasury 05/15/2041 2 1/4% semi-annual 2.04% 06/29/2021 act/act Bond Specifications How much of the Treasury bond is required to be sold short to make the position duration neutral? Use the FixedIncomeFn functions to answer the question.

Bond Specifications Specification BMY Bond 20-Year Treasury Maturity 10/15/2040 08/15/2041 Coupon 4.70% 1 3/4 % Payment Frequency semi-annual Yield 3.18% 2.11% Settlement Date 10/13/2021 10/12/2021 Day Count Convention 30/360 act/act

(b) What are the change in value for the portfolio and the hedge if interest rates increase 1 bp? (3) What is the net P/L? Compute the actual P/L and not the one predicted using DV01.

(c) This hedge will need to be rebalanced to make it duration neutral as yields move a signif- (3) icant amount.

Suppose you dont rebalance, then what is the actual P/L resulting from changing yields, when yields rise 150 bps? (d) Suppose after the yields have risen 150 bps you rebalance the Treasury hedge. What is (1) the rebalanced Treasury position?