1. Using the last 2 digits of your UIN:43,create your yield by adding 0.04 to the last 2 digits divided by 10000 (example: if last 2 digits are 26, then y = 0.04 + 26/10000 = 0.0426). Create your coupon by dividing the last 2 digits by 100 and adding 3.8 to it (example continued: 26/100 + 3.8 = 4.06). Now, using your unique coupon and yield, assume your bond has 28 years to maturity and pays a semiannual coupon (assume settle date is a coupon date). Answer the following questions:

(a) What is the price of the bond? (1)

(b) What is the modified duration? (1)

(c) What is the convexity measure? (1)

(d) What is the DV01 per million dollars? (1)

(e) Now consider 2 scenarios: The required yield rises 150 bps and the required yield falls 150 bps.

(a) Using just duration, what is the predicted price when yields rise 150 bps and when (2) they fall 150 bps?

(b) Using both duration and the convexity measure, what is the predicted price when (2) yields rise 150 bps and when they fall 150 bps?

(c) What are the actual P/Ls that would be realized on $20 million of face if rates rise (2) and fall by 150 bps? (Note: You will compute the actual price change in the scenarios.)

source('FixedIncomefn.r')

id <- 26

y <- 0.04 + id/10000

cpn <- 3.8+id/100

c(cpn,y)

## [1] 4.0600 0.0426

T <- 28

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2. 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 postion duration neutral?

Use the FixedIncomeFn functions to answer the question.

(b) What is 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?