Question

1. Suppose you are a money manager who manages a portfolio of two bonds, A and B. Bond A is a 5% semi-annual coupon bond with 5 years to maturity; its par value is $1000; the YTM is 7%; there are 10,000 units of bond A held in the portfolio. Bond B is a 3-year 6% semi-annual coupon bond, $500 par value, and its YTM is 8%; you hold 5,000 units of Bond B. (You must keep 5 decimal places in all steps, eg. $5.67867, otherwise you get 0)

A. [12 points] What is the duration of Bond A and Bond B? (you can use excel)

B. [6 points] If the YTM for both bonds increases by 50 basis points, what is, in dollar amount, the change in the value of the portfolio? You MUST use modified duration method to solve this problem.

2. You are a US. Treasury bond dealer who trades a 4.75%, 3year, semi-annual coupon bond. Your required YTM is 0.92826126%. How should you quote your asked price in percentage of par value (rounded to two decimal points)?

3. Suppose today is Oct 23, 2013. A bond with a 10% coupon paid semiannually every February 15 and August15 is listed as selling at an ask price of 102:11. If you buy the bond from a dealer today, what invoice price (dirty price) will you pay for it? The coupon period has 182 days.

Answer 1

(1)

(A)

(B)  Change in YTM = 50 bps

% Change in Bond A's price = - (Bond A modified duration) x (50/100) = - 4.31 x 0.5 = - 2.155 %

New Price of Bond A = (1-0.02155) x Old Bond Price = (1-0.02155) x 916.83 = $ 897.07

% Change in Bond B's price = -(Bond B modified duration) x (50/100) = - 2.68 x (50/100) = - 1.34 %

New Price of Bond B = (1-0.0134) x Old Bond Price = (1-0.0134) x 473.79 = $ 467.44

Number of units of Bond A = U(a) = 10000 and Number of units of Bond B = U(b) = 5000

New Portfolio Value = 10000 x 897.07 + 5000 x 467.44 = $ 11307900

Old Portfolio Value = 10000 x 916,83 + 5000 x 473.79 = $ 11537250

Change in Portfolio Value = 11307900 - 11537250 = - $ 229350

NOTE: Please raise a separate query for solutions to the remaining unrelated questions.