Assume the following information about a Treasury bond: Coupon: 5.5% Maturity: N

Question

Assume the following information about a Treasury bond: Coupon: 5.5% Maturity: November 15, 2009 Settlement date: September 13, 2005 (think of this as "today") Yield: 5.25% You may assume that the par value of this bond is 100. Also remember that Treasuries pay coupons SEMI-ANNUALLY. Find the Accrued Interest, the Price, and the Modified Duration of this bond. Using the Modified Duration, what is the approximate percentage change in price for a 25 basis point change in yield? Find the price if the yield is 5.5% (why is the total cost not equal to Par?). Find the price if the yield is 5.0%, did the price change by more or less than was predicted? Why? Suppose you hold this bond for example 6 months and the yield does indeed increase to 5.5%. What is your total return for this bond?

Explanation / Answer

2)Modified duration of this bond can be calculated using Mduration function:

Settlement date

9/13/2005

Maturity date

11/15/2009

Coupon rate

5.50%

Yield

5.25%

FV

1000

Modified duration

3.63

% change in price = Modified duration x change in yield

                                    = 3.63 x0.25%

                                    =0.91%

3) Since at 5.5% yield, coupon rate and yield will be the same, the price of the bond would be equal to par value of the bond that is 1000

4) Price at yield 5%, can be calculated using PRICE function:

Settlement date

9/13/2005

Maturity date

11/15/2009

Coupon rate

5.50%

Yield

5.00%

FV

1000

Price

1018.54

5) Price of the bond at 5.25% yield:

Settlement date

9/13/2005

Maturity date

11/15/2009

Coupon rate

5.50%

Yield

5.25%

FV

1000

Price

1009.18

Buying price of the bond = 1009.18

Price after six months = 1000

Coupon amount = 1000x5.5%/2 =27.50

Total return = (Ending price + coupon – buying price)/ Buying price

                                = (1000+27.50-1009.18)/1009.18

                                = 1.82%

Settlement date

9/13/2005

Maturity date

11/15/2009

Coupon rate

5.50%

Yield

5.25%

FV

1000

Modified duration

3.63

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