The asked quotes in July 2015 for three Treasury securities are shown below. The

Question

The asked quotes in July 2015 for three Treasury securities are shown below. These securities are noncallable. Assume an interest payment was just paid on the bond and note. The face value of each security is $1,000.

Friday, July 31, 2015:

T-Note

Maturity

Coupon

Bid

Asked

Chg

Asked Yield

7/31/2019

0.875

98:0675

98:0725

0:0875

?????

Assume settlement is Tuesday, August 4, 2015 for T-note; so days to maturity is 1,456 days.

T-Bond

Maturity

Coupon

Bid

Asked

Chg

Asked Yield

1/31/2021

2.125

102:055

102:06

0:13

?????

Assume settlement is Tuesday, August 4, 2015 for T-bond; so days to maturity is 2,006 days.

T-Bond, Stripped Principal

Maturity

Bid

Asked

Chg

Asked Yield

1/31/2022

88.581

88.637

0.291

?????

Assume settlement is Tuesday, August 4, 2015 for T-bond Strip; so days to maturity is 2,371 days.

Remember that Treasury bonds and notes are quoted in 32nds. That is, a quote of 101:165 is 101 16.5/32 = 101.515625% x $1,000 = a price of $1,015.15625 or $1,015.16. Strips are quoted as a % of 100.

           

Using the above information, for each security perform the following:

Calculate the yield to maturity. This should be an annual rate. Round to 3 decimal places.

Assume the yield to maturity rises a full 1 percent. Calculate the new asked price.

Calculate the security’s' duration (in years) using the YTM calculated in #1.

Calculate the convexity of the security using the YTM calculated in #1.

Assuming the YTM of the security increases a full 1 percent,

Determine the "duration-estimated" new price. Compare with your results in #2. Explain what has happened.

Determine the "duration-plus-convexity-estimated" new price. Compare with your results in #2 and #5a. Explain what has happened.

T-Note

Maturity

Coupon

Bid

Asked

Chg

Asked Yield

7/31/2019

0.875

98:0675

98:0725

0:0875

?????

Explanation / Answer

Face value of each security: $1,000

Calculate the yield to maturity. This should be an annual rate. Round to 3 decimal places.

T-Note:

Days to maturity, Y = 1,456 days =~4 years

Coupon rate = 0.875%

Coupon Amount, C = 0.875%*1000 = $8.75

Bid Price = 98: 0675 = 98 (6.75/32) = 98.2109% * $1000 = $982.109 = Bond Price

YTM = (Annual Interest + ((Par Value - Market Value)/(Years to Maturity)))/((Par Value + Market Value)/2)

Hence, Yield to Maturity = 1.335% (using calculator)

T-Bond:

Days to maturity, Y = 2,006 days =~5.5 years

Coupon rate = 2.125%

Coupon Amount, C = 2.125%*1000 = $21.25

Bid Price = 102: 055 = 102 (5.5/32) = 102.1719% * $1000 = $1021.719 = Bond Price

YTM = (Annual Interest + ((Par Value - Market Value)/(Years to Maturity)))/((Par Value + Market Value)/2)

Here, Yield to Maturity = 1.711%

T-Bond, Stripped Principal:

Here the annual Interest paid is Zero

Bid Price: 88.581

Maturity: 31st Jan 2022

YTM = (Annual Interest + ((Par Value - Market Value)/(Years to Maturity)))/((Par Value + Market Value)/2)

Here, Yield to Maturity = 1.864%

Assume the yield to maturity rises a full 1 percent. Calculate the new asked price.

T-note: YTM: 1.335%+1% = 2.335%

Based on the above formula,

Ask Price = $945

T-bond: YTM: 1.711%+1% = 2.711%

Based on the above formula,

Ask Price = $981

T-bond, stripped principal: YTM: 1.864%+1% = 2.864%

Based on the above formula,

Ask Price = $832

Calculate the security’s' duration (in years) using the YTM calculated in #1.

T-note: 1,456 days = 1,456/365 = 3.99 years

T-bond: 2.006 days = 2,006/365 = 5.50 years

T-bond, stripped Principal = 2,371 days = 2,371/365 = 6.50 years

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