TI BA II Plus: Calculating Duration, Modified Duration, Price Impact for change in YTM by +50bp

Exam Question: At the end of May 2013, one of your clients wants to invest 10’000 EUR in the bond market to diversify his fixed income portfolio. You will propose a bond 3,5% Italy 31.05.2016 (annual coupon). The yield to maturity of this bond is 2,7%. In case of an increase of 50 basis points, what will be the impact on the bond’s price?

Step 1: Calulate Bond Price with YTM 2.7%

a. use N, I/Y, PMT, FV to calulate current bond price

N = 3 (3 years), I/Y = 2,7 (YTM), PMT = 3,5 FV= 100   –> compute CPT PV = 102,276

Step 2: Calculate Duration of Bond

a. CF Menu: (leave CFO empty) CF1 = 1 * 3,5  N=1  / CF2 = 2 * 3,5  N=1 / CF3 = 3 * 103,50 N =1

b. use NPV key: I = 2,7   CPT NPV = 296,69365

c. Duration =  NPV / PV    so step 2b value divided by step 1a value    =  2,9009   or ~2,901

Step 3: Calculate Modified Duration (MD)

a. MD = D / 1+Y        2,901 * 1,027 = 2,8246 ~2.825

Step 4: Calculate Price Impact of a 50bp (0.005) increase in interest rates using Modified Duration (MD)

= – MD * change in interest rate  = -2.825 * 0.005 = -0.0141 = -1.41% solution: It will lower the bond price by 1,41%

Note: There are other ways to arrive at this solution. I intentionally used the duration example to be able to demonstrate using the Texas Instruments BA II Plus calculator.

Formula: Maculay Duration (Step 2)

FI_maculay-duration_formula

Forumla: Modified Duration , Price Duration (Step 3)

FI_modified_duration_price_duration

Forumla: Price change approximated with Modified Duration (Step 4)

FI_price_change_approximated_with_modified_duration

Numbers as in CIIA Exam 2003; Fo2-September2003-English-MCQ-8

2 thoughts on “TI BA II Plus: Calculating Duration, Modified Duration, Price Impact for change in YTM by +50bp

  1. J Smith

    What do you mean considering 10,000 Euros bond that has a PV of 102,276??? Did you mean 100,000 Euros?

    Reply
    1. mz Post author

      Hi Jason, that’s 102.276 – I’m use to the swiss way of writing numbers. Sorry for confusion. If it had been 102’276 I would’ve written it so.

      Reply

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