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

Suppose you hold a bond with maturity of 3 years and coupon rate of 3.5%. 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:  Calculate Bond Price (PV)

N = 3 (3 years),

I/Y = 2.7 (YTM),

PMT = 35 (Annual Coupon Amount),

FV= 1000 (Face Value/Single Lump Sum)

CPT PV = 1,022.76

Step 2: Calculate Macaulay Duration of Bond

a.     CF Menu: (leave CF0 empty) 

CF1 = 1 * 35     N=1  /

CF2 = 2 * 35     N=1 /

CF3 = 3 * 1035  N =1

b.     use NPV key: I = 2.7   CPT NPV = 2966.9365

c.     Macaulay Duration = NPV/PV

so step 2b value divided by step 1a value    =  2.9009   or ~2.901

*Step 3: Calculate Modified Duration (MD)

MD = D / 1+Y        2.901 / 1.027 = 2.8246 (or ~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%

Formula: Macaulay Duration (Step 2)

Formula: Modified Duration , Price Duration (Step 3)

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