You own a bond portfolio worth $220,462. You estimate that your portfolio has an

Question

You own a bond portfolio worth $220,462. You estimate that your portfolio has an average yield-to-maturity of 3.2% and Macaulay Duration of 10.7 years. If interest rates went down one percentage point and your portfolio's yield-to-maturity changed by the same amount, what would be the new value of your bond portfolio?

(Hint: Not covered in the eText. Check your class notes and the TopHat note titled "Bond risk and duration".

Step 1: Compute DV01 as the portfolio's MacD divided by 1 plus the portfolio's YTM, multiplied by the value of the portfolio and divided by 100.

Step 2: Compute the change in the portfolio's value based on its starting value given in the question and the estimated change in value from Step 1).

Explanation / Answer

DV01 is the change in dollar value of the bond with the change in 1 basis point yield.

DV01 = -MacD/(1+YTM) * P * % change in rate

where MacD = Macaulay Duration, YTM = Yield to maturity, P = Initial price

Let us assume that % change in rate is 1 basis point, i.e. 0.01%

Therefore,

DV01 = [ -10.7/(1 + 0.032) ] * 220,462 * [ 0.01 / 100 ]

= -228.58

Therefore with a basis point increase in interest rate, the value of the portfolio will decrease by $228.58

The new value of the bond portfolio = 220462 - 228.58 = $ 220233.42

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