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# L1.T4.15. Dollar value of an '01 (DV01; aka, DVBP, PV01)

#### David Harper CFA FRM

##### David Harper CFA FRM
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AIMs: Describe four ways in which measures of fixed income price sensitivity are used. Describe an interest rate factor and name common examples of interest rate factors. Define and compute the DV01 of a fixed income security given a change in yield and the resulting change in price.

Questions

15.1. A bond portfolio manager makes the following two statements:

I. "We hedged our bond position (B), which has a duration of 6.5 years, with the hedge portfolio (H), which also has a duration of 6.5 years. Therefore, if interest rates increase by 20 basis points, the percentage decrease in the value of (B) will be equal to the percentage increase in the value of (H)."
II. "We have a short position in a portfolio of plain-vanilla [ie., no embedded options] coupon-bearing bonds, with portfolio duration of 5.0 years. Therefore, if yields increase by 20 basis points, our gain will likely be less than 1.0%, but if yields decrease by 20 basis points, our loss will likely be greater than 1.0%"

Which of the above statement(s) is (are) true?
a. Neither is true
b. I. only
c. II. only
d. Both I. and II. are true

15.2. In regard to interest rate factors, which of the following statements is necessarily TRUE?
a. If we estimate the change in bond price using both duration and convexity, we are using a two-factor model
b. Any single-factor interest rate model, by definition, assumes a parallel shift in the term structure of spot rates
c. The spot (zero) rates, par rate and yield (YTM) can be the single interest rate factor, but a forward rate cannot be the single factor as it represents a curve of several rates
d. The yield-based DV01 is a special case of the DV01 in which the single interest rate factor is yield-to-maturity (YTM)

15.3. A 30-year bond pays a semi-annual coupon with a coupon rate of 2.0%. The bond's yield (YTM) is 7.0% and its current price is $37.64. What is the bond's dollar value of an '01 (DV01; aka, DVBP or PV01)? a.$0.01
b. $0.03 c.$0.06
d. $0.12 15.4. Under semi-annual compounding, what is the DV01 of a$100 face value 10-year zero-coupon bond with a yield of 8.0%?
a. $0.044 b.$0.099
c. $0.152 d.$0.227

15.5. The modified duration is 10.46 years of a bond with a current price of $716.38. What is the bond's DV01? a.$0.40
b. $0.75 c.$1.25
d. Need more information (yield, maturity)

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