FRM2009.E1.37
Category:FRM2009 -> Full1
Question:
[Source 2009 FRM Full Exam 1] 37. Assuming other things constant, bonds of equal maturity will still have different DV01 per USD 100 face value. Their DV01 per USD 100 face value will be in the following sequence of highest value to lowest value:
a. Zero coupon bonds, par bonds, premium bonds
b. Premium bonds, par bonds, zero coupon bonds
c. Premium bonds, zero coupon bonds, par bonds
d. Zero coupon bonds, premium bonds, par bonds
[my adds]
37b. What is the difference between DV01 and modified duration?
37c. What is the impact of maturity on DV01 (e.g., increasing)?
37d. What is the impact of yield (YTM) on DV01
Answers:
Source:
37. CORRECT: B
DV01 is certain multiple of Dirty Price (which includes Coupons) and not Clean Price. Thus, it is proportional to Base Price, which is Dirty Price. Ordinarily, Premium Bond will have the highest (dirty) price followed by Par Bond and with the least price of Zero Coupon Bond. Hence, DV01 of Premium Bond is the highest while that of Zero Coupon Bonds is the lowest.
INCORRECT: A - Premium Bond will have a higher Base Price and hence higher DV01 than that of Zero Coupon Bond.
INCORRECT: C - Base Price of Par Bond is higher than that of Zero Coupon Bond and hence, its DV01 cannot be less than that of Zero Coupon Bond.
INCORRECT: D - DV01 per USD 100 Face Value is an Absolute Amount of USD based on actual Base Price Change. Ordinarily, Base Price of a Zero Coupon Bond will be lower than that of Par & Premium Bond. Hence, DV01 of Zero Coupon Bond is less than that of Premium Bond of same maturity. Reference: Tuckman, “Fixed Income Securities”, Chapter 5.
The explanation above doesn’t help me much! Tuckman is more to the point. First note the definition of duration:
DV01 = Price * Modified Duration / 10,000
DV01 is a function of both price and duration. Says Tuckman, “Not surprisingly, for a given duration, bonds with higher prices tend to have higher absolute price sensitivities. So while duration almost always increases with maturity, (6.32) shows that the behavior of DV01 with maturity also depends on how price changes with maturity. What will be called the duration effect tends to increase DV01 with maturity while what will be called the price effect can either increase or decrease DV01 with maturity.” ...Inspection of equation (6.25) reveals that the DV01 of par bonds always increases with maturity. Since the price of par bonds is always 100, the price effect does not come into play, and, as in the case of duration, longer par bonds have greater price sensitivity. The curve approaches .2, the DV01 of a par perpetuity at a yield of 5%. As discussed in Chapter 3, extending the maturity of a premium bond increases its price. As a result, the price and duration effects combine so that the DV01 of a premium bond increases with maturity faster than the DV01 of a par bond. Of course, at some maturity beyond the graph, the price of the bond increases very slowly and the price effect becomes less important. The DV01 eventually approaches that of a perpetuity with a coupon of 9% (i.e., .36).”
In short, DV01 is a function of price and duration. Recall that a bond is always pulled to par: a discounted (or zero) coupon bond must decrease in price with longer maturity. Therefore, for a discounted bond only, the impact of maturity on DV01 is mixed: higher duration but lower price.
37b. What is the difference between DV01 and modified duration?
Only difference is units: “The major difference between DV01 and duration is that DV01 measures an absolute change in price while duration measures a percentage change. To understand how this difference impacts the behavior of DV01”
37c. What is the impact of maturity on DV01 (e.g., increasing)?
As above, it depends on whether bond is premium/discount/par:
For par or premium bonds (see left chart above): DV01 is increasing with maturity (i.e., both price and duration are increasing!)
For discount (and zero) bonds: DV01 is initially increasing but then decreasing (i.e., as price is decreasing function, which offsets duration increasing)
37d. What is the impact of yield (YTM) on DV01
DV01 is decreasing (i.e. falls) with increasing yield (see chart above at right)