Fixed income: Bond DV01 (aka, price value of basis point, FRM T4-32)

Financial Risk Manager (FRM, Topic 4: Valuation and Risk Models, Fixed Income, Bruce Tuckman Chapter 4, One-factor Risk Metrics and Hedges). The DV01 stands for "dollar value of an .01% (one basis point)." It is also called the Price Value of a Basis Point (PVBP). It is the bond's or fixed income portfolio's dollar change given a one basis point decline in the yield. Discuss this video here in our FRM forum: trtl.bz/2WjLCYF
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[@shubhamsachdevardias8155]

Thank you

[@bhumanyusingh6347]

When you say that dP/dY is dollar duration for a 1 unit increase/decrease in the yield does that mean the yield will become 106% (1.06) from 6% (0.06), if yield were 6%? And if that is true, then how come we don't apply the same 10,000 adjustment while calculating modified duration from the dollar duration. Mod duration = Dollar duration / Price -> wouldn't this expression give us an elasticity where we get the % change in price of bond for 1 unit change (that is 6% to 106% , or 0.06 to 1.06) and not 1% change in the yield?

[@bionicturtle]

Yes, your logic is good and you are correct (except modified duration is a SEMI-elasticity: %ΔP/Δy rather than elasticity's %ΔP/Δy%). Say we have a $100 face 20-year zero-coupon bond with c.c. yield of 6.0%. The price is $100*exp(-6%*20) = $30.12 and the dollar duration is $30.12*20 = 602.39 and the slope of the line ∂P/∂y = -602.39 such that a +1 unit change in the X axis implies--as a LINEAR matter--a drop of 602.39. If we divide this dollar duration by price, we get the modified duration of 602.39/30.12 = 20 years. Similarly, the +1 unit change in the X axis implies a two thousand percent, -2,000% = 20 * 100%, reduction in price. Except we choose to refer to 1/100th of the unit, which is 1.0% as a PERCENTAGE POINT so that we apply in such a re-scaled way to say that a +1.0% (percentage point) yield change implies a 2,000/100 = 20% PERCENT price reduction. That's why I said it's a semi-elasticity: (percent_ΔP/ percentage_point_Δy). In summary, you are correct ;)

[@anirdbify]

at 9:54, you mentioned modified duration unit is years. Isn't that wrong?

[@bionicturtle]

it's correct: the units of modified duration are years.

[@TDesting]

@Bionic Turtle This cannot be true. If P has units dollars, D har units years, then the formula dv01 = (D*P)/10000 should give dv01 unit dollars*years. However, dv01 has units dollars. Hence, modified duration cannot have a unit for the formulas to make sense. It is Macaulay duration which has unit years

[@rodrigoavila5580]

Modified duration is just a %, units of Macaulay Duration is years.

[@fuehrer_tb5597]

Are PV01 and DV01 the same thing?

[@takkarsein1]

Yes

[@kannaiyand2707]

DV01 and Convexity both are same?

[@bionicturtle]

No not the same, DV01 is 1/10,000th of the first derivative; convexity is a function of the 2nd derivative