Michael Brenndoerfer | Data & AI, Private Equity, Technology

Michael Brenndoerfer

Bond Risk Measures and Immunization › Dollar Duration and DV01

Michael BrenndoerferNovember 8, 20252 min read

Quantitative FinanceAll chapters

Part 2 of 15Equity and Fixed Income Markets

Chapter 13Bond Risk Measures and Immunization › Dollar Duration and DV01

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Practitioners often work with dollar-denominated risk measures rather than percentage changes. This preference arises for practical reasons. When hedging a portfolio or calculating profit and loss, dollar amounts matter directly. Two common metrics translate duration into dollar terms.

Money duration (also called dollar duration) is modified duration multiplied by the position's market value. It is the magnitude of the first-order dollar sensitivity to a unit change in decimal yield. Multiply it by 0.01 for a one-percentage-point move:

\text{Dollar Duration} = D_{Mod} \cdot P

where $D_{Mod}$ is modified duration and $P$ is the bond price.

This measure tells us the absolute dollar exposure to interest rate changes. A position with higher dollar duration has greater dollar risk, regardless of whether that position represents a large investment in low-duration bonds or a small investment in high-duration bonds.

DV01 (Dollar Value of a 01, also called "price value of a basis point" or PVBP) measures the dollar change for a one basis point (0.01%) change in yield:

\text{DV01} = D_{Mod} \cdot P \cdot 0.0001

The factor 0.0001 is a one-basis-point yield move expressed in decimal units: 1 bp = 0.01 percentage points = 0.0001.

Use the same decimal-yield unit as the derivative: a one-basis-point increase is $\Delta y=0.0001$ , so the first-order dollar loss is $D_{Mod}P\times0.0001$ . Traders use DV01 to compare dollar sensitivities to small yield movements.

These measures are particularly useful for hedging, as they express risk in dollar terms that can be directly compared across positions. If one unit has a DV01 of $50 and another has a DV01 of $25 to the same yield factor, two short units of the second offset the first-order exposure of one long unit of the first. This does not also match their convexity, curve-shape or credit exposures.

In[18]:

Code

dollar_duration = mod_dur * price
dv01 = mod_dur * price * 0.0001

print("Bond: 10-year, 5% coupon at 5% yield")
print(f"Price: ${price:.2f}")
print(f"Modified Duration: {mod_dur:.4f}")
print(f"Dollar Duration: ${dollar_duration:.2f}")
print(f"DV01: ${dv01:.4f}")
print("\nInterpretation:")
print(
    f"  - A 1 percentage point yield increase causes ~${dollar_duration * 0.01:.2f} price decrease"
)
print(f"  - A 1 bp yield increase causes ~${dv01:.4f} price decrease")

Out[18]:

Console

Bond: 10-year, 5% coupon at 5% yield
Price: $1000.00
Modified Duration: 7.7946
Dollar Duration: $7794.58
DV01: $0.7795

Interpretation:
  - A 1 percentage point yield increase causes ~$77.95 price decrease
  - A 1 bp yield increase causes ~$0.7795 price decrease