# What’s the Difference Between PV01 and DV01 of a Bond?

PV01 and DV01 are two metrics to measure the price sensitivity of bonds with respect to market interest rate and bond yield respectively.

Let us discuss what are PV01 and DV01 and their calculation methods.

# What is the Dollar Duration (DV01) of a Bond?

The dollar valuation (DV01) is a method to assess the sensitivity of the dollar price of a bond against a change in the market interest rate.

Interest rate is often described in terms of basis points. So, the dollar valuation method measures the change in the price of a bond due to a change in the interest rate for every 100 bps.

It means this method is one of the several risk-measuring metrics for bonds. It measures the interest rate risk for bonds and bond portfolios.

Unlike other financial metrics which measure in percentage terms, the dollar duration gives a direct dollar amount result.

# Understanding Dollar Duration DV01 of a Bond

Dollar duration or DV01 is also called the money duration of a bond. It uses a linear expression to describe the change in the price of a bond due to a change in the interest rate.

It can also be used for other fixed-income securities to calculate the dollar price change. However, it is suitable for an instrument with fixed and consistent income returns.

In practice, the expression or the relationship between bond price and interest rate is not linear. Therefore, dollar duration is only applicable for small durations.

The dollar duration method can be applied for bonds with zero-coupon or fixed-rate coupons at small intervals.

Also, the bond price changes are affected by other market factors as well. Therefore, the dollar duration does not cover all of these risks and does not depict a complete scenario of measuring the price change for a bond.

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# How to Calculate the DV01 of a Bond?

The DV01 or the dollar value per basis point is an expression to link the bond price and interest rate changes.

Dollar duration can be calculated using the following formula:

Dollar Duration = DUR x (∆i/1+ i) x P

DUR = duration of the bond

∆i= change in the interest rate

And p = Bond Price

This formula is used for calculating the dollar duration of a single bond. The same formula can be used to calculate the weighted dollar duration of a bond portfolio.

# Pros and Cons of Using DV01 for a Bond

DV01 or the money value of a bond is a useful metric. It has its pros and cons.

Pros Explained

The calculation of DV01 is simple. It can be used to calculate the linear relationship between the dollar price and the change in the market interest rate quickly.

We can use the same formula to assess the sensitivity of the price change of a bond portfolio to the change in the interest rate.

Cons Explained

DV01 is not an effective measure of assessing the interest rate risk of bonds. Several other factors affect the price of a bond.

These risks include price risk, market risk, and reinvestment risks associated with bonds. Therefore, the price change of a bond should reflect the combined impact of all of these risk factors.

Also, the relationship between the two factors in the DV01 formula is not linear. It means it is useful only for small intervals where the change is consistent and fixed.

# What is the Price Value of a Basis Point (PV01) of a Bond?

The price value of a basis point or PV01 is the measure of change in the price of a bond due to a unit change in the yield of the bond.

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It is also called the dollar price change or the value of a base point of a bond. It measures the change in the price of a bond due to a 1 basis point or 0.01% change in the yield.

Bond yield is the interest or coupons received by an investor during the term of the bond. It also includes the face value of the bond which the bond issuer repays to the bond investor at maturity.

A better and more inclusive measure of bond yield is yield to maturity (YTM). YTM measures the returns received by a bond investor in the present value terms or discounted in today’s terms.

# Understanding PV01 of a Bond

The bond price and yield have an inverse relationship. It means the bond prices will fall when yield increases and vice versa.

Several other factors contribute to the change in the market price of a bond. A change in its yield is one of these factors.

The PV01 measures the change in the market price of a bond when the yield changes by 1 basis point of 0.01%.

The inverse relationship between the yield and bond price means an increase in the yield would result in a fall in the bond price and vice versa. The PV01 calculations will reflect the same rule as well.

# How to Calculate the PV01 of a Bond?

The PV 01 of the bond can be calculated directly if the yield of the bond is known.

The PV01 formula is given here.

BPV = Yield x 0.0001

An alternative approach to calculate PV01 is:

BPV = Modified duration x Dirty Price x 0.0001

Here modified duration represents the change in the price of the bond due to a change in the yield.

The dirty price refers to the total price paid to purchase a bond including accrued interest of the bond until the purchase date.

Simplifying the equation means the multiplier of the modified duration and the dirty price will be equal to the yield of the bond.

# Pros and Cons of Using PV01 for a Bond

Let us briefly discuss the pros and cons of PV01.

Pros Explained

PV01 is a simple method of calculating the price volatility of a bond. A significant basis point value means a larger impact on the bond price.

The same formula can be used to measure the price volatility of a bond portfolio. However, it must include other risk factors to assess the bond price change as well.

Cons Explained

PV01 is not an inclusive measure of the price volatility of a bond. Several other factors like coupon rate, time to maturity, and market risks affect bond prices.

Therefore, PV01 can be used with a limited implication on the price sensitivity of bonds.

# PV01 and DV01 Summary of Key Differences

PV01 and DV01 are both price sensitivity measures of bonds.

DV01 measures the linear relationship between the bond price and the interest rates. It is only useful when the bond coupons are fixed and consistent.

Also, DV01 can be useful only for small intervals for consistent results.

PV01 links the yield of a bond with its price. The yield and the bond price have an inverse relationship.

PV01 describes the impact of a 1 basis point change in yield on the bond price.

The drawbacks and limitations of both PV01 and DV01 are similar as these metrics ignore other risk factors affecting directly the prices of bonds.

Therefore, both these metrics have limited utility in practical terms.