### Basis Point Value

Also known as DV01, Delta, BPV, DVBP, Dollar value of a basis point

Provides an estimate for how much a price will change for a 0.01% parallel movement in the yield curve
This is a generic terms and can be used to describe interest rate risk for various instruments
DV01 - This is the dollar value of 1 basis point ??
This is the delta or first order measure
measured in dollar terms

simple to calculate
widely used and understood
can be used for money market instruments and swaps
can be used to calculate simple hedge ratios

does not take into account any changes in the yeild curve
assumes the yield curve moves up and down in a parallel shift

#### Bonds

The change in net present value for a 1 basis point shift in the swap curve

Example
price a bond with a coupon 4.0%
Price a bond with a coupon 4.01%

longer dates bonds have a larger DV01.

This is the price value of a basis point
This is the price change of a basis point
This indicates how much the price will change if the yield changes by 1 basis point.
For small changes in yield (either up or down) the price volatility is the same
You can increase or decrease the yield to calculate the price value of a basis point because price volatility is approximately symmetrical for small yields
The DV01 is smaller the higher the initial yield
At higher yields, price volatility is less
The larger the DV01 the greater the convexity

(h3)Price Change of N basis points
The price change of N basis points is found by calculating the difference between the initial price and the price if the yield changes by N basis points.
The price value of a small number of basis points is roughly that of 1 basis point multiplied by N
When N < 10 you can still increase or decrease the yield to approximate the price volatility.

(h3) Small Yield changes (N>10)
When N is more than 10 basis points a slightly more accurate approximation is to average the two
First calculate the difference between the initial price and the price if the yield changes by increasing it by N basis points
Calculate the difference between the initial price and the price if the yield changes by decreasing it by N basis points
And then average the two

(h3) Bond Portfolio
The price value of a basis point for a portfolio is just the sum of the price value of a basis point for each of the individual bonds

(h3) Percentage change of basis point
The percentage change of a basis point can be calculated by dividing by the initial price

Percentage change = (price change of a basis point / initial price)

(h3) Hedging
If you bought a corporate bond (ie have a long position) and wanted to hedge this position you would need to take a position which will offset any loss from holding this bond.
Once possible strategy might be to sell a treasury bond
To do this effectively the price volatility of your position must equal the price volatility of your hedge.
There are two immediate problems:
1) For a given change in yield the price volatility of the two instruments will be different

Dollar price change of corporate bond = (dollar price change of hedging instrument) x ( (dollar price volatility of corporate bond ) / ( dollar price volatility of hedging instrument) )

Dollar price change of corporate bond = dollar price change of hedging instrument x [ hedge ratio ]

Hedge ratio = [ (price change of 1 basis point for corporate bond) / (price change of 1 basis point for hedging instrument)] x
[ (change in yield for corporate bond) / (change in yield for hedging instrument) ]

2) The other problem is that the factors that will influence a change in yield will affect the two instruments differently.
If the corporate bond yield changes by 2 basis points, the hedging instrument could change by more or less than 2 basis points

For example - Treasury 6.75 2010 pays a £6.75 coupon for every £100 of the nominal and is repaid in 2010

The price of the bond in February 2006 was £88.13

so interest yield = (interest rate (6.75) / market price (88.13) * 100 = 7.66%

Interest Yield is also known as Income Yield, Flat Yield, Running Yield

Redemption Yield - combines the interest yield with the notional gain (or loss) to redemption

Bonds that are below their par value have a gain to redemption
Bonds that are above their par value have a loss to redemption (redemption < interest yield)

Scenario:
March 1995, interest rates 7%
Treasury 13.5 2004-2008 had a price of 128.25
Obviously the assumption was that the government would pay it as soon as possible.

assuming redemption in 2004, interest yield was 10.53%, redemption yield was 8.91%

The redemption yield is only relevant to the investor if they hold the bond until redemption.

In the interim the price will fluctuate but will obviously approach 100 as the redemption date approaches. This is known as the "Pull to redemption"

The redemption yield is the main yard stick used for comparing one bond with another and for calculating the price (?)

Bonds > Yield Curves
A yield curve shows the interest rates that can be locked in now for different periods of time
The y-axis is the annual interest rate available in the market place
The x-axis shows the length of time
The yield curve is a line connecting the different rates of return available in the marketplace.

Government bonds are often used to construct yield curves becuase:
they have a broad range of maturities available
all maturities have The same credit risk
Any differences in coupon rates are nullified by using stripped (or zero coupon) versions of The various bonds

In theory for each future coupon payment, there exists a zero coupon rate that discounts the payment to its present value

It is impossible to estimate the zero coupon curve from an existing par bond yield curve.