Building Curves

Investors will look at individual bond Yield-Curves as well as the general market yield curve.
This type of analysis is known as "relative value" analysis.
All investors will have a specific risk/reward profile they are looking for and Yield-Curves help them find it.
This describes the relationship between a particular maturity date and the corresponding yield (or interest rate).
This is the relationship between the cost of borrowing and time.
It is important that only bonds from the same class of issuer or with the same degree of liquidity, same coupon rate and same features are used to plot the yield curve.
The vertical axis shows the annual interest rate available in the market.
The horizontal axis shows the time of the investment.
A yield curve is the line connecting the interest rate that can be earned for different periods of time.
A yield curve is the graphical representation of the relationship between the interest rate on a particular class of security against time to maturity.

Why do we want to build interest rate curves.
(1) to provide us with projected discount rates so we can discount future cash flows (discounting curve)
(2) to provide us with projected forward rates for cash flows in the future (forwarding curve)

Spot Curve

A spot rate is the discount rate used to calculate todays value of a future cashflow.
Converts a future cash flow to todays value.

Forward Curve

A forward rate is the discount rate used to calculate the value of something in the future.
Implies the value of something on a give date in the future

Interest Rate Curves

Interest rate curves (or projected interest rates) are not published by market participants.
However you can use the prices of market instruments to build such a curve.

Importance of Yield-Curves

Swap valuations uses the zero coupon yield curve and forward rates.
Zero coupon rates are used to calculate discount factors
Forward rates are used to forecast floating payments of the swap.
Yield curves can be used for discounting cash flows

Separate Yield-Curves exist for:
Interbank lending/borrowing rates
Yields on government bonds (bills & note)

Relative Value Analysis

This is the process when investors compare a corporate bond yield curve to the US Treasury yield curve to determine if a bond is worth buying
All investors have a specific risk/reward profile that they are comfortable with and a bonds yield relative to its perceived risk will influence whether they buy or sell

Parallel Shift
Steepness
Curvature
Spread

Par swaps are used to construct yield curves

Factors Affecting Yield-Curves

Inflation
Supply / Demand
Liquidity Desires
The most important factor affecting a yield curve is the currency in which is denominated.
The ecomonic situation in that country is also very important.

Discount Curves - extract discount rates to "value" cashflows
Old Curve - uses specific instruments and bootstrapping
New Curve - uses market observables. Define the curve using discount factors at certain dates. Fits the curve to the market

The yield to maturity of a bond is the most frequently used measure for indicating the interest rate when you hold a bond to maturity.

Important

Yields are normally measured with continuous compounding interest.
When you compare two yield curves you get a yield spread.