# Yield Curve

## Yield Curve: Definition

The **yield curve** represents the relationship between bond yields of similar credit quality but with varying terms to maturity. Traditionally, bond traders construct the yield curve using the treasury bond yields as they are considered a risk free form of bond investing and carry no credit quality risk. Also, treasury securities have no issues with liquidity and therefore provide as a perfect benchmark to construct the curve. Yield curves are a function of liquidity; when there is ample liquidity in the market, the yield spread (difference between short term and long term rates) contracts due to the willingness of investors to chase short term debt and drive up yields.

## What is the Yield Curve used for?

The yield curve serves as an important benchmark as it used to set yields in other debt markets such as corporate debt, bank loans, international bonds, and even the mortgage markets. The shape of the yield curve is closely monitored by the bond community as it helps anticipate future interest rate changes. There are four main variations of the yield curve: normal, humped, inverted, and flat.

As the name suggests, the "**normal yield curve**" represents the typical yield to bond term relationship. The upward sloping curve generally indicates periods of economic prosperity and suggests that long term rates are higher than short term rates. This structure implies that a bond holder will be compensated for the additional risk of holding a bond for a longer period of time. Additionally, the "steepness" of this curve can be a function of strong economic prospects. Higher growth rates in the economy will lead to higher inflation levels in the future and thus higher interest rates.

The **humped yield curve** indicates that long term yields are the same or similar to short term yields and that medium term yields are actually higher than both. This formation is commonly thought of as a precursor to recession as the hump occurs during the transition from a normal to an inverted yield curve.

A **flat yield curve** suggests that short term and long term rates are in equilibrium. A flat yield curve does not compensate the bond holder for the additional risk associated with buying a longer term to maturity bond. Therefore, buying a shorter term bond usually makes more sense in this situation.

An **inverted yield curve** occurs in an interest rate environment in which short term rates are actually higher than longer term rates. This phenomenon is thought of to be a precursor to economic recessions.

## Pricing a Bond Using the Yield Curve

The value of a bond is defined as the present value of future cash flows. To determine the present value of a future coupon payment, an appropriate discount factor must be applied. In essence, we can view each cash flow as its own zero-coupon bond and by adding each cash flow together, we can arrive at the price of the bond. Therefore, we can say that we need to discount each of the future cash flows with a discount factor equal to that of a zero coupon treasury bond with a similar maturity. This discount factor, or yield, is known as the spot rate and the relationship between spot rates and term to maturity is referred to as the spot rate curve. There is one problem however; the Fed does not issue zero coupon bonds with a term greater than 1 year. This makes it impossible to create the spot rate curve without making theoretical assumptions on the yields of treasury securities with similar term structure; this is commonly referred to as bootstrapping. Bootstrapping is why the spot rate curve is also referred to as the theoretical spot rate curve.