Reading the Yield Curve

This is originally posted on Saturday, 9 February 2013 at 14:45

Facing a chart of yield curve(s) may be daunting to many initiates. However the yield curve is not actually that mystical.

A good interpretation of the yield curve involves blending the observations (slope, shifts and volatility) of the yield curve(s) with theory and the background under which it is constructed.

Yield Curve, Term Structure and Sub-Assets

The Yield Curve depicts the relationship between interest rates and maturity terms at a certain point in time. While it is customary to perceive the Yield Curve as a continuous relationship, it is infact make up of many different assets: fixed-income assets of 2 years, 8 years, 20 years and many other maturity terms (horizontal axis) are plotted on a two-dimensional graph with their corresponding Yields (vertical axis).

The Yield Curve therefore depicts the combinations of Yield and Maturity Terms of different fixed-income sub-assets. The relationship is also known as the "Term Structure of Interest Rates".

Fixed-income (bond) refers to any type of investment under which the borrower/issuer is obliged to make payments of a fixed amount on a fixed schedule. In the case of a typical bond, the fixed amount will be the coupon payment and face value- all of which will be paid at a fixed schedule; the coupon is paid at regular intervals while the face value is paid at the bond's maturity.

Within the Fixed-Income (bond) Asset Class, there are sub-assets such as government bonds (aka glits), corporate bonds, emerging market debts and convertible securities.  The existence of sub-assets implies that the Fixed-income market is not a unified entity. Instead it is segmented into different sub-assets. This forms the foundation for the Segmentation theory which will be explored later.

Three Key Concepts associated with Interpreting the Yield Curve

At this point it is worth discussing three key concepts associated with interpreting the Yield Curve. The first will be Fisher Effect, the relationship between Yield and Bond Prices and "Premium".

Fisher Effect (information from Investopedia)

An economic theory proposed by economist Irving Fisher that describes the relationship between inflation and both real and nominal interest rates. The Fisher effect states that the real interest rate equals the nominal interest rate minus the expected inflation rate. Therefore, real interest rates fall as inflation increases, unless nominal rates increase at the same rate as inflation.

Read more: http://www.investopedia.com/terms/f/fishereffect.asp#ixzz2KO8IDHJZ

The crude form of Fisher's Equation can be expressed as 

i = r + [inf]

where i denotes the nominal interest rate and r denotes the real interest rate in the current period.  [inf] denotes the actual inflation rate in the following period. 

The inflation rate in the following period can only be predicted. Hence investors make their current investment decisions based on their expectations of future inflation.

The crude form of Fisher's Equation, taking E[inf] to be the expectation of the inflation rate in the following period, can be rewritten as 

i = r + E[inf] , which adheres to the definition above. 

It is noteworthy that the real interest rate is the investor's required rate of return. The nominal interest rate may fluctuate but as long as the required rate of return is met, the investor will still choose to invest in the asset. Changes in the expectations of future inflation rate will therefore affect the investor's desired level of nominal interest rates in future periods because of the Fisher effect's on real interest rates. s  

Yield and Bond Prices

The Yield (aka Yield to Maturity) is the internal rate of return of the bond. The Bond Price is calculated as the present value of the potential future cashflows that can be obtained from the bond. Therefore by differentiation, it is possible to show that the Yield is inversely related to Bond Price.

The Bond Price is however not dependent on the Yield. Rather it fluctuates according to the demand and supply for the bond. This concept is a critical component of the Segmentation theory.

Premium

The idea behind any kind of Premium is as follows:

Investors buy and hold assets for their returns.

All assets contain certain characteristics. 

However, some of these characteristics may be disadvantageous to the asset's holder.

There is a need to compensate the holder for these disadvantages.

Hence the asset provides a "premium" on its return to compensate specifically for such disadvantages.

Generally, the main disadvantage of holding a bond is the inability for the investor to convert  the bond to cash readily for transaction purposes. There is a need to compensate the holder by offering a "Liquidity Premium" on the returns of the bond ((liquidity refers to the ease of conversion from one asset to another).

Key Theories

1) Pure Expectations Hypothesis

The Pure Expectations Hypothesis is the proposition that long term interest rates are determined by the market's expectations of future short term rates. It is based on the assumptions that sub-assets are perfect substitutes and that expected forward interest rates are exactly identical to actual future spot interest rates because of perfect rationality.

The Pure Expectations hypothesis also incorporates the no-arbitrage argument: the price (present value) of assets with different Maturity Terms will actually equalize when discounted by their spot and forward interest rates, resulting in no scope for arbitrage between short-term and long-term bonds.

All payments in the intermediate periods are also reinvested until the bond expires. 

Mathematically, the long-term interest rate is a geometric average of short-term spot and forward interest rates.

Pure Expectations Hypothesis explains 

1) Shifts in Yield Curve

Shifts in the Yield Curve reflects the coordinated movement of interest rates between sub-assets of different Maturity terms. Expectations are affected by market signals.

If there is a macroeconomic shock leading to higher short-term interest rates in the current and future periods, it will result in higher long-term interest rates and consequently an upward shift of the yield curve.

This is especially pronounced in the case of rapid inflation. By the Fisher effect, the rise in inflation must necessarily lead to the rise in nominal interest rates by at least the same extent to meet the investor's required rate of return (real interest rate).

However the rise in current inflation does not just have an immediate effect on short term interest rates- it will also alter expectations of future inflation rates and therefore the short-term forward interest rates will also rise.

The rise in short-term interest rates across current and future periods will, by Pure Expectations theory, increase the long-term interest rates- this will be reflected by the upwards shift of the yield curve.  

2) Slope of Yield Curve 

The Pure Expectations provides a flexible explaination for almost every shape of the Yield Curve. A volatile yield curve reflects uncertainty and volatile expectations. An upward sloping yield curve reflects market belief that short-term interest rates will continue to rise in the futute. An inverted (downward sloping) yield curve reflects market belief that short-term interest rates will fall in the futute. A humped yield curve can essentially be conceived as a combination of upward and inverted yield curves. 

The key to providing a reasonable interpretiation regarding the slope of the Yield Curve lies in pinning down the root causes that affect market expectations.

For example, in November 2008 (in the midst of the Sub-Prime crisis), the Federal Reserve implemented Quantitative Easing by purchasing Mortgage-Backed Securities in order to increase liquidity in the economy, stimulate spending and lending activity. The yield curve on zero coupon treasury bonds for 31 December 2008 fell sharply to near zero levels for short-term (1 to 2 year) bonds, sloping sharply upwards till the 5 year maturity term, becoming gentler but still sloping upwards till the 20 year maturity term and leveling out thereafter. This can be explained in the following manner:

Although the Fed started QE in late November 2008, there will be an impact lag during which the market adjusts its expectations and the interest rate responds to the improved liquidity in the market.

The sharp upward sloping yield curve for bonds up to the 5 year maturity term reflects market confidence (expectations) in the US economy's potential recovery over the short to medium run; economic recovery tend to be inflationary and therefore accompanied by rising nominal interest (ie. the Fisher effect).

This confidence is partly attributed to the Federal Reserve's credibility and decisiveness in handling the Sub-Prime Crisis, which allays fears and improves the sense of security (risk climate) amongst key lenders such as banks and institutional investors.

However, the sharp upward slope of the yield curve may also reflect alternative expectations of mean-reversion; investors expect nominal interest rates to revert back to their historical averages in the future.

It may also suggest that the market predicts that the Federal Reserve will not maintain "easy credit" (which allegedly sow the seeds for the Crisis) and nominal interest rates are therefore expected to rise in the future.

Pure Expectations Hypothesis could not explain 

For most parts of history, yield curves were persistently upward sloping but seldom inverted, flat or humped. The expectations hypothesis fails to account for this phenomenon. Although expectations fluctuate, why was the predominant shape upward sloping instead of downward-sloping, flat or humped? This suggests that there are other factors other than expectations which affects yield curves. We shall turn to the Segmentation Theory for an answer. 

2) Segmentation Theory 

The Segmentation Theory is the proposition that long term interest rates are not correlated to short term rates across all time periods. It is based on the assumption that sub-assets are segmented into distinct markets by their Maturity Term. 

Investing entities have heterogeneous preferences, concentrating their activity at different spectrum (Maturity Terms) of the market. Prices (inversely related to yields) are determined by the demand and supply within markets of specific Maturity Terms, which are in turn affected by the availability of funds within each market. Therefore sub-assets of different maturities are not substitutes of one another. 

Sub-assets of different Maturity Terms are not perfect subsitutes because different maturities involve different risks of capital gains and losses. At the extreme, it is assumed that investors hold fixed preferences for certain Maturity Terms- they will not switch between sub-assets of different Maturity Terms. Hence short term interest rates will not affect long term interest rates because their assets appeal to different consumers (investors).  

According to the Segmentation Theory, the points along the Yield Curve are uncorrelated to each other; the corresponding levels of Yield and Maturity Terms merely reflect market dynamics within each Maturity Term.

Segmentation Theory explains 

1. Yield curves are usually upward-sloping

Investors are generally risk-averse. Most of them prefer the safety of short-term bonds. With a relatively greater demand, the prices of short term bonds will tend to be higher than long term bonds.

Since prices are inversely related to yields, the Yield Curve will generally reflect lower yields for short term bonds and higher yields for long term bonds.  

2. Humped Yield Curves

The humped yield curve, though a rare phenomenon, can be explained by the actions of institutional investors ("movers and shakers") and their respective preferences. 

Banks and Building Societies concentrate a large part of their activity at the short term bonds, as part of daily cash management (known as asset and liability management) and for regulatory purposes (known as liquidity requirements).

Fund managers such as Pension Funds and insurance companies are active at the long end of the market.

Few institutional investors have any preference for medium-dated bonds.

Therefore the behavior of institutional investors will lead to high prices (low yields) at both the short and long ends of the Yield Curve and lower prices (higher yields) in the middle. The resultant shape is a humped yield curve.