## 7.2 The Term and Risk Structure of Interest Rates

By taking credit risk and the length of the lending period into account, differences in nominal interest rates, at a point in time, can be explained with the following equation:

imarket = {r* + E[πt]} + ρ + λ

The first two components in brackets are the desired rate of return and expected inflation that make up the core of any interest rate at a point in time. The third component 'ρ' is known as the risk premium established by credit markets for different categories of risk. This value may be large or small depending on how risk averse lenders might be at any point in time.

The last component 'λ' is known as the liquidity premium which represents the amount of compensation required by a lender for lending to the long end of the market. For example if the T-Note rate is 4.24% and the T-Bond rate is 6.21%. The 1.97% difference implies that lenders require an additional \$19.70 per \$1,000 lent for 30 year loans relative to 5-10 year loans to the Federal government. Greater uncertainty about future rates of inflation or future political events will often widen the spread between the medium and long term. The differences that exist in nominal rates due to this liquidity premium are summarized in the frequently published yield curve constructed by using the different treasury rates (risk-premium = 0) that exist on a given date.

#### 7.2.1 The (Credit) Risk Premium

Different classes of borrowers can be assigned different levels of risk. This measure of risk, known as credit risk, reflects information about different types of borrowers (or related projects) who have different probabilities of being able to service their debt (make scheduled interest payments) and being able to repay the principal of the debt. These risk categories are commonly established by various credit agencies; the most popular being Standard & Poor's (listed above) and Moody's.

There is a No Risk category that corresponds to Federal Government debt (T-bills, T-Notes, and T-Bonds). In this category, there is absolute certainty that the borrower (the Federal Government) will be able to properly service the debt and repay the principal at all times. This is possible because the Federal Government can always borrow new funds at what ever rate of interest necessary to pay existing interest obligations or to repay any existing debt. The government is not constrained by an income statement of annual profit and loss as are private companies. In addition, unlike state and local governments the Federal Government has the power to establish or perhaps create the currency necessary to meet its existing obligations.

A Low Risk category corresponds to a S&P classification of AAA-AA or investment grade lending. Borrowers in this category have a strong history of debt repayment and a solid stream or revenues to service any future debt. Lenders in this category are very risk averse seeking to protect their asset base (the principal) by avoiding those borrowers who might default on their debt repayment.

The classification of A-BB represents somewhat speculative grade lending or Medium Risk. Borrowers in this category often have a good credit history, however, there is some uncertainty about future revenues to service additional debt. Lenders involved in this type of debt are willing to speculate that all interest payments and principal repayment will take place in return for a slightly higher return on their investment.

Finally the High Risk category carries a S&P rating of B-CCC also known as "junk" or highly speculative lending. Lenders in this category are willing to put their assets at risk in return for a high return as measured by usually double-digit yields for a limited period of time. There is a strong probability of default on debt in this category.

#### 7.2.2 The Liquidity Premium and Term Structure

In the above table, each row represents different lending/ borrowing periods. Short-term lending corresponds to anytime between one day and one year. The Medium-term corresponds to a lending period between one and ten years. Long-term lending is with respect to debt contracts for a time period greater than ten years.

Differing lengths in the lending period correspond to different degrees of uncertainty about future events. Very little change takes place in the political or economic structure of a nation or the world in any given year--the short-term. However, over a 30 year period of time typical for some types of government borrowing (T-Bonds) and private borrowing (home mortgages), massive changes may take place in rates of inflation, political conflict, and the global balance of power.

In the long-term tremendous uncertainty exists and yet there are institutional lenders that actively seek the long term. For example, pension funds and life insurance companies that need to plan for exact financial obligations well into the future.

###### 7.2.2.1 The Yield Curve

The term structure of interest rates can act as a leading indicator about the direction of economic activity. Holding risk constant by making use of yields on treasuries (t-bills, t-notes, and t-bonds), we can plot this term structure at a point in time a relationship known as the Yield Curve. If the economy is strengthening (growing) there will be more long-term investment taking place putting upward pressure on long-term rates. There will be a positive difference between the long-term and short-term such that term-premiums are positive and this yield curve will be upward sloping. Anticipated weakness in the economy will push short-term rates up and long-term rates down such that the yield curve will flatten or become inverted. Often an inverted yield curve is a signal that the aggregate economy is approaching a recession.

 . Year: 1960 2019

Three widely accepted hypotheses exist describing the term structure of interest rates and determination of the liquidity premium. Two of these hypotheses, Segmented Markets and the Expectations Hypothesis represent extreme propositions with regard to the ability to substitute between short-term and long-term assets. The third hypothesis, Preferred Habitat, is an attempt to find some middle ground.

###### 7.2.2.2 Segmented Markets

At one extreme is the notion that short term and long term assets are highly imperfect substitutes. In this approach the borrowers and lenders (sellers and buyers) in short term markets are very different individuals and agents from those who interact on long term markets. Short term borrowers include those who need to finance seasonal inventory or need to smooth out their cash position over a fiscal period. Lenders include those with cash surpluses who do not want to sacrifice much in the way of liquidity. The price (and thus the yield) on short term assets are determined by the interaction of these individuals in primary and secondary markets.

A different set of agents interact in the long term market. The borrowers in this end of the market are those financing homes in mortgage markets or seeking capital to build factories or other similar long term projects. Attempting to borrow short term would make it difficult to service such large loans relative to annual income or revenue. Lenders would include pension funds, insurance companies and others collecting current premiums but with well-identified long term obligations. Buying and selling between these agents determine long term asset prices and yields.

Differences in yields that may exist between the short term and long term are explained only though the forces of supply and demand in each market. Accordingly, long term yells could be greater than, equal to, or less than short term yields.

###### 7.2.2.3 The Expectations Hypothesis

At the other extreme is the idea that short term and long term debt instruments are perfect substitutes for one-another.

An important consideration here is that lenders have more flexibility with regards to the length of the lending period relative to borrowers. Many borrowers enter the long term market precisely because the nature of their project is long term. For these projects to be financially feasible the borrower needs to rely on a long continuous stream of revenues to repay the debt. Such projects are just not possible in a one to ten year horizon. Many home owners find that housing is affordable only if they can stretch the loan payments over a 30 year period of time given their annual income.

Lenders, however, have a choice. A lender can make a loan for 30 years or that individual can make six sequential five-year loans. The 30 year loan locks in an interest rate for the duration of the loan at the prevailing long-term rate whereas the sequence of six medium-term loans exposes the lender to changes in nominal rates each time the funds are reinvested. The long-term loan exposes the lender to the uncertainty of distant future events in contrast to the medium term sequence which allows the lender to react to changing economic conditions. There is a balancing act taking place between uncertainty about future economic conditions and the direction of future interest rates

For example, suppose that a lender chooses to lend a principal sum 'P' for two years. The agent has a choice of making a single loan at the present two-year rate '2rt' or making a one year loan at the existing short-term (one-year) rate '1rt' and reinvesting at the expected prevailing short-term rate in the following year 'E[1rt+1]'. The notation presented 'krt' tracks the term of a loan 'k' and the time period 't'. Thus for the lender:

P(1 + 2rt)2 = P(1 + 1rt)(1 + E[1rt+1])

or

1 + 2(2rt) = 1 + 1rt + E[1rt+]

or

2rt = {1rt + E[1rt+1]}/2

This last expression states that the current two-year rate will be an average of the current one-year rate and the expected one-year rate next year. If the two year rate is greater than this average, the lender will invest in the longer-end of the market seeking the higher yield. This buying of the two-year instrument will drive its price upward and the two-year yield (interest rate) downward until both sides of the above expression are equal. The liquidity premium will be directly influenced by expectations of future short-term rates.

###### 7.2.2.4 Preferred Habitat

This third hypothesis is an attempt to marry the relevant features of the above two approaches. This hypothesis begins with the notion that lenders prefer the short term over the long term the latter exposing these agents to many types of future uncertainties. However, these agents can be induced into the long term via payment of a term-premium 'Φ' over-and-above and average of current and expected future short-term rates:

2rt = {1rt + E[1rt+1]}/2 + Φ

The actual derivation of liquidity and risk premiums take place in financial markets through the process of buying and selling financial instruments--concepts that will be discussed in later sections.

Concepts for Review:
 Credit Risk Expectations Hypothesis Expected Inflation Highly-Speculative Grade (debt) Imperfect Substitutes Investment Grade (debt) Long-term (assets/debt) Liquidity Premium Medium-term (assets/debt) Nominal Interest Rate Perfect Substitutes Preferred Habitat Hypothesis Real Interest Rate Risk Premium Segmented Markets Hypothesis Short-term (assets/debt) Speculative Gradedebt) ( T-Bill (Treasury Bill) T-Bond (Treasury Bond) T-Note (Treasury Note) Yield Curve

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