## 7.0 Nominal and Real Interest Rates

Upon casual inspection of any business periodical, one will find that at any point in time there are many different nominal interest rates. In this module, we began to explain why all interest rates may change in reaction to changes in the supply or demand for loanable funds in addition to changes in inflationary expectations. These type of changes cause the entire structure of interest rates to move up or down over time.

At any moment in time, however, there are differences in nominal rates driven by changes in uncertainty about the future, changes in risk related to a borrower's ability to service a loan (i.e., make periodic interest payments) or to repay the loan, and to changes in a lender's preference for risk in an investment portfolio. Uncertainty and risk lead to changing spreads among nominal rates in reaction to changing economic events.

It is through these changes and variations that we can label the structure of interest rates as a barometer of macroeconomic activity.

#### 7.0.1 the Fisher Equation

In describing the macroeconomy and within our economic models, we often speak of a single interest rate. In reality, there are many different interest rates found in financial markets. These different rates tend to rise and fall together reacting to real economic events and to changes in expectations about future inflation.

At any point in time there are many different nominal interest rates. The following table maybe useful in organizing a few of these nominal rates:

 2012 No Risk Low Risk Medium Risk High Risk Term Treasuries (AAA-AA) (A-BB) (B-CC) Short-term (1-year or less) 0.03% 3.25% 3.29% 3.14% Medium-term (1 - 10 years) 0.77% 3.92% Long-term (10+ years) 1.85% 3.79% 3.54

Each column in the above table represents a different level of risk associated with a certain class of borrowers. This risk is also known as credit risk where different types of borrowers (or related projects) 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 and Poor's (listed above) and Moody's.

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.

In the upper-left corner of the table is a short-term risk-free interest rate -- the T-Bill (Treasury Bill) rate. This rate may be thought of as a core metric of current macroeconomic conditions: the level of real economic activity and expectations about inflation. This nominal rate of interest (looking forward) on a short-term debt contract (one year or less) is developed as follows:

imarket= r* + E[πt]

where 'E[πt]' represents the expected rate of inflation.

Borrowers and lenders agree to add an inflation premium to interest rates to allow for expectations about future inflation -- an acknowledgement that inflation erodes the purchasing power of money over time. An individual lending money in an inflationary environment will be repaid in dollars which possess less purchasing power upon maturity of the debt contract. An inflation premium is often built into nominal interest rates to protect against this loss of purchasing power.

At the termination of the debt contract an ex-post real rate of interest 'r'can be developed as follows:

r = imarket - π

This relationship among the nominal interest rate, inflation and the real interest rate is known as the Fisher equation.

Concepts for Review:
 Credit risk Ex-post Real Interest Rate Inflationary Expectations Inflation Inflation Premium (Interest Rate) Spreads Loanable Funds Long term (rates) Medium term (rates) Nominal Interest Rates Purchasing Power Risk Short term (rates) Structure of Interest Rates Uncertainty

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