**3.11 Real and Nominal Interest Rates**

An interest rate measures the opportunity cost of immediate consumption. Interest rates fluctuate over time and in order to understand these fluctuations consider what influences immediate consumption. One of the most important determinants of interest rates is expected inflation. Suppose the consumer price index is expected to jump because the price of goods and services are expected to increase. Consumers are now likely to accelerate consumption plans to avoid the likely price rises.

How would you expect interest rates to respond to this event?

If inflation expectations increase and there is a shift from savings to consumption, then fixed income security prices will fall in response to the selling resulting from the decrease in savings. If prices fall interest rates will rise. Therefore interest rates increase with expectations of inflation.

To isolate the effect of inflation expectations on interest rates the economist Irving Fisher made a distinction between real and nominal interest rates and correspondingly real cash flows and nominal cash flows.

**The Fisher Equation**

This equation states:

(1 + Nominal Rate) = (1 + Real Rate) * (1 + Inflation Rate)

That is, Fisher's identity lets you decompose a nominal or spot rate of interest into two major drivers --- inflationary expectations and growth expectations. An immediate implication of this work, suggested by Fisher, is to link bond coupon rates to inflation via the face value of the fixed income security. Over eighty years later this was implemented by the US Government with the launching of Treasury Inflation-Protected Securities (TIPS) in 1997

The launching of these instruments coincide with the ability of being able to extract additional information from the observed yield curve. In particular, Fisher's TIPS allow for inflation expectations to be inferred directly from the yield curve.

In the interactive calculator, select "Inflation Expectation" from the dropdown on the left to see this information for the current US Treasury prices. This graph is updated automatically every day. You can see what the current implied trends are from 5-year horizons to 20-year horizons along with underlying moving average trends and volatility bounds below. The 2-sigma volatility bounds let you assess the statistical significance of a move in inflationary expectations. You can also cursor over any of the dots on the graphs to read off the numeric value associated with the point.

**Implied Inflation Expectations
from US Treasury Yield Curve**

**TIPS (Real Rates)**

As noted above the Treasury now issue Inflation Protected Securities. These securities have their face amount adjusted in response to changes in the CPI Index. The coupon rate is applied to a larger principal over time in response to inflationary changes. As such, the yield to maturity is interpreted as a real rate of interest.

A common question that arises from investors is whether it is better to purchase TIPS or regular Treasury instruments?

From a trading perspective if the difference between the nominal and real rates are positive (as they normally are) then an investor is better off with the nominal rate if annual inflation rates stay below this difference otherwise the investor is better of with TIPS. As a result, the this difference in relation to inflationary expectations drive the realized return differences between TIPS and regular Treasury instruments.

So the immediate question that follows from above is what determines the real rate of interest which in turn determines this difference between nominal and real rates?

Suppose the economy is expected to move into a recession and thus job security is at risk. Again, nominal rates of interest will be resposive to this event. Traders in the fixed income markets are likley to revise fixed income security price expectations up because consumers are likely to start postponing some of their immediate consumption, resulting in increased savings and stronger fixed income prices.

In the interactive graphs below you can explore current real rate behavior and their underlying trends. You can select from the dropdown the data you want to examine.

**Current Rates from the TIPS Markets**

In the interactive charts you can look at current trends as well as long term trends in real rates.

I**nteractive Exercise: ** Assess whether the recent trend in real rates
as measured is consistent with an improving or weakening economy..