resources

1. Chapter Six
Real Interest
Rates

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• Investors care about how much they can
purchase with the dollars they earn, not merely
the quantity of dollars
– When investments do not keep pace with inflation, investors lose
purchasing power
– A more accurate measure of well-being is based on the amount
of goods and services one can buy, not how much income is
earned
• “Real” figures account for inflation in financial
matters
– Nominal interest rate = the amount of interest paid expressed
as a percentage of the principal
– Real interest rate = the nominal interest rate adjusted for
expected or actual inflation
What Are Real Interest Rates?

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• Expected inflation is more often used to
adjust the nominal interest rate
– What matters in people’s decisions to borrow or lend
is what they think they will be paying or earning
• This is known as the expected real
interest rate (or ex-ante real interest rate)
Expected real interest rate = nominal interest rate – expected inflation rate
Expectations of Inflation

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• The realized real interest rate (or ex-
post real interest rate) is the nominal
rate adjusted for actual inflation
– This measure matters more “after the fact”
– The expected real interest rate is more
relevant in decision-making because we
cannot know for certain what the actual
inflation rate will be
Realized real interest rate = nominal interest rate – actual inflation rate
Expectations of Inflation (cont’d)

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• Who gains and who loses from
unexpected inflation?
– Lower than expected inflation hurts the
borrower and helps the lender, who is
paid back in dollars worth more than they
had predicted when making the loan
– Higher than expected inflation hurts the
lender and helps the borrower, who pays
back their loan with dollars worth less
than those they originally spent
Impact of Unexpected Inflation

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• When actual & expected inflation differ, the
expected real rate differs from the realized real rate
• When actual inflation is less than expected, realized
real rates increase
• When actual inflation is greater than expected,
realized real rates decrease
Unexpected Inflation (cont’d)

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Why Inflation Risk is a Problem
• Investors deplore inflation for two reasons
– The value of their returns is reduced by inflation
– The unpredictability of inflation increases the risk
to the real return on their investments
• The riskiness of inflation matters just as much
as the rate of inflation to investors
• The risk to real return can be expressed as
the of the probabilities and outcomes
standard deviation faced by the investor
• Higher standard deviations signify higher risk
of inflation, and hence higher risk to real
returns

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Avoiding the Problems of
Unexpected Inflation
• Investors and borrowers have several ways
of avoiding the risk and uncertainty of inflation
• Adjustable rate mortgages allow interest
rates on a loan to adjust as market interest
rates change
• Inflation-indexed securities offer
opportunities to borrow and lend in real
rather than nominal terms

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• Allows concept of “real interest rates” to be
applied to past returns, expected returns,
and yields to maturity
• Present value formulas are used with real
terms in lieu of dollar terms
Real Present Value

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• There exist a variety of uses for this formula
– The present value P of given future real amounts (the
f terms) for a given expected real interest rate r
– Future real amounts (the f terms) given an expected
real interest rate r and a current principal value P
– The average past return r given real income received
(the f terms) and the original amount invested P
– The expected future return r given expected future
income (the f terms) and the original amount invested
P
– The real yield to maturity of a security r given
promised future payments (the f terms) and the
current price of the security P
Real Present Value (cont’d)

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• Investment decisions would be easier if
changes in real interest rates were
predictable
• Two factors may cause changes in expected
real interest rates
– Changes in the expected inflation rate
– Changes in phases of the business cycle
What Affects Real Interest Rates?

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• Data on nominal interest rates and actual inflation
rates are easily obtainable, while measuring
expected inflation rates is more difficult.
• Forecasts of the future inflation rate by economists
are useful, and with them one can calculate
– Expected real interest rates
– Realized real interest rates
• What do we find?
– Expected and real interest rates often move together
Measuring Real Interest Rates

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Despite some large points of divergence, real
interest rates and realized real interest rates
move relatively closely together
Measuring Real Interest Rates (cont’d)

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• A rise in the expected inflation rates leads to a
rise in the nominal interest rate, while expected
real interest rates remain the same
– Anticipated inflation affects the prices of goods, as
well as the number of dollars a security pays, but not
any inflation-adjusted amount
– That is, dollar payments adjust to the same change in
the inflation rate
– Example: If inflation is 4% instead of 3%, all dollar
payments will compensate by being 1% higher
The Fisher Hypothesis

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When expected inflation rises, the supply of bonds
increases and the demand decreases in proportionate
amounts. Thus, the nominal interest rate, the price of
borrowing, also increases by the same amount.
Please insert Figure 6.4
The Fisher Hypothesis (cont’d)

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• We expect less borrowing during a
recession, which should lower the
expected real interest rate
• But people may also save less, which
would raise the expected real interest rate
by decreasing demand for debt securities
• As demand and supply both decrease, the
resulting effect is ambiguous
Real Interest Rates in Recession

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Overall trend is for supply to decrease more than
demand, causing expected real interest rates to
decline during a recession.
Please insert Figure 6.5
Real Interest Rates in Recession (cont’d)

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• Like inflation, taxes also reduce the return
of investors
• The government often “earns” more in real
dollars than the investor, as taxes are
imposed on nominal, not real, returns
• When accounting for inflation, effective
real tax rates are much higher than stated
tax rates
• “A significant …loss even at a low rate of
inflation” (Feldstein)
Application to Everyday Life:
The Effect of Taxes on Interest Rates

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• In general, higher tax rates reduce economic
efficiency
• Because of the additional erosion of returns due
to taxes, people save and invest less when
inflation is high than when inflation is low
• Reducing inflation thus leads to large social
benefits
• After-tax realized real interest rates have often
been negative, discouraging saving and investing
and slowing economic growth
The Societal Effects of Taxation

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A tendency to move in the same direction is present, but
only when other variables are not in play
Expected Inflation and
Real Interest Rates

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• Demand and supply for debt securities depends
more on after-tax expected real interest rates
than before-tax expected real interest rates
• Can the distortions of taxes be eliminated?
– Impose taxes on real interest income
• Calculation can be difficult
– Reduce inflation to zero
• Though progress has been made, seems unlikely
The Societal Effects of Taxation (cont’d)