Investments, tenth edition

interest rate   —the growth rate of your money—and a    real  interest  rate   —the  growth  rate 

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bod61671_ch05_117-167.indd   118

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  C H A P T E R  

5

  Risk, Return, and the Historical Record 

119

of your purchasing power. If we call  rn  the nominal rate,  rr  the real rate, and  i  the inflation 

rate, then we conclude

 

   rr < rn 2 i 

 (5.1)   

 In words, the real rate of interest is the nominal rate reduced by the loss of purchasing 

power resulting from inflation. 

 In fact, the exact relationship between the real and nominal interest rate is given by   

 

1 1 rr 5

1 1 rn

1 1 i

 

 (5.2)   

 This is because the growth factor of your purchasing power, 1   1     rr,  equals the growth 

factor of your money, 1  1   rn,  divided by the growth factor of prices, 1  1   i.  The exact rela-

tionship can be rearranged to   

 

rr 5

rn 2 i

1 1 i

 

 (5.3)   

 which shows that the approximation rule (Equation 5.1) overstates the real rate by the 

 factor  1  1   i.  

 

 If the nominal interest rate on a 1-year CD is 8%, and you expect inflation to be 5% 

over the coming year, then using the approximation formula, you expect the real 

rate of interest to be  rr    5   8%   2   5%   5   3%. Using the exact formula, the real rate 

is    rr 5

.08 2 .05

1 1 .05

5

.0286,  or 2.86%. Therefore, the approximation rule overstates the 

expected real rate by .14% (14 basis points). The approximation rule is more exact for 

small inflation rates and is perfectly exact for continuously compounded rates. We discuss 

further details in the next section. 

 Example  5.1 

Approximating the Real Rate 

  

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 You can find the  real  rate for a desired maturity from inflation-indexed bonds issued by the U.S. Treasury, called 

TIPS. (See Chapter 14 for a fuller discussion.) The difference between TIPS yields and yields on comparable 

nominal Treasury bonds provides an estimate of the market’s expectation of future inflation.  

 

Notice that conventional certificates of deposit offer a guaranteed  

nominal 

 rate of 

interest. Thus you can only infer the expected real rate on these investments by adjusting 

for your expectation of the rate of inflation. 

 It is always possible to calculate the real rate after the fact. The inflation rate is pub-

lished by the Bureau of Labor Statistics (BLS). The future real rate, however, is unknown, 

and one has to rely on expectations. In other words, because future inflation is risky, the 

real rate of return is risky even when the nominal rate is risk-free.  

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