Investments, tenth edition

  

  Annualized Average Rates  

  Annualized Standard Deviations  *  

  

  T-Bills  

  Inflation  

  Real T-Bill  

  T-Bills  

  Inflation  

  Real T-Bill  

 All months 

 3.55  

3.04  

0.52  

2.95  

4.06  

3.95 

 First half 

 1.79  

1.74  

0.10  

1.56  

4.66  

4.98 

 Recent half 

 5.35  

4.36  

0.95  

3.02  

2.82  

2.44 

  *Annualized standard deviations include the effect of serial correlations at lags 1–11 months.  

Sources: Annual rates of return from rolling over 1-month T-bills: Kenneth French and Morningstar, Inc.; 

annual inflation rates: Bureau of Labor Statistics.

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126

P A R T   I I

  Portfolio Theory and Practice

 An important lesson from this history is that even a moderate rate of inflation can erase 

most of the nominal gains provided by these low-risk investments. In both halves of the 

sample, the real return was less than one-fifth the nominal return. 

 We can demonstrate the cumulative gain from a particular investment over a given 

period using a  wealth index.  Assuming $1 was invested at the beginning of a period, we 

compound the investment value, year by year, by 1 plus the gross annual rate of return. 

The wealth index at the end of the last year shows the total increase in wealth per dollar 

invested over the full investment period.  Figure 5.2  shows that $1 invested in T-bills at the 

beginning of 1970 would have grown to $9.20 by September 2012, a seemingly impres-

sive gain for a low-risk investment. However, the wealth index in real (inflation-adjusted) 

dollars shows a meager ending value of only $1.20. Similarly, a dollar invested in T-bills 

for the entire 1926–2012 period is shown (in the inset) to reach $20.25, but with a real 

value of only $1.55.  

  

 

 The standard deviation (SD) panel in  Table  5.2  shows a lower SD of inflation in the 

recent half, 2.82%, than in the earlier period, 4.66%. This contributed to a lower standard 

deviation of the real rate in the recent half of the sample, 2.44%, compared with the earlier 

half, 4.98%. Notice that the SD of the nominal rate actually was higher in the recent period 

(3.02%) than in the earlier one (1.56%), indicating that the lower variation in realized real 

returns must be attributed to T-bill rates more closely tracking inflation in that period. 

Indeed,  Figure 5.3  documents a moderation in the rate of inflation as well as a consider-

ably tighter fit between inflation and nominal rates.  

  

 

 As we emphasized earlier, investors presumably focus on the real returns they can 

earn on their investments. For them to realize an acceptable real rate, they must earn a 

higher nominal rate when inflation is expected to be higher. Therefore, the nominal T-bill 

rate observed at the beginning of a period should reflect anticipations of inflation over 

that period. When the expected real rate is stable and realized inflation matches initial 

0

1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

1

2

3

4

Wealth Index

5

6

7

8

9

10

0

1926

1936

1946

1956

1966

1976

1986

1996

2006

2016

2

4

6

8

10

12

14

16

18

20

Nominal Bills

Real Bills