Chapter 05  Learning About Return and Risk from the Historical Record
51
CHAPTER 5: LEARNING ABOUT RETURN AND RISK
FROM THE HISTORICAL RECORD
PROBLEM SETS
1.
The Fisher equation predicts that the nominal rate will equal the equilibrium real rate
plus the expected inflation rate. Hence, if the inflation rate increases from 3% to 5%
while there is no change in the real rate, then the nominal rate will increase by 2%. On
the other hand, it is possible that an increase in the expected inflation rate would be
accompanied by a change in the real rate of interest. While it is conceivable that the
nominal interest rate could remain constant as the inflation rate increased, implying that
the real rate decreased as inflation increased, this is not a likely scenario.
2.
If we assume that the distribution of returns remains reasonably stable over the entire
history, then a longer sample period (i.e., a larger sample) increases the precision of the
estimate of the expected rate of return; this is a consequence of the fact that the standard
error decreases as the sample size increases. However, if we assume that the mean of the
distribution of returns is changing over time but we are not in a position to determine the
nature of this change, then the expected return must be estimated from a more recent
part of the historical period. In this scenario, we must determine how far back,
historically, to go in selecting the relevant sample. Here, it is likely to be
disadvantageous to use the entire dataset back to 1880.
3.
The true statements are (c) and (e). The explanations follow.
Statement (c): Let
= the annual standard deviation of the risky investments and
=
the standard deviation of the first investment alternative over the twoyear period. Then:
Therefore, the annualized standard deviation for the first investment alternative is equal
to:
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Statement (e): The first investment alternative is more attractive to investors with lower
degrees of risk aversion. The first alternative (entailing a sequence of two identically
distributed and uncorrelated risky investments) is riskier than the second alternative (the
risky investment followed by a riskfree investment). Therefore, the first alternative is
more attractive to investors with lower degrees of risk aversion. Notice, however, that if
you mistakenly believed that ‘time diversification’ can reduce the total risk of a
sequence of risky investments, you would have been tempted to conclude that the first
alternative is less risky and therefore more attractive to more riskaverse investors. This
is clearly not the case; the twoyear standard deviation of the first alternative is greater
than the twoyear standard deviation of the second alternative.
4.
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 Spring '09
 WILSONCHOI
 Standard Deviation, Inflation, Interest Rates, Interest

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