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
σ
= the annual standard deviation of the risky
investments and
1
σ
= the standard deviation of the first investment alternative
over the two-year period.
Then:
σ
σ
×
=
2
1
Therefore, the annualized standard deviation for the first investment
alternative is equal to:
σ
σ
σ
<
=
2
2
1
5-1

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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 risk-
free 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

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