Chapter 5: Introduction to Risk, Return, and the
CHAPTER 5: INTRODUCTION TO RISK, RETURN, AND 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 1 = the standard deviation of the first investment alternative over the two-year period. Then:
1 2
Therefore, the annualized standard deviation for the first investment alternative is equal to:
1
2
2
5-1
Statement (e): The first investment alternative is more attractive to investors with lower degrees of risk aversion.
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 1 = the standard deviation of the first investment alternative over the two-year period. Then:
1 2
Therefore, the annualized standard deviation for the first investment alternative is equal to:
1
2
2
5-1
Statement (e): The first investment alternative is more attractive to investors with lower degrees of risk aversion.