Cornell University
Fall 2010
Economics 3330: Problem Set 4 Solutions
1.
True/False/Explain
State whether each of the following is true or false and explain your answer.
Please limit your
explanations to no more than two sentences.
a. The “rule of 72” holds that it is the last 72 years of data that are relevant for estimating the
future returns of an asset.
False. The “rule of 72” says that the approximate amount of time for an asset to double in value is
approximately equal to 72 divided by the interest rate.
b. The Sharpe ratio is not changed by using the standard deviation of the return of the asset in
place of the standard deviation of the excess return of the asset.
False. If the riskfree rate of return is varies over time, then the two standard deviations will
differ.
c. Even if the arithmetic average return is negative, the geometric average will be lower than the
arithmetic.
There are two acceptable answers to this question.
1) True. Variance reduces the geometric
return regardless of the sign of the returns. 2) False. In the special case when the average return is
constant, the arithmetic and geometric returns will be the same.
2.
Indexing and Risk (Question 6 of Text, modified)
There are two U.S. government bonds with the same maturity: one is not indexed and offers a 5%
return, and the other is indexed and offers a 1.5% return plus the CPI.
a. Suppose that inflation will average 3.5% until the bond’s mature. What would be the safer asset
for a retiree? What would be the safer asset for a bond manager benchmarked to a nominal index?
The safer one for the retiree is the indexed bond because it reduces variation in consumption. For
the manager it is the nominal bond, because it reduces benchmark tracking error.
b. If we observe the riskfree nominal rate of 5% and a riskfree real rate of 1.5%, can we infer
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