Cornell University
Fall 2009
Economics 3330: Problem Set 2 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.
If a bond falls in value by $12 when the discount rate rises from 0.03 to 0.04, then it cannot
fall an additional $14.40 when the discount rate rises further to 0.05.
True.
This follows
from the convexity of bond prices.
b.
According to Hyman Minsky’s “Financial Instability Hypothesis” article, “hedge finance”
units neither gain nor lose money when interest rates change because they are fully hedged.
(Article is available in Course Documents section of Blackboard site.)
False. According to
the article, hedge financial units are able to meet interest obligations are able to meet their
interest obligations out of asset returns; they may still be affected by interest rate changes.
c.
If the NPV of a project is positive, then the IRR must be less than the discount rate.
False.
It
follows from the definition that the IRR must be greater than the discount rate.
(Recall that
we have defined the term “project” to mean an initial cash outlay followed by a series of cash
receipts.)
2.
Valuing Management Fees
A common fee structure in hedge funds is for the manager to receive 2% of the assets under
management per year as well as a performance fee of 20% of the annual returns over a
benchmark.
This question addresses the compensation of managers who do not generate any
returns over their benchmark, so for simplicity we will assume that there no performance fee is
assessed because the mangers is earning exactly the benchmark.
The lock-up period refers to the
period of time when assets cannot be withdrawn from management. Suppose that the initial assets
under management (AUM) are 100.
For purposes of this question, assume that the management
fee is charged at the end of the year but based on the AUM at the beginning of the year.
(This
assumption is not realistic but simplifies calculations.)
Suppose first that there is a management fee of 2% per year and that the manager earns a 2%
return on the invested funds.
a.
How much does the manager receive at the end of the first year?
At the end of the second
year? 2, 2
b.
The fees can be viewed as the cash flows of a perpetuity.
If the discount rate is 2%, what is
the value of the perpetuity? What is your answer as a percentage of AUM? 100, 100%.
(Note: If you assume that the fee is charged at the beginning of the year, then answers are
unchanged.)
c.
If the discount rate were 5%, what would be the value of the perpetuity?
By what percentage
of the AUM does this differ from your answer to (b)? Briefly explain the intuition for the
difference.
The value falls to 40.

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