## Take Home Exam

Instructions
Answer all questions on a separate document, typed 12 point font, submitted
via Canvas to me as a pdf, no later than noon Eastern Standard Time
on Sunday, December 12.
If within the questions the terms appear not to be adequately defined,
the notation and terminology are as given in the text book.Grading
Given that the test has unlimited time for its completion, each question is
graded either correct or incorrect. There will be no partial credit given for
any answer. Each answer is worth 4 points.

Numerical Questions
To get the answer correct, you must have the right answer and show how
you computed your answer.

If you have the correct approach but the answer is wrong, the question
will be graded incorrect.
If you have the correct answer, but the approach is wrong, the question
will be graded incorrect.

## Essay Questions

Short and concise answers to the essay questions are required. Each essay
has only a few key points that need to be mentioned to get the answer
correct.
An answer will be graded incorrect if all the key points are not included.
An answer will be graded incorrect if any incorrect statements are made,
even if the correct answer is included as a subset of the provided explanation.
An answer will be graded incorrect if the grammar is poor and it is
difficult to read and understand the answer.

1 Question
Given an interest rate of $3 \%$ per year, what is the return to a dollar invested today for $1.4$ years using a simple interest rate?
In what applications are simple rates common?
2 Question
A reverse repurchase agreement can be used to short a Treasury security. Explain how this is done with a reverse repurchase agreement.
3 Question
The U.S. Treasury auctions Treasury securities using a uniform price auction. Explain what a uniform price auction is with respect to the winning bids and what are its benefits to the competitive bidder and the U.S. Treasury.
4 Question
A professor states that given two coupon bonds of equal credit risk, the bond with the highest yield is always the best buy because it will have the largest expected return. Is this correct? Explain your answer
5 Question
Using a discrete time model $(t=0,1,2,3, \ldots, T)$, compute the yield, duration and modified duration of the following two bonds.
\begin{tabular}{|c|c|c|c|c|}
\hline Name & dollar coupon & maturity & face value & price at time 0 \
\hline \hline $\mathrm{A}$ & 6 & 4 & 100 & $P=100$ \
\hline $\mathrm{B}$ & 0 & 3 & 100 & $B=93.50$ \
\hline
\end{tabular}
If you want to hedge 1 unit of bond $\mathrm{A}$ with $n$ units of bond $\mathrm{B}$, what is the modified duration hedge ratio?

6 Question
A recent article in the Wall Street Journal stated that hedge fund A hedged its interest rate using modified duration hedging during the financial crisis, and that because of this, the hedge fund had no interest rate risk. We also know, by looking at historial data, that the yield curve changed its shape during the financial crisis.
Is this WSJ statement true? Explain your answer?
7 Question
You read an article in the financial press that states that U.S. Treasury securities are default free, which implies the promised payoffs on U.S. Treasury securities are paid with probability one. Does everyone in the market agree with this statement? Explain your answer.
8 Question
Using a discrete time model $(t=0,1,2,3, \ldots, T)$ with the following zero coupon bond prices:
\begin{tabular}{|c|c|}
\hline Maturity & Zero Coupon Price \
\hline \hline 0 & 1 \
\hline 1 & $.97$ \
\hline 2 & $.95$ \
\hline 3 & $.93$ \
\hline 4 & $.91$ \
\hline
\end{tabular}
Compute the term structure of forward rates.
$9 \quad$ Question
An economic professor states that if the local expectations hypothesis is true, then interest rate risk management is unnecessary. If this true? Explain your answer.

Does the empirical evidence support the local expectations hypothesis? Explain your answer.

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# 概率论代考

## 离散数学代写

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