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Determine the number of units of each asset in the portfolio

Assignment Help Finance Basics
Reference no: EM131418116

Question 1

1. Assume all rates are annualized with semi-annual compounding. Please be explicit about how you derive your results and round to four decimals after the comma. ?
$100 par of a 0.5-year 12%-coupon bond has a price of $104. $100 par of a 1-year 14%-coupon bond has a price of $108.

a. What is the price of $1 par of a 0.5-year zero?

b. What is the price of $1 par of a 1-year zero?

c. Suppose $100 of a 1-year 10%-coupon bond has a price of $99. Is there an arbitrage ?opportunity? If so, how?

d. What is the 0.5-year zero rate?

e. What is the 1-year zero rate?

f. What is the 1-year par rate, i.e., what coupon rate would make the price of a 1-year ?coupon bond equal to par?

g. Considering the shape of the yield curve, should the yield on the 1-year 14%-coupon ?bond be higher or lower than the 1-year par rate?

Question 2

2. Suppose the yield curve is upward-sloping and there is no arbitrage. Two ordinary fixed coupon bonds, bond A and bond B, have the same maturity, but bond A has a higher yield. Which bond has the higher coupon?

Question 3

3. Assume all rates are annualized with semi-annual compounding. Please be explicit about how you derive your results and round to four decimals after the comma.

Suppose that at time 0 you buy a 10%-coupon 20-year bond priced at par, and at time 0.5 you sell this bond at a yield of 12%.
a. What is your time 0.5 payoff per $1 of initial investment? ?
b. What is the rate of return on your investment (annualized, with semi-annual ?compounding)?

Question 4
4. Assume all rates are annualized with semi-annual compounding. Please be explicit about how you derive your results and round to four decimals after the comma.
The 0.5-year zero rate is 7% and the 1-year zero rate is 9%.
a. What is the price of:?
i. $1 par of a 0.5-year zero??
ii. $1 par of a 1-year zero??
iii. $100 par of a 1-year 10%-coupon bond
b. What is the dollar duration of:?
i. $1 par of a 0.5-year zero??
ii. $1 par of a 1-year zero??
iii. $100 par of a 1-year 10%-coupon bond
c. What is the duration of:?
i. $1 par of a 0.5-year zero??
ii. $1 par of a 1-year zero??
iii. $100 par of a 1-year 10%-coupon bond

d.Use dollar duration to estimate the change in value of $1,000 par of the 1-year 10%- coupon bond if all zero rates rise 100 basis points.

Question 5

Your liabilities have a market value of $1,120,000 and a duration of 7.5. You want to immunize your position by constructing a portfolio of two assets below that has the same market value and duration as your liabilities.

Asset

Market Value

 

Duration

#1

600

 

10

#2

200

  

3

a. Write down equations that determine the number of units of each asset in the portfolio. Use notation N1 and N2 to represent the number of units of asset #1 and #2, respectively.

b. Solve the equations for N1 and N2.

Question 6

Suppose you have a short position in a 30-year 5%-coupon bond and a long position in a zero- coupon bond with exactly the same market value and duration. If all zero rates fall by 25 basis points, will your net position rise or fall in value? Explain.

Question 7

Assume all rates are annualized with semi-annual compounding. Please be explicit about how you derive your results and round to four decimals after the comma.

The current price of $1 par of a zero maturing at time 2 is $0.97
a. What is the 2-year spot rate? ?
b. What is the dollar duration of $1 par of the 2-year zero? ?
The current price of $1 par of a zero maturing at time 3 is $0.92 ?
c. What is the 3-year spot rate??
d. What is the dollar duration of $1 par of the 3-year zero?

You can enter into a forward contract today to buy, at time 2, $1 par of a zero maturing at time 3. The price you would pay at time 2 is the forward price. The cost today of entering into this contract is zero.
e. Construct a portfolio of 2- and 3-year zeroes that synthesizes this forward contract. ?
f. What is the no arbitrage forward price? ?
g. What is the dollar duration of the forward contract?

Question 8

Assume all rates are annualized with semi-annual compounding. Please be explicit about how you derive your results and round to four decimals after the comma.

(Part I) At time 0, Investor A enters into a forward contract, at no cost, to buy, at time 2, $100,000 par of a zero maturing at time 3. The forward price this investor locks in to pay at time 2 is $93,000.

a. What forward rate does this investor lock in at time 0, through this forward contract, for lending from time 2 to time 3?

(Part II) At time 1, the spot price of $1 par of a zero maturing at time 2 is 0.97 and the spot price of $1 par of a zero maturing at time 3 is 0.93.

a. At time 1, what is the forward price an investor could lock in to pay, at time 2, for $100,000 par of a zero maturing at time 3?
b. What is the value, at time 1, of Investor A's position in the forward contract from Part I?

Verified Expert

The task consists of eight problems of finance from the topic of the time value of money. All the solutions have been given in excel with detailed description as required. The problems have been solved by the application of relevant finance formula and explanations have been provided wherever required.

Reference no: EM131418116

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Reviews

inf1418116

3/17/2017 6:05:05 AM

Much obliged to proficient staff at ExpertsMind for giving me qualified help my assignments. I fizzled my instructive arrangements for this semester because of individual reasons, yet they figured out how to help me escape this. You can depend on these individuals.

inf1418116

3/17/2017 6:03:45 AM

Please state all the formulas & steps clearly ! if the solutions are sending over in word file, please state all the formulas & steps clearly too, as the requirement of this assignment is focusing on the calculation process (what's the formula used & how the answers is derived) So, I prefer to receive the answer in "Excel" with formula & steps. One more reminder: Other than providing answers, formulas & calculation process on the steps of how to answers are being derived, please provide explanation too ! Especially for yes/no question, please don't just give answer yes or no, but provide the reasons behind too !!!! Thanks for your prompt reply. Say for example, Question 2 of the Finance Basics question, E.g. Which bond has higher coupon ? For this type of question, please provide the explanation of the reasons behind.

inf1418116

3/17/2017 6:03:39 AM

Actually what I have attached is the same as the previous doc. Just in case the expert feels the pdf version is easier to read. God Bless ! Hi Expert, the two set of questions should be the same, as I copy the wordings in jpg/PDF file to words file. JPG/PDF file is the original file. Just that one is in word format, and the other one is in jpg/PDF . For the PDF format, I realise there's some mistakes on the pages name Page 1 should be the PDF file labeled as page 3 Page 2 should be the PDF file labeled as page 1 Page 3 should be the PDF file labeled as page 2 ** if u ar using the original (Jpg/PDF file), there should be 3 pages with eight questions in total.

inf1418116

3/17/2017 6:02:53 AM

Thanks for your help & guidance. Can you provide the answer in excel spreadsheet ? Also, here's the important note. ** Be explicit about how exactly how you derive the solution, i.e., show all steps that lead to the solution. Make explicit which formulas you are using and how you manipulate them to arrive at your numerical answer. ** Please round to four decimals after the comma. There won’t be any deductions for rounding errors ?as long as they can be clearly identified as those. Round prices as x.xxxx and rates as x.xxxx%. ? Also, since it is pretty urgent, hope I can receive the answer asap. Million Million thanks ! Btw, so sorry that when I choose the deadline (I thought it's mentioning India time zone) Can I have it within 8 hours. Anyway, I really need it asap ! Your help & guidance is much much appreciated ! God Bless you !! Hiya just in case my previous question is not too clear. Here I would like to provide the question again in pdf version (same content). Feel free to forward to the expert. Page 1 21564971_1Q page 1.jpg Page 2 21564932_1Q page 2.jpg Page 3 21564984_1Q page 3.jpg

len1418116

3/7/2017 7:41:18 AM

???Please round to four decimals after the comma. There won’t be any deductions for rounding errors ?as long as they can be clearly identified as those. Round prices as x.xxxx and rates as x.xxxx%. ? . ???Be explicit about how exactly how you derive the solution, i.e., show all steps that lead to the solution. If you cannot make transparent how you derive your solution, you won’t get full points. Make explicit which formulas you are using and how you manipulate them to arrive at your numerical answer.

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