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Final exam instruction for FNCE90056 Semester 1, 2022

Exam date/time and location

-      Exam date: Thursday 9 June 2022.

-     Exam time: From 3pm AEST to 5:30pm AEST

(Reading Time: 30 minutes + Writing Time: 2 hours)

-     Your exam time is from 3pm to 5:30pm AEST. You have in total 2hours and 30minutes to read and write your exam.

-      For submission, please make sure 1) you hit submitbutton for your multiple-choice    LMS quiz before 5:30pm AEST and 2) upload all short essay answers on the Gradescope before 6pm AEST.

-     Only for short essay answers (not for multiple choice LMS quiz), there is additional          30min submission time from 5:30pm-6pm. You must complete uploading all your short essay answers and check your files on the Gradescope by 6pm AEST. You will not be able to submit short essay answers after 6pm AEST.

-     Canvas and Gradescope logs will be used to confirm that the hours have been adhered to. Please use a timer to monitor the allotted time.

-      Exam location: Exams are available via the LMS online. For multiple choice questions, go to LMS Quiz (similar to the midterm exams). For short essay questions, go to LMS Modules to find the questions in a pdf file, and submit your short essay answers on the Gradescope      (similar to online quiz9 and quiz10).

Late submission

1.    Canvas Multiple-Choice Quiz

Canvas Quiz that are submitted between 5:31pm and 6pm will incur a 10% late penalty (of the total maximum mark for the exam). Students must click 'submit' before or at 5:30pm to not     incur a late penalty. Students who are prevented from submitting on time or at all due to         technical difficulties will need to apply for technical consideration with supporting                      documentation.

2.    Gradescope Short Essay

Final exam requires file uploads. These files may take some time to complete their upload in     peak exam times.  Students are permitted 30 minutes (5:30pm-6pm AEST) to upload and check files (without incurring any late penalties). File uploads must be fully completed by 6pm AEST.

Students will not be able to make a submission after this time. Students who were prevented from submitting on time or at all due to technical difficulties will need to apply for                    technical/special consideration with supporting documentation.

Exam format

The exam consists of two formats: 1) 11 multiple choice questions (similar to the midterm exams); and 2) 4 short essay questions (with sub-questions). Please complete both parts and answer each question in each part.

Short essay questions will be uploaded separately as a pdf file on the LMS Modules, and you may   submit typed or handwritten (and scanned) answers or a combination through Gradescope. Please use blank papers to write your answers. Make sure that all your answer files are uploaded and        submitted before the specified time (6pm AEST).

-     Total mark for multiple choice questions: 25.

-     Total mark for short essay questions: 25.

-     Total mark for the final exam: 50.

1.   After uploading your file in Gradescope, please indicate which page(s) refers to which question before completing your submission. This allows you to check that you have  answered each question and facilitates the marking procedure.

2.   You may submit typed or handwritten answers or a combination.

a.    Please do not answer two questions (e.g., Q1 & Q2) on the same sheet/page. You    may answer more than one sub-question belonging to the same question on the     same page (e.g., Q1a) and Q1b) ), and you may use more than one page to answer  all sub-questions relating to a single question (e.g., Q1a) and Q1b) on page 1, and    Q1c) and Q1d) on page 2), but each of the short-essay questions should use its own page(s). You do not need to answer questions in a specific order as long as you         indicate during the submission process which page belongs to which question. To    summarise (assuming there are 3 questions with Q1 having sub-questions a)-d)):

i.   Allowed:

1.    page 1: Q1a) and Q1b);

2.    page 2: Q1c) and Q1d);

3.    page 3: Q2

4.    page 4: Q3

ii.   Not allowed:

1.    page 1: Q1a)-d) and Q2

2.    page 2: Q3

3.    In your write-up, please indicate clearly which question and sub-question the answer refers to.

4.    Please include your worked solution, not just the final answer.

5.   Answers to all questions combined should be submitted through Gradescope, uploaded to the LMS.

a.    If you are unsure, please refer to the Gradescope getting started guide:

https://lms.unimelb.edu.au/students/student-guides/gradescope

b.   You may upload multiple versions if you would like to update your answers. Only the last received version will be used for grading. Please always update a full set of           answers; i.e., if you would like to change the answer to only a single question, please ensure to upload the answers to all other questions as well.

If at some point you are unable to answer a question and you need that information to answer a    subsequent question, you may proceed to that subsequent question by making an assumption and stating clearly and justifying what that assumption is.

Open Book Status: Yes

You are allowed to use notes, textbooks or resource materials, as authorised by the Board of Examiners.

Exam weight

This examination contributes 50% to the final subject mark.

Exam hurdle

Please note that Final Examination has no hurdle requirement.

Contact during the exam

I will be available on the Zoom link (same as the Consultation hours), which is available in Subject Guide, from 3pm-4pm. You can ask any clarifying questions related to the exam questions.

Alternatively, you can call the following numbers for assistance during the exam if you are       experiencing technical difficulties. Inside Australia: 13MELB (13 6352) (select Option 1 for         current students then select Option 1 again for exam enquiries). Outside Australia: +61 3 9035 5511 (select Option 1 for current students and then select Option 1 again for exam enquiries)


Part A: Multiple choice questions [25pts]

Please refer to the LMS quiz for the multiple-choice questions and submit your answers there.

The quiz will be available for the duration of the exam, but once you submit, you cannot view or edit your answers anymore.

Part B: Short essay questions [25pts]

(Note that different answers from rounding will get full marks. But for this, make sure you show your steps numerically. Providing only the final answer will not get full marks for short essay questions.     The following questions are a sample just to get you familiarized with the format of the short essay   questions. This does not necessarily represent the difficulty level of the final exam.)

Question B. 1 [3 + 3 = 6pts, 10min]

Suppose that the term structure of zero rates is upward sloping. Specifically, the interest rates of zero-coupon treasury bond from today up to year 1, year 2, and year 3 is 2%, 4%, and 6%,             respectively. Zero rates are an annualized compound rates.

(a) Please compute discount factors from today up to year 1, year 2, and year 3, respectively. Please round them to two decimal places. Do discount factors satisfy the no arbitrage relationship?

(b) If the expectations hypothesis holds, what are the expected future 1-year spot rate for the next two years, i.e., E[r1,2] and E[r2,3]? What is the expected future annualized spot rate from year 1 to   year 3, i.e., E[r1,3]?

Question B.2 [4 + 3 = 7pts, 20min]

Dr. Kim can buy or sell Treasury notes at the following prices for the face value of $100 on 15 October 2018.

Yield to

                                                                         Maturity                                              

 

A

15 Oct 2023

0%

4%

?

5

B

15 Oct 2021

8%

?

100.00

?

C

unknown

unknown

unknown

100.00

0

D

15 Oct 2028

0%

?

67.08

?

Coupon rate is an annualized percentage rate and coupons are paid semi-annually. Yield to maturity  is an annualized simple interest rate compounded semi-annually. Dr. Kim puts together the following portfolio today:

- Invests $1,000,000 in bond C.

- Buys bond D, a total face value of $600,000.

(a) Fill in all of the blanks (“?”) in the table or note that they are not computable.

(Hint: You can figure out from the table if Duration” on the last column of the table refers to Macaulay duration or modified duration. For bond A Quote, please keep it to the nearest two decimals.)

(b) Compute the Macaulay duration and modified duration of Dr. Kim’s assets (portfolio of bonds that Dr.Kim buys).

Question B.3 [2 + 2 + 2 = 6pts, 15min]

Suppose that Dr. Kim has an obligation to pay back $100,000 in 2.5 years. To immunise this               obligation, Dr. Kim plans to invest in 3-year x% coupon bond at a yield of 25.73% pa. Coupon rate is an annualized percentage rate and coupons are paid annually. Yield to maturity is an annualized      simple interest rate compounded annually.

(a) Please find coupon rate x% that will immunize Dr. Kim’s obligation.

(b) How much Dr.Kim should invest today in this coupon bond for immunization?

(c) Using the coupon rate you computed in part (a), please find the total dollar amount of par value of the coupon bond that Dr. Kim should invest in.

(In case you didn’t get an answer for part (a), please assume the coupon rate is 10%. I will still give you full mark for part (c) if the rest of steps are all correct.)

Question B.4 [6pts, 20min]

You would like to construct an optimal portfolio to maximize your mean-variance utility Ui  = E[ri] – ½*A*Variancei with a risk-aversion A=2. Your investment horizon is one year from today, and only two bonds are available for trading as below:

1. One-year risk-free zero-coupon bond: Face value of $100 and currently traded at $99.

2. One-year risky coupon bond: Face value of $100 with the coupon rate of 10% (coupon rate is an annualized percentage rate and coupon is paid annually, i.e., coupon is paid once in year1 when it matures.), currently traded at $80. At maturity, with the default probability of 40%, the risky bond will recover 60% of the face value and 60% of the coupon payment.

Please construct the optimal portfolio, i.e., weights of the two assets.