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Finance 537 Financial Risk Management Spring 2024 Neil D. Pearson 1
Homework 6 Due Sunday, March 3, 2024 at 10:00 p.m. US central time Total 10 points Instructions
. This is a group assignment. Groups may include up to 4 people. Please submit a Word or .pdf document with your solutions via the Canvas site prior to 10:00 p.m. on Sunday, March 3. You should also upload the computer codes and data files you use. Assignment.
This assignment asks you use continuously compounded returns on the XLF to estimate several GARCH, NGARCH, and ARCH models and use them to forecast volatility. Column F of the .csv file “ETFreturns.csv contains simple returns on the XLF. You should convert these simple returns to continuously compounded returns, and then use the most recent 1,000 returns. These are the returns in rows 4,789 through 5,788. 1.
GARCH(1,1) estimated 2 ways.
(total 2 points) (a)
(1 point) The GARCH(1,1) likelihood can be written as a function of the four parameters α
, β
, σ
, and σ
1
. Use the 1,000 continuously compounded returns on the XLF to estimate the GARCH(1,1) parameters, treating all four as unknown parameters to be estimated. What are the estimate of the four parameters α
, β
, σ
, and σ
1
? (Note that the question asks for the estimates of σ
, and σ
1
, not σ
2
and σ
1
2
.) Remark
: You should do this using R and one of the general optimization functions such as optim()
. To do this you will have to write your own R function to compute the negative of the log likelihood. The last page of this assignment displays an example of a function that computes the (negative of the) GARC(1,1) log likelihood. (b)
(1 point) Using the same data, set both the long-run variance σ
2
and the
initial variance σ
1
2
equal to the sample variance of the data used for estimation. If you do this, the GARCH(1,1) likelihood can be written as a function of the two unknown parameters α
and β
. Use maximum likelihood to estimate these two parameters. What are your estimates of the long-run standard deviation σ
and the
initial standard deviation σ
1
? What are your estimates of the parameters α
and β
? 2.
Using the GARCH(1,1) model to forecast variance and standard deviation (
total 2 points
)
This question asks you to use the estimates from Question 1(a) to compute forecast variance and standard deviation. (a)
(1/2 point) Use the estimates from Question 1(a) to forecast the return variance and standard deviation for January 3, 2023, which is the first trading day of 2023. What are your estimates of the variance and standard deviation? (b)
(1 point) Next, use the parameter estimates from Question 1(a) to forecast the variance of the 21-day return ∑
𝑅𝑅
𝑡𝑡+𝑘𝑘
21
𝑘𝑘=1
. In this formula, assume that the current date t
is just after the close of trading on December 30, 2022, and you have estimated the GARCH(1,1) model in Question 1(a). What is your forecast of the variance of the 21-day return ∑
𝑅𝑅
𝑡𝑡+𝑘𝑘
21
𝑘𝑘=1
?
Finance 537 Financial Risk Management Spring 2024 Neil D. Pearson 2
(c)
(1/2 point) Express your forecast in terms of the annualized volatility. (Take the square root, and then annualize by multiplying by 21
/
252
. Or else annualize by multiplying by 252/21, and then take the square root.) 3.
GARCH(1,1) using existing R functions
(total 2 points) In this question use the same continuously compounded returns you used in Question 1. (a)
(1 point) Use the R function garch()
from the R package tseries
to estimate the parameters of a GARCH(1,1) model. (
https://www.rdocumentation.org/packages/tseries/versions/0.10-
42/topics/garch
) Does the function return estimates of all four parameters α
, β
, σ
, and σ
1
? If not, which parameters does it estimate? What are the estimated parameters? Hint
: You might want to use your estimates from Question 1(a) as your initial guesses. (But you are not required to do this.) (b)
(1 point) Now use the R function garchFit()
from the R package fGarch
to estimate the parameters of a GARCH(1,1) model. (See https://cran.r-
project.org/web/packages/fGarch/fGarch.pdf
) Does the function return estimates of all four parameters α
, β
, σ
, and σ
1
? If not, which parameters does it estimate? What are the estimated parameters? 4.
N
GARCH(1,1) (total 2 points) The NGARCH(1,1) likelihood can be written as a function of the five unknown parameters α
, β
, θ
, σ
, and σ
1
. (a)
(1 point) Use the continuously compounded XLF returns to estimate the NGARCH(1,1) parameters, treating all five as unknown parameters to be estimated. What are the estimated parameters α
, β
, θ
, σ
, and σ
1
? Remark
: You should do this using R and one of the general optimization functions such as optim()
. To do this you will have to write your own R function to compute the (negative of the) log likelihood. (b)
(1 point) Using the results from Questions 1(a) and 4(a), carry out a likelihood ratio test of the hypothesis that θ
= 0. 5.
ARCH(1) (2 points) The ARCH(1) model is a special case of the GARCH(1,1) model in which β
= 0. (a)
(1 point) Please use the XLF returns data to estimate the parameters α
, σ
, and σ
1
of the ARCH(1) model. (b)
(1 point) Compare the performance of the GARCH(1,1) model from Question 1(a) and the ARCH(1) model by carrying out a likelihood ratio test of the hypothesis that β
= 0.
Finance 537 Financial Risk Management Spring 2024 Neil D. Pearson 3
Example of a function to compute the (negative of the) GARCH(1,1) log likelihood #Objective function (negative log likelihood) garch11a <- function(x) { sigmasqhat = rep(0.0,length(ret)) sigmasqhat[1] = x[4]^2 #(negative) log likelihood if (x[1]+x[2]>=1 || x[1]<0 || x[2]<0 || x[3]<0.001|| x[4]<0.001){ NeglogLH = 9999 } else { for (i in 1:(length(ret)-1)) { sigmasqhat[i+1] = (1-x[1]-x[2])*x[3]^2+x[1]*ret[i]^2+x[2]*sigmasqhat[i] } f <-(1/(sqrt(2*pi*sigmasqhat)))*exp(-0.5*ret^2/sigmasqhat) NeglogLH = -sum(log(f)) } return(NeglogLH) }
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Information pertaining to Noskey Corporation's sales revenue follows:
November 2021
(Actual)
$ 180,000
December 2021
(Budgeted)
$ 160,000
500,000
January 2022
(Budgeted)
Cash sales
000'09
$ 540,000
Credit sales
$ 360,000
000'09
Total sales
000'099 2$
Management estimates 5% of credit sales to be uncollectible. Of collectible credit sales, 60% is collected in the month of sale and the
remainder in the month following the month of sale. Purchases of inventory each month include 70% of the next month's projected
total sales (stated at cost) plus 30% of projected sales for the current month (stated at cost). All inventory purchases are on-account;
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Proceeds from Notes Payable
On January 26, Bella Co. borrowed cash from Conrad Bank by issuing a 30-day note with a face amount of $48,000. Assume a 360-day year.
a. Determine the proceeds of the note, assuming the note carries an interest rate of 6%.
b. Determine the proceeds of the note, assuming the note is discounted at 6%.
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The proceeds equal the cash initially received. Proceeds represents how much in value the borrower is walking away with in cash on
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Exercise 11-13 a-b (Part Level Submission)
According to a payroll register summary of Bramble Company, the amount of employees' gross pay in December was $862,000, of which $87,000 was not subject to Social Security
taxes of 6.2% and $761,000 was not subject to state and federal unemployment taxes.
(a)
X Your answer is incorrect. Try again.
Determine the employer's payroll tax expense for the month, using the following rates: FICA 7.65%, state unemployment 5.4%, and federal unemplayment 0.8%. (Round
answer to 0 decimal places, e.g. 125.)
Payroll tax expense
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On October 1, Head and Heart Company's petty cash fund of $150 is replenished. The fund contains cash of $30, and receipts for
supplies of $75 and postage of $45.
Prepare the journal entry to record the replenishment of the petty cash fund. (Credit account titles are automatically indented
when the amount is entered. Do not indent manually.)
Debit
Credit
Account Titles and Explanation
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Homework Assignment #3 Due in drop box 4/8 by 11:59 p.m.
Chapter 6
2. John Walters is comparing the cost of credit to the cash price of an item. If John makes an $80
down payment and pays $35 a month for 24 months, how much more will that amount be than
the cash price of $685?
5. A work-at-home opportunity is available in which you will receive 3 percent of the sales for
customers you refer to the company. The cost of your "franchise fee" is $600. How much would
your customers have to buy to cover the cost of this fee?
Chapter 7
7. Which mortgage would result in higher total payments?
Mortgage A: $985 a month for 30 years
Mortgage B: $780 a month for 5 years and $1,056 for 25 years
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Exercise 9-12 a-b (Part Level Submission)
Oriole Supply Co. has the following transactions related to notes receivable during the last 2 months of 2020. The company does not make entries to accrue interest except at
December 31.
Nov. 1
Loaned $23,50Chcash to Manny Lopez on a 12-month, 12% note.
Dec. 11
Sold goods to Ralph Kremer, Inc., receiving a $61,200, 90-day, 10% note.
16
Received a $97,200, 180 day, 8% note in exchange for Joe Fernetti's outstanding accounts receivable.
31
Accrued interest revenue on all notes receivable.
(a)
Your answer is correct.
lournalize the transactions for Oriole Supply Co. (Ignore entries for cost of goods sold.) (Credit account titles are…
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te with security updates, fixes, and Improvements, choose Check for Updates.
Minnie has asked you to review the methods Min Armin Wastege uses when dealing with
Accounts Receivable. Minnie has compiled the following information for the past 2 months and
wants you to update her records on August 31, 2020.
On June 30, 2020 the Account Receivable balance for Min Armin Wastege was $13,585 Dr with
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Sales (net of GST)
Sales Returns & Allowances (net of GST)
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Bad Debts to be written off (Including GST)
$4 800
400
3 550
660
The bad debts listed above have not been written off as yet. Minnie has also calculated based on
past experience that 7% of net credit sales go bad. All sales are made on credit.
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At the beginning of the current period, Vaughn had balances in Accounts Receivable of $273,000 and in Allowance for Doubtful Accounts of $9,200 (credit). During the period, it had net credit sales of
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(a - d)
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(b) Prepare the entry to record the…
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The YuRaeKa charity was established in 1960. The charity’s aim is to provide support to children from disadvantaged backgrounds who wish to take part in sports such as tennis, badminton, squash, basketball and football.
YuRaeKa has a detailed constitution[1] which explains how the charity’s income can be spent. The constitution also notes that administration expenditure cannot exceed 10% of income in any year.
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Analysis of Receivables Method
At the end of the current year, Accounts Receivable has
balance of $4,375,000; Allowance for Doubtful Accounts has a debit balance of $21,300; and sale
for the year total $102,480,000. Using the aging method, the balance of Allowance for Doubtful Accounts is estimated as $205,000.
a. Determine the amount of the adjusting entry for uncollectible acfounts.
b. Determine the adjusted balances of Accounts Receivable, Allowance for Doubtful Accounts, and Bad Debt Expense.
Accounts Receivable
Allowance for Doubtful Accounts
Bad Debt Expense
c. Determine the net realizable value of accounts receivable.
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Using the information from the accounts title picture fill in the the orange and green document using the directions on the right side. If this doesn’t make sense, I’m sorry.
This worksheet is for the period ended December 31 and the company name is Del's Delivery.
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Problem 1.
2.
Odette Electronics has 90 operating plants in seven southwestern states. Sales for
last year were P100 million, and the statement of financial position at year-end is
similar in percentage of sales to that of previous years (and this will continue in the
future). All assets (including fixed assets) and current liabilities will vary directly with
sales.
Statement of Financial Position
(in P millions)
Assets
Liabilities and Equity
Cash.....
P2
Accounts payable....
P15
Accounts receivable...
20
Accrued wages....
2
Inventory....
23
Accrued taxes.
8
Current assets..
P45
Current liabilities.
P25
Fixed assets...
40
Notes payable...
10
Ordinary shares.
15
Retained earnings...
35
Total assets..
P85
Total liabilities and equity..
P85
Odette's has an after-tax…
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logo design company purchases four new computers for $12,500. The company finances the cost of the computers for 3 years at an annual interest rate of 5.175% compounded monthly. Find the month
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At August 31, Coffman Company has this bank information: cash balance per bank $6,450; outstanding checks $2,762; deposits in
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- P 00 it View History Bookmarks Window Help 00 A ezto.mheducation.com nt Portal Course Modules: Budgeting and Forecasting 62211 Week 4: Homework Question 3 - Week 4: Homework - Co omework G Saved Help Save & Exit Submit Check my work Information pertaining to Noskey Corporation's sales revenue follows: November 2021 (Actual) $ 180,000 December 2021 (Budgeted) $ 160,000 500,000 January 2022 (Budgeted) Cash sales 000'09 $ 540,000 Credit sales $ 360,000 000'09 Total sales 000'099 2$ Management estimates 5% of credit sales to be uncollectible. Of collectible credit sales, 60% is collected in the month of sale and the remainder in the month following the month of sale. Purchases of inventory each month include 70% of the next month's projected total sales (stated at cost) plus 30% of projected sales for the current month (stated at cost). All inventory purchases are on-account; 25% is paid in the month of purchase, and the remainder is paid in the month following the month of purchase.…arrow_forwardplz solve with explanation within 30-40 min and get multiple upvotesarrow_forward* CengageNOWv2 | On x * Cengage Learning B Milestone Two Guidel G module 5 problem set x blem Set: Mod x now.com/ilm/takeAssignment/takeAssignmentMain.do?invoker=&takeAssignmentSessionLocator=&inprogres.. eBook Show Me How Proceeds from Notes Payable On January 26, Bella Co. borrowed cash from Conrad Bank by issuing a 30-day note with a face amount of $48,000. Assume a 360-day year. a. Determine the proceeds of the note, assuming the note carries an interest rate of 6%. b. Determine the proceeds of the note, assuming the note is discounted at 6%. Check My Work The proceeds equal the cash initially received. Proceeds represents how much in value the borrower is walking away with in cash on merchandise. Previous Next Check My Work 1:36 PM 54°F A O E A 4 11/28/2021 %23arrow_forward
- Bookmarks Window Help Q 8 Tue May 4 4:20 PM A edugen.wileyplus.com SOFTWARE UPDATE 25m ago Return to Blackboard macOS Big Sur 11.3.1 is available and will be installed later tonight. Weygandt, Accounting Principles, 13th Edition, Custom WileyPLUS Course for Bronx Community College Help | System Announcements CALCULATOR PRINTER VERSION 4BACK NEXT Exercise 11-13 a-b (Part Level Submission) According to a payroll register summary of Bramble Company, the amount of employees' gross pay in December was $862,000, of which $87,000 was not subject to Social Security taxes of 6.2% and $761,000 was not subject to state and federal unemployment taxes. (a) X Your answer is incorrect. Try again. Determine the employer's payroll tax expense for the month, using the following rates: FICA 7.65%, state unemployment 5.4%, and federal unemplayment 0.8%. (Round answer to 0 decimal places, e.g. 125.) Payroll tax expense $: Click if you would like to Show Work for this question: Open Show Work SUBMIT A W…arrow_forwardView History Bookmarks Window Help A education.wiley.com IN Netflix A Assignments Week 8 - Sp22 BTEC 142. NWP Assessment Player UI Application - /3 三 Question 7 of 10 View Policies Current Attempt in Progress On October 1, Head and Heart Company's petty cash fund of $150 is replenished. The fund contains cash of $30, and receipts for supplies of $75 and postage of $45. Prepare the journal entry to record the replenishment of the petty cash fund. (Credit account titles are automatically indented when the amount is entered. Do not indent manually.) Debit Credit Account Titles and Explanation Attempts: 0 of 1 used Submit Answer Save for Later 4. tv ... 80 00 DII DD F1 F2 F3 F4 FS F6 F7 F8 F9 F10 @ # $ & * 2 3 4 5 6 7 8 9 W E Y P Rarrow_forwardFMfcgxwLsmmztLTTFHnxfgtfwHRqwdvc?projector=18&messagePartld=0.3 Homework Assignment #3 Due in drop box 4/8 by 11:59 p.m. Chapter 6 2. John Walters is comparing the cost of credit to the cash price of an item. If John makes an $80 down payment and pays $35 a month for 24 months, how much more will that amount be than the cash price of $685? 5. A work-at-home opportunity is available in which you will receive 3 percent of the sales for customers you refer to the company. The cost of your "franchise fee" is $600. How much would your customers have to buy to cover the cost of this fee? Chapter 7 7. Which mortgage would result in higher total payments? Mortgage A: $985 a month for 30 years Mortgage B: $780 a month for 5 years and $1,056 for 25 years end F12 home prt sc F10 F6 F7 F8 F9 F11 F3 F4 F5 %23 % 5 6 7 8 9arrow_forward
- Bookmarks Window Help Fri Apr 30 7:38 PM edugen.wileyplus.com W WileyPLUS Bb Upload Assignment: Exercise16b - 2021 Spring Term (1)... Return to Blackboard Weygandt, Accounting Principles, 13th Edition, Custom WileyPLUS Course for Bronx Community College Help | System Announcements CALCULATOR PRINTER VERSION 4 ВАСK NEXT Exercise 9-12 a-b (Part Level Submission) Oriole Supply Co. has the following transactions related to notes receivable during the last 2 months of 2020. The company does not make entries to accrue interest except at December 31. Nov. 1 Loaned $23,50Chcash to Manny Lopez on a 12-month, 12% note. Dec. 11 Sold goods to Ralph Kremer, Inc., receiving a $61,200, 90-day, 10% note. 16 Received a $97,200, 180 day, 8% note in exchange for Joe Fernetti's outstanding accounts receivable. 31 Accrued interest revenue on all notes receivable. (a) Your answer is correct. lournalize the transactions for Oriole Supply Co. (Ignore entries for cost of goods sold.) (Credit account titles are…arrow_forwardA- A- Bapk Title Emphasis Heading 1 Heading 2 Heading 3 Heading 4 Heading 5 abe X, x? A - te with security updates, fixes, and Improvements, choose Check for Updates. Minnie has asked you to review the methods Min Armin Wastege uses when dealing with Accounts Receivable. Minnie has compiled the following information for the past 2 months and wants you to update her records on August 31, 2020. On June 30, 2020 the Account Receivable balance for Min Armin Wastege was $13,585 Dr with an Allowance for Doubtful Debts of $462 Cr. In the last two months Sales (net of GST) Sales Returns & Allowances (net of GST) Cash Collected Bad Debts to be written off (Including GST) $4 800 400 3 550 660 The bad debts listed above have not been written off as yet. Minnie has also calculated based on past experience that 7% of net credit sales go bad. All sales are made on credit. REQUIRED: А. Prepare the following General Journal entries to 1. account for the write off of the bad debt during the past two…arrow_forwardCreate the journal entry for the transactions belowarrow_forward
- Please show all workarrow_forwardedugen.wileyplus.com SOFTWARE UPDATE Return to Blackboard 7:12 PM IS Weygandt, Accounting Principles, 13th Edition, Custom WileyPLUS Course for Bronx Community College Help | System Announcements macOS Big Sur 11.3.1 is available and will be installed later tonight. CALCULATOR Exercise 9-04 a-f (Part Level Submission) PRINTER VERSION ВАСK NEXT At the beginning of the current period, Vaughn had balances in Accounts Receivable of $273,000 and in Allowance for Doubtful Accounts of $9,200 (credit). During the period, it had net credit sales of $870,000 and collections of $826,500. It wrote off as uncollectible accounts receivable of $6,700. However, a $3,000 account previously written off as uncollectible was recovered before the end of the current period. Uncollectible accounts are estimated to total $25,200 at the end of the period. (Omit cost of goods sold entries.) (a - d) (a) Prepare the entries to record sales and collections during the period. (b) Prepare the entry to record the…arrow_forwardAuditing || fall20 Dashboard My courses ACCT4141_iram_fall20 WEEK 7: 25 OCTOBER - 31 OCTOBER Case study 2 Separate groups: 5 My Submissions Case 2 Title Start Date Due Date Post Date Marks Available Case study 2 - Case 2 27 Oct 2020 - 08:00 28 Oct 2020 - 06:00 28 Oct 2020 - 19:00 100 Summary: On Chapters 9, 10, and 11: The YuRaeKa charity was established in 1960. The charity’s aim is to provide support to children from disadvantaged backgrounds who wish to take part in sports such as tennis, badminton, squash, basketball and football. YuRaeKa has a detailed constitution[1] which explains how the charity’s income can be spent. The constitution also notes that administration expenditure cannot exceed 10% of income in any year. The charity’s income is derived wholly from voluntary donations. Sources of donations include: (i) Cash collected by volunteers asking the public for donations in shopping areas, (ii) Cheques sent to the charity’s head office, (iii) Donations…arrow_forward
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