F537.s2024.HW06

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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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* 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 %23

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Create the journal entry for the transactions below

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edugen.wileyplus.com | 山 + G Return to Blackboard Weygandt, Accounting Principles, 13th Edition, Custom WileyPLUS Course for Bronx Community College Help | System Announcements CALCULATOR PRINTER VERSION 1 BACK NEXT Exercise 133 a-b On September 30, after all monthly postings had been completed, the Accounts Receivable control account in the general ledger had a debit balance of $245,000; the Accounts Payable control account had a credit balance of $109,000. The October transactions recorded in the special journals are presented below. Special Journals October Transactions Sales journal Total sales $183,000 Purchases journal Total purchases 75,000 Cash receipts journal Accounts receivable column total 128,000 Cash payments journal Accounts payable column total 49,000 Compute the balance of the accounts receivable control accounts after the monthly postings on October 31. Accounts Receivable Compute the balances of the accounts payable control accounts after the monthly postings on…

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FINANCIAL MANAGEMENT 1.docx - O Search (Alt+Q) Cel File Home Insert Draw Design Layout References Mailings Review View Help A Share P Comments ... I .. I . 1 . . I . 2. : . . 3 ... L . 4 . . . L. .. 5... I .. 6. . I :7.. | 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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New tab x Content x Quiz 3-MAT-143, section 03F, Fax + https://www.webassign.net/web/Student/Assignment-Responses/last?dep=34832472 a A ✰ DETAILS MY NOTES ASK YOUR TEACHE A newspaper editor starts a retirement savings plan in which $225 per month is deposited at the beginning of each month into an account that earns an annual interest rate of 6.4% compounded monthly. Find the value of this investment (in dollars) after 20 years. (Round your answer to the nearest cent.) $ DETAILS MY NOTES ASK YOUR TEACHI 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 ayment (in dollars) for this loan. (Round your answer to the nearest cent. See Example 8 in this section.) Submit Assignment Home My Assignments Request Extension Copyright © 1998-2024 Cengage Learning, Inc. All Rights Reserved | TERMS OF USE PRIVACY 12:03 PM

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Cashaun Wo x CCU brightspace.wiltech.edu/d2l/le/7659/discussions/topics/2429/View Subscribe New Wave Images is a graphics design firm that prepares its financial statements using a calendar year. Manny Kinn, the company treasurer and vice president of finance, has prepared a classified balance sheet as of December 31. In January, this balance sheet will be submitted along with an application for a loan from First Peoples Community Bank. An excerpt from the balance sheet follows: Cash $ 25,000 Accounts Receivable 85,000 Total Assets $ 250,000 The accounts receivable balance includes a $56,000 loan to Tom Morrow, the company president. Tom borrowed the money from New Wave 18 months earlier for a down payment on a new home. Tom has orally assured Manny that he will pay off the loan within the next year. Because Tom is the company president, Manny treats the amount due as a trade account receivable. In addition, Manny knows that the bank will consider a large balance in trade accounts…

Make a general ledger for each account title from the general journal below.

16% D Fri le Edit View History Bookmarks Window Help A education.wiley.com W https://msroederbhs.weebly.com/uploads/2/2/4/0/= NWP Assessment Player UI Application - Quiz 2 -/3 E Question 9 of 10 < View Policies Current Attempt in Progress At August 31, Coffman Company has this bank information: cash balance per bank $6,450; outstanding checks $2,762; deposits in transit $1,700; and a bank service charge $20. Determine the adjusted cash balance per bank at August 31, 2021. Adjusted cash balance per bank 2$ Attempts: 0 of 1 used Submit Answer Save for Later 7.288 MAR 4 étv P. Maclook A 000 80 DII DD F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 @ # $ % A & * 2 3 5 6 8

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