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### ECON3107 Week 7 Tut 6

Course: ECON 3107, Spring 2012
School: UNSW
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Word Count: 628

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of ECON3107 Economics Finance S1 2012 Tutorial 6 Week 7 Jeremy Jastrzab Housekeeping Next week *Mid Session exam: 24 April 2012 *According to the course outline: -Will cover Lectures Week 1 to 6 *No tutorial next week (Anzac Day) Jeremy Jastrzab 2012 From Week 6... Question : The time-state prices of the stock are shown in the tree diagram below. The oneperiod interest rate is 10 percent. Why do we need...

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of ECON3107 Economics Finance S1 2012 Tutorial 6 Week 7 Jeremy Jastrzab Housekeeping Next week *Mid Session exam: 24 April 2012 *According to the course outline: -Will cover Lectures Week 1 to 6 *No tutorial next week (Anzac Day) Jeremy Jastrzab 2012 From Week 6... Question : The time-state prices of the stock are shown in the tree diagram below. The oneperiod interest rate is 10 percent. Why do we need this? Jeremy Jastrzab 2012 It is the return on purchasing a bond: Note this when calculating your payment matrix for Option pricing Jeremy Jastrzab 2012 Now... Discount Factors Discount Factor df(t): Nominally, the present value (t=0) of one unit of currency to be paid with certainty at time t E.g. If Discount factor for year 1 [df(1)] = 0.9 The return of 1 in year 1 is worth 0.9 today Note: This solely is in relation to Bonds Jeremy Jastrzab 2012 Previously... OR.. . (In relation to Bonds) Jeremy Jastrzab 2012 Working with the second formula Jeremy Jastrzab 2012 Notation -Discount factors vector (1 x periods) -Cash flow vector (certain return) (periods x 1) (c vector) Jeremy Jastrzab 2012 Calculating Discount Factor (df) *The price of a bond should equal its discounted present value: -where: p = Bond price vector Q = payoff matrix *Therefore... Jeremy Jastrzab 2012 Question 1 Consider the following three Bonds that make the coupon payments listed below: Q= where: Jeremy Jastrzab 2012 Question 1 i) Compute the discount factors for Years 1, 2 and 3 Jeremy Jastrzab 2012 Question 1 ii) Construct a portfolio from the three Bonds that will generate the payoff vector below. As before... Jeremy Jastrzab 2012 Question 1 ii) ii) Construct a portfolio from the three Bonds that will generate the payoff vector below. Jeremy Jastrzab 2012 Question 1 ii) ii) What is the arbitrage free price of this portfolio? Previously: Remembering that: So: Jeremy Jastrzab 2012 Question 1 ii) ii) Can we check this arbitrage-free price? Yes we can... How much does it cost to create this portfolio? Jeremy Jastrzab 2012 Question 1 iii) Compute the interest rates i(2) i(1), and i(3): Explain in words the interpretation of i(3) First... How to calculate the interest rate of a given year? Jeremy Jastrzab 2012 Question 1 iii) Compute the interest rates i(1), i(2) and i(3): Jeremy Jastrzab 2012 Question 1 iii) Explain in words the interpretation on i(3): i(3) measures the average annual rate of return an investor would receive if they invested an amount for three (3) years => in this case: 10.06% This interpretation holds for all i(t) Jeremy Jastrzab 2012 Question 2 Consider the following three Bonds that make the coupon payments listed below: Q= where: Jeremy Jastrzab 2012 Question 2 i) Compute the discount factors df(1), df(2) and df(3): Jeremy Jastrzab 2012 Question 2 ii) Compute the (Macauley) Duration for the three bonds What is Duration? An indicator of the Bonds sensitivity to changes in interest rates measured in years Duration tells us for how long we can expect the Bond to be paying us returns ->The duration of the Jastrzab 2012 Jeremy cash flows Question 2 ii) Compute the (Macauley) Duration for the three bonds Step 1: Calculate the PV of each cash flow: Let v be a vector of present values from each Bond... Where well have 3 vectors for each Bond Jeremy Jastrzab 2012 Question 2 ii) The present value of Bond 1 cash flows: The present value of Bond 2 cash flows: The present value of Bond 3 cash flow: Jeremy Jastrzab 2012 Question 2 ii) Putting all of these together, the overall present value of the cash flow from each Bond: Jeremy Jastrzab 2012 Question 2 ii) Step 2: Calculate w(t) the fraction or weight of the bonds present value paid in year t: e.g. Jeremy Jastrzab 2012 Question 2 ii) Divide each value in V by the present value of the bond (bond price): Jeremy Jastrzab 2012 Question 2 ii) Step 3: Calculate Duration: Jeremy Jastrzab 2012 Question 2 ii) - Duration Bond 1: Duration = 1.9114 years Maturity = 2 years => Cash flows from Bond 1 stop before maturity Bond 2: Duration = 2.8532 years Maturity = 3 years => Cash flows from Bond 2 stop before maturity Jeremy Jastrzab 2012
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UNSW - ECON - 3107
TUTORIAL 1 WEEK 2ECON3107/5106 Economics of FinanceANSWERS1. The inverse matrix is:0.375 2. 5X 1 = 2.00.8750.8752. 52.00.3752. 87517. 512.01. 6253. 37522. 518.0 2. 125The following fragment of MATLAB code entered in the command promp
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TUTORIAL 3 WEEK 4ECON3107/ECON5106 Economics of FinanceANSWERS1. (i) The opportunity set describes what combinations of GA and BA can be obtained for 1PA.Let Q cfw_states*securities be the payment matrix of the two securities:Q:Good WeatherBad Weat
UNSW - ECON - 3107
The Setup: Three Period Binomial ModelTwo-period zero-coupon bond with initial value of \$1.00. Itsprice increases 5% of its prior value in every period.The Stock pays no dividends. Its initial value is \$1.00.Its price increases 26% of its prior value
UNSW - ECON - 3107
ValuationDenition: Valuation is the process of determining the presentvalue of a security or productive investment.Example 2.1: How much is a tree worth today ( at time 0)?pG = 0.285pB = 0.665Time 063 applesGood Weather48 applesBad WeatherTime
UNSW - ECON - 3107
The Opportunity SetDenition: A set of feasible future payos available with a wealthof one unit of present value.Example: The opportunities for future apples for a present appleinvested:Q cfw_states*securities is the payment matrix of the two securiti
UNSW - ECON - 3107
Completing the MarketConsider an example. Markets are incomplete:20 43 Good WeatherQ = 20 28 Fair WeatherpS = 19 35(32)(12)BondStock20 28Bad WeatherBond StockSuppose that an investor asks an investment rm to create aproduct with the following
UNSW - ECON - 3107
Multi-period Discount FactorsDenition: A nominal discount factor, df (t ), is the present valueof one unit of currency to be paid with certainty at time t .Notation:Discount function cfw_1periods:df = df (1) df (2) df (3)Vector of cash ows known to
UNSW - ECON - 3107
Forward PriceDenition: Forward price, f (t ), is the agreed amount determinedat the present time that have to be paid at the specied futuretime, t .Relation with present (spot) price:p = df (t )f (t ) f (t ) = p /df (t ) = p (1 + i (t )tExample: Two
UNSW - ECON - 3107
Uncertainty: An ExampleTwo periods: today (time 0) and future (time 1)Todays state of nature s0 is known. Alternatively, theprobability that s0 occurs (s0 ) = 1;Set of possible future events - good weather (GW) and badweather (BW): S = cfw_GW , BW .
UNSW - ECON - 3107
Portfolios of Two AssetsCombining a Riskless Asset with a Risky Asset IValentyn Panchenko UNSWPortfolios of Two AssetsCombining a Riskless Asset with a Risky Asset IIValentyn Panchenko UNSWPortfolios of Two AssetsCombining a Riskless Asset with a R
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Ecient PortfoliosMean-variance theory assumes that Investors prefer:(1) higher expected returns for a given level of standarddeviation(2) lower standard deviations for a given a level of expectedreturn.Portfolios that provide the maximum expected re
UNSW - ECON - 3107
Certainty EquivalenceDeriving expected return-risk frontier: some usefulformulaeLet X and Y be random variables with expectations E (X ) andE (Y ) , variances Var(X ) and Var(Y ) and covariance Cov(X, Y ).Let a and b be real numbers, then:E (aX + bY
UNSW - ACCT - 2522
Chapter 1Management accounting: informationfor creating value and managingresourcesCopyright 2012 McGraw-Hill Australia Pty LtdPowerPoint slides to accompany Management Accounting: Information for managing and creating value 6eSlides prepared by Kim
UNSW - ACCT - 2522
Chapter 2Management accounting: cost termsand conceptsCopyright 2012 McGraw-Hill Australia Pty LtdPowerPoint slides to accompany Management Accounting: Information for managing and creating value 6eSlides prepared by Kim Langfield-Smith2-1Outline
UNSW - ACCT - 2522
Chapter 3Cost behaviour, cost drivers andcost estimationCopyright 2012 McGraw-Hill Australia Pty LtdPowerPoint slides to accompany Management Accounting: Information for managing and creating value 6eSlides prepared by Kim Langfield-Smith3-1Outline
UNSW - ACCT - 2522
Chapter 4Product costing systemsCopyright 2012 McGraw-Hill Australia Pty LtdPowerPoint slides to accompany Management Accounting: Information for managing and creating value 6eSlides prepared by Kim Langfield-Smith4-1OutlineProduct costingDifferen
UNSW - ACCT - 2522
Chapter 5Process costing and operationcostingCopyright 2012 McGraw-Hill Australia Pty LtdPowerPoint slides to accompany Management Accounting: Information for managing and creating value 6eSlides prepared by Kim Langfield-Smith5-1OutlineProcess co
UNSW - ACCT - 2522
Chapter 6Service costingCopyright 2012 McGraw-Hill Australia Pty LtdPowerPoint slides to accompany Management Accounting: Information for managing and creating value 6eSlides prepared by Kim Langfield-Smith6-1Outline What are service organisations?
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Chapter 7A closer look atoverhead costsCopyright 2012 McGraw-Hill Australia Pty LtdPowerPoint slides to accompany Management Accounting: Information for managing and creating value 6eSlides prepared by Kim Langfield-Smith7-1OutlineWhat are overhea
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Chapter 8Activity-based costingCopyright 2012 McGraw-Hill Australia Pty LtdPowerPoint slides to accompany Management Accounting: Information for managing and creating value 6eSlides prepared by Kim Langfield-Smith8-1Outline Problems with convention
UNSW - ACCT - 2522
Chapter 9Budgeting systemsCopyright 2012 McGraw-Hill Australia Pty LtdPowerPoint slides to accompany Management Accounting: Information for managing and creating value 6eSlides prepared by Kim Langfield-Smith9-1OutlineStrategic planning and budgeti
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Chapter 10Standard costs for control: directmaterial and direct labourCopyright 2012 McGraw-Hill Australia Pty LtdPowerPoint slides to accompany Management Accounting: Information for managing and creating value 6eSlides prepared by Kim Langfield-Smi
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Chapter 11Standard costs for control: flexiblebudgets and manufacturing overheadCopyright 2012 McGraw-Hill Australia Pty LtdPowerPoint slides to accompany Management Accounting: Information for managing and creating value 6eSlides prepared by Kim Lan
UNSW - ACCT - 2522
Chapter 12Financial performance reports andtransfer pricingCopyright 2012 McGraw-Hill Australia Pty LtdPowerPoint slides to accompany Management Accounting: Information for managing and creating value 6eSlides prepared by Kim Langfield-Smith12-1Out
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Chapter 13Financial performance measuresfor investment centres, and rewardsystemsCopyright 2012 McGraw-Hill Australia Pty LtdPowerPoint slides to accompany Management Accounting: Information for managing and creating value 6eSlides prepared by Kim L
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Chapter 14Contemporary approaches tomeasuring and managingperformanceCopyright 2012 McGraw-Hill Australia Pty LtdPowerPoint slides to accompany Management Accounting: Information for managing and creating value 6eSlides prepared by Kim Langfield-Smi
UNSW - ACCT - 2522
Chapter 15Managing suppliers and customersCopyright 2012 McGraw-Hill Australia Pty LtdPowerPoint slides to accompany Management Accounting: Information for managing and creating value 6eSlides prepared by Kim Langfield-Smith15-1Outline Supply chain
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Chapter 16Managing costs and qualityCopyright 2012 McGraw-Hill Australia Pty LtdPowerPoint slides to accompany Management Accounting: Information for managing and creating value 6eSlides prepared by Kim Langfield-Smith16-1OutlineCost managementAct
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Chapter 17Sustainability and managementaccountingCopyright 2012 McGraw-Hill Australia Pty LtdPowerPoint slides to accompany Management Accounting: Information for managing and creating value 6eSlides prepared by Kim Langfield-Smith17-1OutlineSusta
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Chapter 18Cost volume profit analysisCopyright 2012 McGraw-Hill Australia Pty LtdPowerPoint slides to accompany Management Accounting: Information for managing and creating value 6eSlides prepared by Kim Langfield-Smith18-1OutlineWhat is CVP analys
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Chapter 19Information for decisions: relevantcosts and benefitsCopyright 2012 McGraw-Hill Australia Pty LtdPowerPoint slides to accompany Management Accounting: Information for managing and creating value 6eSlides prepared by Kim Langfield-Smith19-1
UNSW - ACCT - 2522
Chapter 20Pricing and product mix decisionsCopyright 2012 McGraw-Hill Australia Pty LtdPowerPoint slides to accompany Management Accounting: Information for managing and creating value 6eSlides prepared by Kim Langfield-Smith20-1Outline Major influ
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Chapter 21Information for capital expendituredecisionsCopyright 2012 McGraw-Hill Australia Pty LtdPowerPoint slides to accompany Management Accounting: Information for managing and creating value 6eSlides prepared by Kim Langfield-Smith21-1Outline
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MotionGoal: Students will be able to analyze anobjects motion using position, time,speed/velocity and acceleration1. Measure motion1.Defining Motion2.Distinguish between velocity and speed3.Define Acceleration4.Describe an Objects Motion based
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Forensic and Investigative AccountingForensicChapter 2Forensic Accounting Education,Institutions, and Specialties 2011 CCH. All Rights Reserved.4025 W. Peterson Ave.Chicago, IL 60646-60851 800 248 3248www.CCHGroup.comTermites, Rust, and FraudJu
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Forensic and Investigative AccountingForensicChapter 3Fraudulent Financial Reporting 2011 CCH. All Rights Reserved.4025 W. Peterson Ave.Chicago, IL 60646-60851 800 248 3248www.CCHGroup.comAn International ProblemFraud is an international phenome
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Forensic and Investigative AccountingForensicChapter 9Proper Evidence Management 2011 CCH. All Rights Reserved.4025 W. Peterson Ave.Chicago, IL 60646-60851 800 248 3248www.CCHGroup.comRules of EvidenceThe rules of evidence are the rules governin
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Forensic and Investigative AccountingForensicChapter 11Litigation Support inSpecial Situations 2011 CCH. All Rights Reserved.4025 W. Peterson Ave.Chicago, IL 60646-60851 800 248 3248www.CCHGroup.comAntitrust LawsAntitrust laws are an outgrowth
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10.2Rational ExponentsRationalExponentsRational exponents have been defined in such a wayso as to make their properties the same as theproperties for integer exponents.In this section we explore the meaning of a baseraised to a rational (fractiona
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