A Guide to the Pricing Conventions of SFE Interest Rate Products


 Toby Cox
 4 years ago
 Views:
Transcription
1 A Guide to the Pricig Covetios of SFE Iterest Rate Products SFE 30 Day Iterbak Cash Rate Futures Physical 90 Day Bak Bills SFE 90 Day Bak Bill Futures SFE 90 Day Bak Bill Futures Tick Value Calculatios SFE 90 Day Bak Bill Optios Australia Commowealth Treasury Bods SFE 10 Year Treasury Bod Futures SFE 10 Year Treasury Bod Futures Tick Value Calculatios SFE 10 Year Treasury Bod Optios SFE 3 Year Treasury Bod Futures Tick Value Calculatios SFE 3 Year Bod Optios Iterest Rate Swap Futures 3 Year Iterest Rate Swap Futures 10 Year Iterest Rate Swap Futures This brochure provides market users ad back office system suppliers with a guide as to the pricig covetios of SFE iterest rate futures ad optios. The pricig covetios used for the majority of SFE's iterest rate products differ from that used i may offshore futures markets. Ulike i Europe ad the Uited States where iterest rate securities are traded i the cash market o the basis of their capital price, the covetio adopted i Australia is to price such istrumets o the basis of their yield to maturity. Due to this covetio, SFE's iterest rate cotracts are similarly traded o the basis of yield with the futures price quoted as 100 mius the yield to maturity expressed i per cet per aum. While the obvious advatage of pricig iterest rate cotracts i this fashio is that their yield is trasparet ad ca be easily compared to yields o cash market istrumets, a importat byproduct is that the tick value o these products does ot remai costat but rather chages i accordace with movemets i the uderlyig iterest rate. This variatio is most proouced i the 10 Year Treasury Bod futures cotract ad is less substatial for the 3 Year Treasury Bod futures cotract ad 90 Day Bak Bill futures cotracts. For all these cotracts, the tick value decreases as iterest rates rise ad icreases as iterest rates fall. 30 Day Iterbak Cash Rate Futures Ulike SFE s 90 day Bak Bill Futures ad 3 ad 10 year Treasury Bod Futures, the 30 Day Cash Rate Futures cotract has a fixed tick. Uder a fixed tick regime, the variatio margis are calculated by multiplyig the umber of price movemets (i poits terms) by the fixed tick dollar value of AUD24.66 per 0.01% move by the umber of cotracts traded. For example: Trade Price = Number of Cotracts = 100 Ed of Day Settlemet Price = Variatio Margi o Positio = $3, (1.5pts x AUD24.66 x 100 cotracts) The cash rate futures cotract gives a exposure to AUD3,000,000 per cotract. Hece, the cotract value of a positio i the 30 Day Iterbak Cash Rate Futures is equivalet to the face value of the cotract multiplied by the umber of cotracts bought or sold. Physical 90 Day Bak Bills Ulike its best kow equivalet i the Uited States  the Eurodollar time deposit  the value of a physical 90 Day Bak Bill is calculated accordig to a yield to maturity formula that discouts the face value to establish the appropriate iterest cost over the 90 days.
2 The formula for the preset value (P) of a bak bill is: P = FaceValue 365 yield Days to Maturity 100 The face value represets the bill's future value, i.e. its value at the ed of its 90 day term. Please ote the Australia covetio is to use a 365 rather tha a 360 day year. I order to calculate the preset value (P) of a 90 Day Bak Bill which has a face value of $100,000 ad is tradig at a yield to maturity of 5.50%, the followig calculatios are performed: 100, P = = $98, This same formula ca be applied to value Bak Bills with varyig maturities (i.e. 30, 60, 90, 180 days) ad face values (i.e. $100,000, $500,000, $1,000,000). These values would simply be iserted ito the formula where appropriate. SFE 90 Day Bak Bills For SFE 90 Day Bak Bill Futures, where the cotract value is always $1,000,000, ad the term to maturity is exactly 90 days, the bak bill formula ca be rewritte as: P = 1,000, yield where the yield is the futures price deducted from 100. Therefore if a Bak Bill futures cotract was tradig at (ie. a yield of 5%) the value of the cotract would be: 1,000, P = = $987, SFE 90 Day Bak Bill Futures Tick Value Calculatios The dollar value of a 0.01% chage i yield does ot remai costat but rather varies i accordace with chages i the uderlyig iterest rate. Accordigly, to establish what the dollar value of a futures tick will be at a give price, the followig calculatios are made: 1. Use the cotract valuatio formula (as described above) to calculate the uderlyig value of the cotract at the omiated futures price. 2. Apply the same formula to that same futures price mius 0.01 (i.e., icrease the yield by 0.01%). 3. The differece betwee the two cotract values represets the dollar value of the tick at the omiated futures price. To determie the dollar value of a 0.01% chage i yield of a Bak Bill futures cotract which is tradig at a price of (ie. a yield of 5.00%) the followig calculatios are performed: 1. Futures cotract value at (5.00%)= $987, (rouded to two decimal places) 2. Futures cotract value at (5.01%)= $987, (rouded to two decimal places) 3. Differece (value of 0.01% of premium)= $24.06
3 SFE 90 Day Bak Bill Optios Premiums for optios o 90 Day Bak Bill futures are quoted i terms of aual percetage yield (e.g. 0.60% pa or 1.05% pa) with the value of a sigle poit of premium (ie. 0.01% pa) calculated by comparig its cotract value at the exercise price (expressed as 100 mius aual yield) ad its value at that same exercise price less oe poit (0.01%). For example, a 90 Day Bak Bill optio with a exercise price of ad a premium of 0.065% pa would be valued as follows: 1. Futures cotract value at (5.00%)= $987, (rouded to two decimal places) 2. Futures cotract value at (5.01%)= $987, (rouded to two decimal places) 3. Differece (value of 0.01% of premium)= $24.06 Sice we have 6.5 poits of premium, the fial premium i dollars is $ To exactly match the premium i dollars as calculated by SFE Clearig the premium should be calculated i the followig maer: $24.06 x = (rouded to four decimal places) x 100 = $ A fial importat poit to ote is that, for a optio with a particular exercise price, the value of 0.01% of premium is costat, while the tick value of the uderlyig futures cotract is variable with the level of iterest rates. To put it aother way, the value of a move of a certai size i the futures market will ot equate exactly i dollar terms with a move of the same size i the optio premium. Ivestors should also be cautious about implemetig coversio strategies owig to the differeces i tick sizes betwee a optio strike price ad the prevailig futures price. For example, it ca happe that a optio appears to be priced slightly below its itrisic value i terms of the yield whe i fact, i dollar terms, the pricig is correct. Australia Commowealth Treasury Bods The formula for calculatig the price per A$100 of a Australia Commowealth Treasury Bod as supplied by the Reserve Bak of Australia is: where v = 1/(1+i) where i is the aual percetage yield divided by 200. f = the umber of days from the date of settlemet to the ext iterest paymet date d = the umber of days i the half year edig o the ext iterest paymet date c = the amout of iterest paymet (if ay) per $100 face value at the ext iterest paymet date g = the fixed halfyearly iterest rate payable (equal to the aual fixed rate divided by 2). = the umber of full halfyears betwee the ext iterest paymet date ad the date of maturity (equal to 2 times the umber of years util maturity) a = v + v +.+ v = (1 v )/i The covetio adopted with Commowealth Treasury Bods is that iterest is paid o the fifteeth day of the appropriate moth with the last iterest paymet made at maturity. Usig the Reserve Bak pricig formula, the calculatios which would be performed to value a Commowealth Treasury Bod with a maturity of 15 October 2007, a coupo rate of 10.00%, a market yield of 5.70% ad a settlemet day of 7 April 1998 would be: i = v = f = (2/4/98 + T3 busiess (7/04/98) to 15/4/98) = 8 d = 182 g = 5
4 = 20 f/d = c = 5 Usig the above iputs, the bod would have a value of A$ per $100 face value (iclusive of accrued iterest). SFE 10 Year Treasury Bod Futures For SFE Treasury Bod futures, the pricig formula ca be simplified because there is always a exact umber of half years to maturity ad hece there is o requiremet to calculate accrued iterest. The formula for the value (P) of a 10 Year Bod futures cotract o SFE is writte as: 20 ( 1 v ) c P = v i 20 where: i = yield % pa divided by 200 v = 1/(1+i) = 20 c = coupo rate/2 Thus to value a 6% coupo 10 Year Treasury Bod cotract which is tradig at a price of (i.e. A yield of 4.50% pa.), the iputs would be: i = v = = 20 c = 3 Whe these iputs are icluded i the formula, the cotract value for the above cotract will be A$111, Note that the mathematical covetio is that multiplicatio ad divisio take precedece over, additio ad subtractio. I the futures formula, this meas that the divisio by i is performed before the additio of 100v 20. To exactly match the cotract value as calculated by SFE Clearig, steps C, D ad G must be rouded to exactly eight decimal places, with 0.5 beig rouded up. No other steps are rouded except K, which is rouded to two decimal places. SFE Clearig makes the calculatio i the followig maer: Futures Price A price B I = A/ C v = 1/(1 + B) D v E 1  v 20 = 1  D F 3(1  v 20 ) = 3 x E G 3(1  v 20 )/i = F/B H 100v 20 = 100 x D I G + H J I x 1,000 $111, K Rouded $111, SFE 10 Year Treasury Bod Futures Tick Value Calculatios The methodology used to calculate tick values for the 10 Year Treasury Bod Futures is idetical to that outlied i the previous example for 90 Day Bak Bill Futures.
5 For example, to determie the dollar value of a 0.01% chage i yield o a 10 Year Bod cotract tradig at a price of (ie. A yield of 5.64%), the followig calculatios are performed. 1. Futures cotract value at (5.64%) = $102, Futures cotract value at (5.65%) = $102, Differece (value of 0.01% of premium) = $ or $76.87 rouded to two decimal places. SFE 10 Year Treasury Bod Optios Like Bak Bill optios, 10 Year bod optios are quoted i terms of aual percetage yield (e.g % or 0.525%), with the value of a sigle poit of premium (ie. 0.01%) calculated as the differece betwee the cotract value at the exercise price (expressed as 100 mius the aual yield) ad its value at that exercise price less oe poit (0.01%). Please ote that whe makig these calculatios, cotract values are ot rouded to the earest cet before calculatig this differece. Accordigly, the dollar value of a optio o a 10 Year Treasury bod optio with a exercise price of ad a premium of 0.140% would be calculated as follows: 1. Futures cotract value at = $100, Futures cotract value at = $99, Differece (value 0.01% of premium) = $ Sice there is 14 poits of premium, the fial premium i dollars is calculated as: $ x 14 = $1, which whe rouded to the earest cet gives $ SFE 3 Year Treasury Bod Futures Tick Value Calculatios For SFE Treasury Bod futures, the Reserve Bak of Australia govermet bod pricig formula ca be simplified because there is always a exact umber of half years to maturity ad hece there is o requiremet to calculate accrued iterest. The formula for the value (P) of a 3 Year Bod Futures cotract o SFE is writte as: 6 ( 1 v ) c P = v i 6 where: i = yield % pa divided by 200 v = 1/(1+i) = umber of coupo paymets. For the 3 Year cotract this is 6. c = coupo rate/2 Thus to value a 6% coupo 3 Year Treasury Bod cotract which is tradig at a price of (i.e. a yield of 4.495% pa.), the iputs would be: i = v = = 6 c = 3 Whe these iputs are icluded i the formula, the cotract value for the above cotract will be A$104, Note that the mathematical covetio is that multiplicatio ad divisio take precedece over, additio ad subtractio. I the futures formula, this meas that the divisio by i is performed before the additio of 100v 6. To exactly match the cotract value as calculated by SFE Clearig, steps C, D ad G must be rouded to exactly eight decimal places, with 0.5 beig rouded up. No other steps are rouded except K, which is rouded to two decimal places. SFE Clearig makes the calculatio i the followig maer:
6 Futures Price A price B I = A/ C v = 1/(1 + B) D V E 1 v 6 = 1  D F 3(1 v 6 ) = 3 x E G 3(1 v 6 )/i = F/B H 100v 6 = 100 x D I G + H J I x 1,000 $104, K Rouded $104, Determiig Variatio Margis for 3 Year Treasury Bod Futures SFE Clearig determies the variatio or marked to market margi for variable tick cotracts i the followig by comparig the cotract value for the previous ed of day price (or the trade price if the cotract was bought or sold that day) ad that day's ed of day settlemet price or exit price. For example: 1. Bought 10 3 Year Treasury Bod Futures at price of (yield = 4.495%). The cotract value determied usig the bod formula is $104, per cotract. The cotract value for 10 cotracts is $1,041, Ed of day settlemet price for 3 Year Treasury Bod Futures is (yield = 5.510%). The cotract value is $101, x 10 cotracts = $1,013, Variatio Margi, determied by calculatig the differece betwee the two cotract values, that is, $1,041, $1,013, = $28, The margi paymet made o the 10 lot positio is $28, Calculatig the Tick Value for SFE 3 Year Treasury Bod Futures The dollar value of a 0.010% chage i yield does ot remai costat but rather varies i accordace with chages i the uderlyig iterest rate. Accordigly, to establish what the dollar value of a futures tick will be at a give price, the followig calculatios are made: 4. Use the cotract valuatio formula (as described above) to calculate the uderlyig value of the cotract at the omiated futures price. 5. Apply the same formula to that same futures price mius (i.e., icrease the yield by 0.010%). 6. The differece betwee the two cotract values represets the dollar value of the tick at the omiated futures price. For example, to calculate the dollar value of a 0.010% chage i yield whe the 6% coupo 3 Year cotract is tradig at a price of (i.e. a yield of 5.240%), the followig calculatios are performed. 1. Futures cotract value at (5.240%) = $102, Futures cotract value at (5.250%) = $102, Differece (value 0.01% of premium) = $ Which whe rouded to the earest cet gives $27.77 SFE 3 Year Bod Optios Premiums for the 3 Year Bod optios are calculated i exactly the same way as for 10 Year Bod optios, by referece to the value of a oepoit move i the uderlyig futures cotract from the exercise price to the exercise price less oe poit.
7 To value a 6% coupo 3 Year Treasury Bod optio which has a strike price of ad a premium of poits, the followig calculatios are made: 1. Futures cotract value at = $101, Futures cotract value at = $101, Differece (value 0.010% of premium) = $ Sice there is 24 poits of premium, the fial premium i dollars is calculated as: $ x 24 = $ which whe rouded to the earest cet gives $ A fial importat poit to ote is that, for a optio with a particular exercise price, the value of 0.010% of premium is costat, while the tick value of the uderlyig futures cotract is variable with the level of iterest rates. To put it aother way, the value of a move of a certai size i the futures market will ot equate exactly i dollar terms with a move of the same size i the optio premium. Ivestors should also be cautious about implemetig coversio strategies owig to the differeces i tick sizes betwee a optio strike price ad the prevailig futures price. For example, it ca happe that a optio appears to be priced slightly below its itrisic value i terms of the yield whe i fact, i dollar terms, the pricig is correct. 3 Year ad 10 Year Iterest Rate Swap Futures The cotract value formula for Iterest Rate Swap Futures is a modified versio of the Treasury Bod Futures pricig formula. The differece betwee the two formulas is the coupo rate. Iterest Rate Swap Futures have a coupo rate of 6.5% as opposed to the 6% used for Treasury Bod Futures. 3 Year Iterest Rate Swap Futures The formula for the value (P) of 3 Year Iterest Rate Swap Futures at SFE is writte as: ( 1 v ) c P = v i where: i = yield % pa divided by 200 v = 1/(1+i) = the umber of coupo paymets c = coupo rate/2 Thus to value a 6.5% coupo 3 Year Iterest Rate Swap Futures cotract which is tradig at a price of (ie. a yield of 5.70% pa.), the iputs would be: i = v = = 6 c = 3.25 Whe these iputs are icluded i the formula, the cotract value for the above cotract will be A$102, Note that the mathematical covetio is that multiplicatio ad divisio take precedece over, additio ad subtractio. I the futures formula, this meas that the divisio by i is performed before the additio of 100v 6. To exactly match the cotract value as calculated by SFE Clearig Corporatio (SFECC), steps C, D ad G must be rouded to exactly eight decimal places, with 0.5 beig rouded up. No other steps are rouded except K, which is rouded to 2 decimal places. The SFECC makes the calculatio i the followig maer: Futures Price A 100 price 5.70 B i = A/
8 C v = 1/(1 + B) D v E 1 v 6 = 1  D F 3.25(1 v 6 ) = 3.25 x E G 3.25(1 v 6 )/i = F/B H 100v 6 = 100 x D I G + H J I x 1,000 $102, K Rouded $102, Year Iterest Rate Swap Futures The formula for the value (P) of 10 Year Iterest Rate Swap Futures at SFE is writte as: ( 1 v ) c P = v i where: i = yield % pa divided by 200 v = 1/(1+i) = the umber of coupo paymets c = coupo rate/2 Thus to value a 6.5% coupo 10 Year Iterest Rate Swap Futures cotract which is tradig at a price of (ie. a yield of 4.500% pa.), the iputs would be: i = v = = 20 c = 3.25 Whe these iputs are icluded i the formula, the cotract value for the above cotract will be A$115, Note that the mathematical covetio is that multiplicatio ad divisio take precedece over, additio ad subtractio. I the futures formula, this meas that the divisio by i is performed before the additio of 100v 20. To exactly match the cotract value as calculated by SFE Clearig Corporatio (SFECC), steps C, D ad G must be rouded to exactly eight decimal places, with 0.5 beig rouded up. No other steps are rouded except K, which is rouded to 2 decimal places. The SFECC makes the calculatio i the followig maer: Futures Price A 100 price B i = A/ C v = 1/(1 + B) D v E 1  v 20 = 1  D F 3.25(1  v 20 ) = 3.25 x E G 3.25(1  v 20 )/i = F/B H 100v 20 = 100 x D I G + H J I x 1,000 $115, K Rouded $115,963.71
9 This documet was prepared by the Busiess Developmet Group of the Sydey Futures Exchage. SFE takes o resposibility for errors or omissios or losses arisig from actios based o this iformatio. This documet does ot substitute for the SFE Busiess Rules ad i the case of icosistecy, the Busiess Rules prevail. For further iformatio o SFE, or its products, please cotact the Busiess Developmet Group. Copyright Sydey Futures Exchage Limited 1998 Last Updated December 2005
CHAPTER 11 Financial mathematics
CHAPTER 11 Fiacial mathematics I this chapter you will: Calculate iterest usig the simple iterest formula ( ) Use the simple iterest formula to calculate the pricipal (P) Use the simple iterest formula
More information5.4 Amortization. Question 1: How do you find the present value of an annuity? Question 2: How is a loan amortized?
5.4 Amortizatio Questio 1: How do you fid the preset value of a auity? Questio 2: How is a loa amortized? Questio 3: How do you make a amortizatio table? Oe of the most commo fiacial istrumets a perso
More informationQuestion 2: How is a loan amortized?
Questio 2: How is a loa amortized? Decreasig auities may be used i auto or home loas. I these types of loas, some amout of moey is borrowed. Fixed paymets are made to pay off the loa as well as ay accrued
More information.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth
Questio 1: What is a ordiary auity? Let s look at a ordiary auity that is certai ad simple. By this, we mea a auity over a fixed term whose paymet period matches the iterest coversio period. Additioally,
More informationCHAPTER 3 THE TIME VALUE OF MONEY
CHAPTER 3 THE TIME VALUE OF MONEY OVERVIEW A dollar i the had today is worth more tha a dollar to be received i the future because, if you had it ow, you could ivest that dollar ad ear iterest. Of all
More informationBond Valuation I. What is a bond? Cash Flows of A Typical Bond. Bond Valuation. Coupon Rate and Current Yield. Cash Flows of A Typical Bond
What is a bod? Bod Valuatio I Bod is a I.O.U. Bod is a borrowig agreemet Bod issuers borrow moey from bod holders Bod is a fixedicome security that typically pays periodic coupo paymets, ad a pricipal
More informationChapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions
Chapter 5 Uit Aual Amout ad Gradiet Fuctios IET 350 Egieerig Ecoomics Learig Objectives Chapter 5 Upo completio of this chapter you should uderstad: Calculatig future values from aual amouts. Calculatig
More informationNATIONAL SENIOR CERTIFICATE GRADE 12
NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P EXEMPLAR 04 MARKS: 50 TIME: 3 hours This questio paper cosists of 8 pages ad iformatio sheet. Please tur over Mathematics/P DBE/04 NSC Grade Eemplar INSTRUCTIONS
More informationTerminology for Bonds and Loans
³ ² ± Termiology for Bods ad Loas Pricipal give to borrower whe loa is made Simple loa: pricipal plus iterest repaid at oe date Fixedpaymet loa: series of (ofte equal) repaymets Bod is issued at some
More informationFM4 CREDIT AND BORROWING
FM4 CREDIT AND BORROWING Whe you purchase big ticket items such as cars, boats, televisios ad the like, retailers ad fiacial istitutios have various terms ad coditios that are implemeted for the cosumer
More informationInstitute of Actuaries of India Subject CT1 Financial Mathematics
Istitute of Actuaries of Idia Subject CT1 Fiacial Mathematics For 2014 Examiatios Subject CT1 Fiacial Mathematics Core Techical Aim The aim of the Fiacial Mathematics subject is to provide a groudig i
More informationSole trader financial statements
3 Sole trader fiacial statemets this chapter covers... I this chapter we look at preparig the year ed fiacial statemets of sole traders (that is, oe perso ruig their ow busiess). We preset the fiacial
More informationDefinition. A variable X that takes on values X 1, X 2, X 3,...X k with respective frequencies f 1, f 2, f 3,...f k has mean
1 Social Studies 201 October 13, 2004 Note: The examples i these otes may be differet tha used i class. However, the examples are similar ad the methods used are idetical to what was preseted i class.
More informationCDs Bought at a Bank verses CD s Bought from a Brokerage. Floyd Vest
CDs Bought at a Bak verses CD s Bought from a Brokerage Floyd Vest CDs bought at a bak. CD stads for Certificate of Deposit with the CD origiatig i a FDIC isured bak so that the CD is isured by the Uited
More informationCHAPTER 3 DIGITAL CODING OF SIGNALS
CHAPTER 3 DIGITAL CODING OF SIGNALS Computers are ofte used to automate the recordig of measuremets. The trasducers ad sigal coditioig circuits produce a voltage sigal that is proportioal to a quatity
More informationConfidence Intervals for One Mean
Chapter 420 Cofidece Itervals for Oe Mea Itroductio This routie calculates the sample size ecessary to achieve a specified distace from the mea to the cofidece limit(s) at a stated cofidece level for a
More informationBENEFITCOST ANALYSIS Financial and Economic Appraisal using Spreadsheets
BENEITCST ANALYSIS iacial ad Ecoomic Appraisal usig Spreadsheets Ch. 2: Ivestmet Appraisal  Priciples Harry Campbell & Richard Brow School of Ecoomics The Uiversity of Queeslad Review of basic cocepts
More informationINVESTMENT PERFORMANCE COUNCIL (IPC)
INVESTMENT PEFOMANCE COUNCIL (IPC) INVITATION TO COMMENT: Global Ivestmet Performace Stadards (GIPS ) Guidace Statemet o Calculatio Methodology The Associatio for Ivestmet Maagemet ad esearch (AIM) seeks
More informationAmendments to employer debt Regulations
March 2008 Pesios Legal Alert Amedmets to employer debt Regulatios The Govermet has at last issued Regulatios which will amed the law as to employer debts uder s75 Pesios Act 1995. The amedig Regulatios
More informationI. Why is there a time value to money (TVM)?
Itroductio to the Time Value of Moey Lecture Outlie I. Why is there the cocept of time value? II. Sigle cash flows over multiple periods III. Groups of cash flows IV. Warigs o doig time value calculatios
More informationRainbow options. A rainbow is an option on a basket that pays in its most common form, a nonequally
Raibow optios INRODUCION A raibow is a optio o a basket that pays i its most commo form, a oequally weighted average of the assets of the basket accordig to their performace. he umber of assets is called
More informationSolving Logarithms and Exponential Equations
Solvig Logarithms ad Epoetial Equatios Logarithmic Equatios There are two major ideas required whe solvig Logarithmic Equatios. The first is the Defiitio of a Logarithm. You may recall from a earlier topic:
More informationBond Mathematics & Valuation
Bod Mathematics & Valuatio Below is some legalese o the use of this documet. If you d like to avoid a headache, it basically asks you to use some commo sese. We have put some effort ito this, ad we wat
More informationSECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES
SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES Read Sectio 1.5 (pages 5 9) Overview I Sectio 1.5 we lear to work with summatio otatio ad formulas. We will also itroduce a brief overview of sequeces,
More informationTHE ARITHMETIC OF INTEGERS.  multiplication, exponentiation, division, addition, and subtraction
THE ARITHMETIC OF INTEGERS  multiplicatio, expoetiatio, divisio, additio, ad subtractio What to do ad what ot to do. THE INTEGERS Recall that a iteger is oe of the whole umbers, which may be either positive,
More informationSubject CT5 Contingencies Core Technical Syllabus
Subject CT5 Cotigecies Core Techical Syllabus for the 2015 exams 1 Jue 2014 Aim The aim of the Cotigecies subject is to provide a groudig i the mathematical techiques which ca be used to model ad value
More informationInterest Rate Derivatives
Interest Rate Derivatives Price and Valuation Guide The pricing conventions used for most ASX 24 interest rate futures products differ from that used in many offshore futures markets. Unlike in Europe
More informationLearning objectives. Duc K. Nguyen  Corporate Finance 21/10/2014
1 Lecture 3 Time Value of Moey ad Project Valuatio The timelie Three rules of time travels NPV of a stream of cash flows Perpetuities, auities ad other special cases Learig objectives 2 Uderstad the timevalue
More informationwhere: T = number of years of cash flow in investment's life n = the year in which the cash flow X n i = IRR = the internal rate of return
EVALUATING ALTERNATIVE CAPITAL INVESTMENT PROGRAMS By Ke D. Duft, Extesio Ecoomist I the March 98 issue of this publicatio we reviewed the procedure by which a capital ivestmet project was assessed. The
More informationBasic Elements of Arithmetic Sequences and Series
MA40S PRECALCULUS UNIT G GEOMETRIC SEQUENCES CLASS NOTES (COMPLETED NO NEED TO COPY NOTES FROM OVERHEAD) Basic Elemets of Arithmetic Sequeces ad Series Objective: To establish basic elemets of arithmetic
More informationThis document contains a collection of formulas and constants useful for SPC chart construction. It assumes you are already familiar with SPC.
SPC Formulas ad Tables 1 This documet cotais a collectio of formulas ad costats useful for SPC chart costructio. It assumes you are already familiar with SPC. Termiology Geerally, a bar draw over a symbol
More informationFI A CIAL MATHEMATICS
CHAPTER 7 FI A CIAL MATHEMATICS Page Cotets 7.1 Compoud Value 117 7.2 Compoud Value of a Auity 118 7.3 Sikig Fuds 119 7.4 Preset Value 122 7.5 Preset Value of a Auity 122 7.6 Term Loas ad Amortizatio 123
More informationINVESTMENT PERFORMANCE COUNCIL (IPC) Guidance Statement on Calculation Methodology
Adoptio Date: 4 March 2004 Effective Date: 1 Jue 2004 Retroactive Applicatio: No Public Commet Period: Aug Nov 2002 INVESTMENT PERFORMANCE COUNCIL (IPC) Preface Guidace Statemet o Calculatio Methodology
More informationCHAPTER 4: NET PRESENT VALUE
EMBA 807 Corporate Fiace Dr. Rodey Boehe CHAPTER 4: NET PRESENT VALUE (Assiged probles are, 2, 7, 8,, 6, 23, 25, 28, 29, 3, 33, 36, 4, 42, 46, 50, ad 52) The title of this chapter ay be Net Preset Value,
More informationPreSuit Collection Strategies
PreSuit Collectio Strategies Writte by Charles PT Phoeix How to Decide Whether to Pursue Collectio Calculatig the Value of Collectio As with ay busiess litigatio, all factors associated with the process
More informationTime Value of Money. First some technical stuff. HP10B II users
Time Value of Moey Basis for the course Power of compoud iterest $3,600 each year ito a 401(k) pla yields $2,390,000 i 40 years First some techical stuff You will use your fiacial calculator i every sigle
More informationGround rules. Guide to Calculation Methods for the FTSE Fixed Income Indexes v1.3
Groud rules Guide to Calculatio Methods for the FTSE Fixed Icome Idexes v1.3 ftserussell.com October 2015 Cotets 1.0 Itroductio... 3 2.0 Idex level calculatios... 5 3.0 Bod level calculatios... 10 Appedix
More informationGround Rules. Guide to Calculation Methods for the Fixed Income Indexes v1.5
Groud Rules Guide to Calculatio Methods for the Fixed Icome Idexes v1.5 ftserussell.com December 2015 Cotets 1.0 Itroductio... 3 2.0 Idex level calculatios... 5 3.0 Bod level calculatios... 11 Appedix
More informationDilution Example. Chapter 24 Warrants and Convertibles. Warrants. The Difference Between Warrants and Call Options. Warrants
Chapter 24 Warrats ad Covertibles Warrats The Differece betee Warrats ad Call Optios Warrat Pricig ad the BlackScholes Model Covertible Bods The Value of Covertible Bods Reasos for Issuig Warrats ad Covertibles
More informationLesson 17 Pearson s Correlation Coefficient
Outlie Measures of Relatioships Pearso s Correlatio Coefficiet (r) types of data scatter plots measure of directio measure of stregth Computatio covariatio of X ad Y uique variatio i X ad Y measurig
More informationMMQ Problems Solutions with Calculators. Managerial Finance
MMQ Problems Solutios with Calculators Maagerial Fiace 2008 Adrew Hall. MMQ Solutios With Calculators. Page 1 MMQ 1: Suppose Newma s spi lads o the prize of $100 to be collected i exactly 2 years, but
More informationWorking with numbers
4 Workig with umbers this chapter covers... This chapter is a practical guide showig you how to carry out the types of basic calculatio that you are likely to ecouter whe workig i accoutig ad fiace. The
More informationExample: Probability ($1 million in S&P 500 Index will decline by more than 20% within a
Value at Risk For a give portfolio, ValueatRisk (VAR) is defied as the umber VAR such that: Pr( Portfolio loses more tha VAR withi time period t)
More informationMainStay Funds IRA/SEP/Roth IRA Distribution Form
MaiStay Fuds IRA/SEP/Roth IRA Distributio Form Do ot use for IRA Trasfers or SIMPLE IRA INSTRUCTIONS Before completig this form, please refer to the applicable Custodial Agreemet ad Disclosure Statemet
More informationMathematical goals. Starting points. Materials required. Time needed
Level A1 of challege: C A1 Mathematical goals Startig poits Materials required Time eeded Iterpretig algebraic expressios To help learers to: traslate betwee words, symbols, tables, ad area represetatios
More information2 Time Value of Money
2 Time Value of Moey BASIC CONCEPTS AND FORMULAE 1. Time Value of Moey It meas moey has time value. A rupee today is more valuable tha a rupee a year hece. We use rate of iterest to express the time value
More informationFrance caters to innovative companies and offers the best research tax credit in Europe
1/5 The Frech Govermet has three objectives : > improve Frace s fiscal competitiveess > cosolidate R&D activities > make Frace a attractive coutry for iovatio Tax icetives have become a key elemet of public
More information1. C. The formula for the confidence interval for a population mean is: x t, which was
s 1. C. The formula for the cofidece iterval for a populatio mea is: x t, which was based o the sample Mea. So, x is guarateed to be i the iterval you form.. D. Use the rule : pvalue
More informationSwaps: Constant maturity swaps (CMS) and constant maturity. Treasury (CMT) swaps
Swaps: Costat maturity swaps (CMS) ad costat maturity reasury (CM) swaps A Costat Maturity Swap (CMS) swap is a swap where oe of the legs pays (respectively receives) a swap rate of a fixed maturity, while
More informationTHE TIME VALUE OF MONEY
QRMC04 9/17/01 4:43 PM Page 51 CHAPTER FOUR THE TIME VALUE OF MONEY 4.1 INTRODUCTION AND FUTURE VALUE The perspective ad the orgaizatio of this chapter differs from that of chapters 2 ad 3 i that topics
More information*The most important feature of MRP as compared with ordinary inventory control analysis is its time phasing feature.
Itegrated Productio ad Ivetory Cotrol System MRP ad MRP II Framework of Maufacturig System Ivetory cotrol, productio schedulig, capacity plaig ad fiacial ad busiess decisios i a productio system are iterrelated.
More informationForecasting. Forecasting Application. Practical Forecasting. Chapter 7 OVERVIEW KEY CONCEPTS. Chapter 7. Chapter 7
Forecastig Chapter 7 Chapter 7 OVERVIEW Forecastig Applicatios Qualitative Aalysis Tred Aalysis ad Projectio Busiess Cycle Expoetial Smoothig Ecoometric Forecastig Judgig Forecast Reliability Choosig the
More informationRepeating Decimals are decimal numbers that have number(s) after the decimal point that repeat in a pattern.
5.5 Fractios ad Decimals Steps for Chagig a Fractio to a Decimal. Simplify the fractio, if possible. 2. Divide the umerator by the deomiator. d d Repeatig Decimals Repeatig Decimals are decimal umbers
More informationPresent Value Factor To bring one dollar in the future back to present, one uses the Present Value Factor (PVF): Concept 9: Present Value
Cocept 9: Preset Value Is the value of a dollar received today the same as received a year from today? A dollar today is worth more tha a dollar tomorrow because of iflatio, opportuity cost, ad risk Brigig
More informationSoving Recurrence Relations
Sovig Recurrece Relatios Part 1. Homogeeous liear 2d degree relatios with costat coefficiets. Cosider the recurrece relatio ( ) T () + at ( 1) + bt ( 2) = 0 This is called a homogeeous liear 2d degree
More informationIn nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008
I ite Sequeces Dr. Philippe B. Laval Keesaw State Uiversity October 9, 2008 Abstract This had out is a itroductio to i ite sequeces. mai de itios ad presets some elemetary results. It gives the I ite Sequeces
More informationFor customers Key features of the Guaranteed Pension Annuity
For customers Key features of the Guarateed Pesio Auity The Fiacial Coduct Authority is a fiacial services regulator. It requires us, Aego, to give you this importat iformatio to help you to decide whether
More informationDetermining the sample size
Determiig the sample size Oe of the most commo questios ay statisticia gets asked is How large a sample size do I eed? Researchers are ofte surprised to fid out that the aswer depeds o a umber of factors
More informationStatement of cash flows
6 Statemet of cash flows this chapter covers... I this chapter we study the statemet of cash flows, which liks profit from the statemet of profit or loss ad other comprehesive icome with chages i assets
More informationBaan Service Master Data Management
Baa Service Master Data Maagemet Module Procedure UP069A US Documetiformatio Documet Documet code : UP069A US Documet group : User Documetatio Documet title : Master Data Maagemet Applicatio/Package :
More informationInformation about Bankruptcy
Iformatio about Bakruptcy Isolvecy Service of Irelad Seirbhís Dócmhaieachta a héirea Isolvecy Service of Irelad Seirbhís Dócmhaieachta a héirea What is the? The Isolvecy Service of Irelad () is a idepedet
More informationPresent Value Tax Expenditure Estimate of Tax Assistance for Retirement Saving
Preset Value Tax Expediture Estimate of Tax Assistace for Retiremet Savig Tax Policy Brach Departmet of Fiace Jue 30, 1998 2 Preset Value Tax Expediture Estimate of Tax Assistace for Retiremet Savig This
More informationExample 2 Find the square root of 0. The only square root of 0 is 0 (since 0 is not positive or negative, so those choices don t exist here).
BEGINNING ALGEBRA Roots ad Radicals (revised summer, 00 Olso) Packet to Supplemet the Curret Textbook  Part Review of Square Roots & Irratioals (This portio ca be ay time before Part ad should mostly
More informationDWS Investment GmbH. DWS Aktien Strategie Deutschland Sales Prospectus including Terms of Contract
DWS Ivestmet GmbH DWS Aktie Strategie Deutschlad Sales Prospectus icludig Terms of Cotract Jauary 1, 2012 Sales Prospectus ad Terms of Cotract Sales Prospectus Geeral sectio Geeral priciples 1 Maagemet
More informationBest of security and convenience
Get More with Additioal Cardholders. Importat iformatio. Add a coapplicat or authorized user to your accout ad you ca take advatage of the followig beefits: RBC Royal Bak Visa Customer Service Cosolidate
More informationCHAPTER 5: EQUITY MARKETS
CHAPTER 5: EQUITY MARKETS Overview Whe we buy stock i a corporatio, we exchage cash for a share of hopedfor future profits of the compay. These profits ca come via capital appreciatio ad through receipt
More informationValuing Firms in Distress
Valuig Firms i Distress Aswath Damodara http://www.damodara.com Aswath Damodara 1 The Goig Cocer Assumptio Traditioal valuatio techiques are built o the assumptio of a goig cocer, I.e., a firm that has
More informationAudit of Assumptions for the March 2001 Budget. REPORT BY THE COMPTROLLER AND AUDITOR GENERAL HC 304 Session 2000 2001: 7 March 2001
Audit of Assumptios for the March 2001 Budget REPORT BY THE COMPTROLLER AND AUDITOR GENERAL HC 304 Sessio 2000 2001: 7 March 2001 Audit of Assumptios for the March 2001 Budget REPORT BY THE COMPTROLLER
More informationBCP ABSOLUTE RETURN BOND 16
AVAILABLE TO INVESTMENT PENSION ARF/AMRF INVESTORS BCP ABSOLUTE A CAPITAL SECURE, ACTIVELY MANAGED, ABSOLUTE RETURN BOND THAT AIMS TO ACHIEVE CONSISTENT, POSITIVE RETURNS Uderlyig Fud has a exceptioal
More informationHere are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed.
This documet was writte ad copyrighted by Paul Dawkis. Use of this documet ad its olie versio is govered by the Terms ad Coditios of Use located at http://tutorial.math.lamar.edu/terms.asp. The olie versio
More informationI apply to subscribe for a Stocks & Shares NISA for the tax year 2015/2016 and each subsequent year until further notice.
IFSL Brooks Macdoald Fud Stocks & Shares NISA trasfer applicatio form IFSL Brooks Macdoald Fud Stocks & Shares NISA trasfer applicatio form Please complete usig BLOCK CAPITALS ad retur the completed form
More informationEnhance Your Financial Legacy Variable Annuity Death Benefits from Pacific Life
Ehace Your Fiacial Legacy Variable Auity Death Beefits from Pacific Life 7/15 2017215B As You Pla for Retiremet, Protect Your Loved Oes A Pacific Life variable auity ca offer three death beefits that
More informationTO: Users of the ACTEX Review Seminar on DVD for SOA Exam FM/CAS Exam 2
TO: Users of the ACTEX Review Semiar o DVD for SOA Exam FM/CAS Exam FROM: Richard L. (Dick) Lodo, FSA Dear Studets, Thak you for purchasig the DVD recordig of the ACTEX Review Semiar for SOA Exam FM (CAS
More informationIntroducing Your New Wells Fargo Trust and Investment Statement. Your Account Information Simply Stated.
Itroducig Your New Wells Fargo Trust ad Ivestmet Statemet. Your Accout Iformatio Simply Stated. We are pleased to itroduce your ew easytoread statemet. It provides a overview of your accout ad a complete
More information5: Introduction to Estimation
5: Itroductio to Estimatio Cotets Acroyms ad symbols... 1 Statistical iferece... Estimatig µ with cofidece... 3 Samplig distributio of the mea... 3 Cofidece Iterval for μ whe σ is kow before had... 4 Sample
More informationPENSION ANNUITY. Policy Conditions Document reference: PPAS1(7) This is an important document. Please keep it in a safe place.
PENSION ANNUITY Policy Coditios Documet referece: PPAS1(7) This is a importat documet. Please keep it i a safe place. Pesio Auity Policy Coditios Welcome to LV=, ad thak you for choosig our Pesio Auity.
More informationInvesting in Stocks WHAT ARE THE DIFFERENT CLASSIFICATIONS OF STOCKS? WHY INVEST IN STOCKS? CAN YOU LOSE MONEY?
Ivestig i Stocks Ivestig i Stocks Busiesses sell shares of stock to ivestors as a way to raise moey to fiace expasio, pay off debt ad provide operatig capital. Ecoomic coditios: Employmet, iflatio, ivetory
More informationGuide to Calculation FTSE Global Equity Index Series v3.0
Guide to Calculatio FTSE Global Equity Idex Series v3.0 ftserussell.com October 2015 Cotets 1.0 Purpose of the guide... 3 2.0 Defiitio of terms... 4 3.0 Capital retur idexes... 5 4.0 Total retur idexes...
More informationSimple Annuities Present Value.
Simple Auities Preset Value. OBJECTIVES (i) To uderstad the uderlyig priciple of a preset value auity. (ii) To use a CASIO CFX9850GB PLUS to efficietly compute values associated with preset value auities.
More informationRISK TRANSFER FOR DESIGNBUILD TEAMS
WILLIS CONSTRUCTION PRACTICE IBEAM Jauary 2010 www.willis.com RISK TRANSFER FOR DESIGNBUILD TEAMS DesigbuilD work is icreasig each quarter. cosequetly, we are fieldig more iquiries from cliets regardig
More informationIncremental calculation of weighted mean and variance
Icremetal calculatio of weighted mea ad variace Toy Fich faf@cam.ac.uk dot@dotat.at Uiversity of Cambridge Computig Service February 009 Abstract I these otes I eplai how to derive formulae for umerically
More informationHow to read A Mutual Fund shareholder report
Ivestor BulletI How to read A Mutual Fud shareholder report The SEC s Office of Ivestor Educatio ad Advocacy is issuig this Ivestor Bulleti to educate idividual ivestors about mutual fud shareholder reports.
More informationEduRisk International Financial Risk Management & Training Justin Clarke +353 87 901 4483 justin.clarke@edurisk.ie www.edurisk.ie
EduRisk Iteratioal Fiacial Risk Maagemet & Traiig Justi Clarke +5 87 90 8 usti.clarke@edurisk.ie www.edurisk.ie Swap Discoutig & Pricig Usig the OIS Itroductio Sice August 007 ad the start of the fiacial
More informationA NOTE ON THE CALCULATION OF THE AFTERTAX COST OF DEBT
INTERNATIONAL JOURNAL OF BUSINESS, 1(1), 1996 ISSN:10834346 A NOTE ON THE CALCULATION OF THE AFTERTAX COST OF DEBT Wm R McDaiel, Daiel E. McCarty, ad Keeth A. Jessell Whe oe examies stadard fiacial maagemet
More informationLearning Objectives. Chapter 2 Pricing of Bonds. Future Value (FV)
Leaig Objectives Chapte 2 Picig of Bods time value of moey Calculate the pice of a bod estimate the expected cash flows detemie the yield to discout Bod pice chages evesely with the yield 21 22 Leaig
More informationBiology 171L Environment and Ecology Lab Lab 2: Descriptive Statistics, Presenting Data and Graphing Relationships
Biology 171L Eviromet ad Ecology Lab Lab : Descriptive Statistics, Presetig Data ad Graphig Relatioships Itroductio Log lists of data are ofte ot very useful for idetifyig geeral treds i the data or the
More informationGCSE STATISTICS. 4) How to calculate the range: The difference between the biggest number and the smallest number.
GCSE STATISTICS You should kow: 1) How to draw a frequecy diagram: e.g. NUMBER TALLY FREQUENCY 1 3 5 ) How to draw a bar chart, a pictogram, ad a pie chart. 3) How to use averages: a) Mea  add up all
More informationCHAPTER 7: Central Limit Theorem: CLT for Averages (Means)
CHAPTER 7: Cetral Limit Theorem: CLT for Averages (Meas) X = the umber obtaied whe rollig oe six sided die oce. If we roll a six sided die oce, the mea of the probability distributio is X P(X = x) Simulatio:
More informationBCP EQUITY INDEX BONDS
AVAILABLE TO INVESTMENT PENSION ARF/AMRF INVESTORS BCP EQUITY INDEX BONDS TWO CAPITAL SECURE BONDS THAT PROVIDE ACCESS TO LEADING EUROPEAN AND WORLD EQUITY INDICES Track the performace of the Fivex S&E
More informationsummary of cover CONTRACT WORKS INSURANCE
1 SUMMARY OF COVER CONTRACT WORKS summary of cover CONTRACT WORKS INSURANCE This documet details the cover we ca provide for our commercial or church policyholders whe udertakig buildig or reovatio works.
More informationEstimating Probability Distributions by Observing Betting Practices
5th Iteratioal Symposium o Imprecise Probability: Theories ad Applicatios, Prague, Czech Republic, 007 Estimatig Probability Distributios by Observig Bettig Practices Dr C Lych Natioal Uiversity of Irelad,
More informationPAYG instalments how to complete your activity statement
Istructios for busiesses ad ivestors PAYG istalmets how to complete your activity statemet For more iformatio visit www.ato.gov.au NAT 739311.2012 Our commitmet to you We are committed to providig you
More informationAnnuities Under Random Rates of Interest II By Abraham Zaks. Technion I.I.T. Haifa ISRAEL and Haifa University Haifa ISRAEL.
Auities Uder Radom Rates of Iterest II By Abraham Zas Techio I.I.T. Haifa ISRAEL ad Haifa Uiversity Haifa ISRAEL Departmet of Mathematics, Techio  Israel Istitute of Techology, 3000, Haifa, Israel I memory
More informationBLUE SKY SRA ALLIANCE FUND
BLUE SKY SRA ALLIANCE FUND ARSN 140 253 685 PRODUCT DISCLOSURE STATEMENT Ivestmet Sciece 4 Uits (APIR Code COL0018AU) Ivestmet Sciece 9 Uits (APIR Code COL0019AU) 3 JUNE 2014 Ivestmet Sciece 16E Uits (APIR
More informationChapter 7: Confidence Interval and Sample Size
Chapter 7: Cofidece Iterval ad Sample Size Learig Objectives Upo successful completio of Chapter 7, you will be able to: Fid the cofidece iterval for the mea, proportio, ad variace. Determie the miimum
More informationCS103X: Discrete Structures Homework 4 Solutions
CS103X: Discrete Structures Homewor 4 Solutios Due February 22, 2008 Exercise 1 10 poits. Silico Valley questios: a How may possible sixfigure salaries i whole dollar amouts are there that cotai at least
More informationChoosing a Mortgage FIXEDRATE MORTGAGES. ADJUSTABLERATE MORTGAGES (ARMs)
Choosig A Mortgage Like homes, home mortgages come i all shapes ad sizes: shortterm, logterm, fixed, adjustable, jumbo, balloo these are all terms that will soo be familiar to you, if they re ot already.
More informationOption pricing. Elke Korn Ralf Korn 1. This publication is part of the book Mathematics and Economy, which is supported by the BertelsmannStiftung.
MaMaEuSch Maagemet Mathematics for Europea Schools http://www.mathematik.uikl.de/~mamaeusch/ Optio pricig Elke Kor Ralf Kor This publicatio is part of the book Mathematics ad Ecoomy, which is supported
More informationMeasures of Spread and Boxplots Discrete Math, Section 9.4
Measures of Spread ad Boxplots Discrete Math, Sectio 9.4 We start with a example: Example 1: Comparig Mea ad Media Compute the mea ad media of each data set: S 1 = {4, 6, 8, 10, 1, 14, 16} S = {4, 7, 9,
More informationSection 3: Renters and Rental Units
Sectio 3: Reters ad Retal Uits About two millio New York City households roughly twothirds ret their homes. Over the past decade retal housig has become less affordable to may New Yorkers. Give the dowtur
More information