A Guide to the Pricing Conventions of SFE Interest Rate Products

Size: px
Start display at page:

Download "A Guide to the Pricing Conventions of SFE Interest Rate Products"

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 by-product 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 half-yearly iterest rate payable (equal to the aual fixed rate divided by 2). = the umber of full half-years 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 oe-poit 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 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 information

5.4 Amortization. Question 1: How do you find the present value of an annuity? Question 2: How is a loan amortized?

5.4 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 information

Question 2: How is a loan amortized?

Question 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

.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 information

CHAPTER 3 THE TIME VALUE OF MONEY

CHAPTER 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 information

Bond 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

Bond 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 fixed-icome security that typically pays periodic coupo paymets, ad a pricipal

More information

Chapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions

Chapter 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 information

NATIONAL SENIOR CERTIFICATE GRADE 12

NATIONAL 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 information

Terminology for Bonds and Loans

Terminology 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 Fixed-paymet loa: series of (ofte equal) repaymets Bod is issued at some

More information

FM4 CREDIT AND BORROWING

FM4 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 information

Institute of Actuaries of India Subject CT1 Financial Mathematics

Institute 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 information

Sole trader financial statements

Sole 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 information

Definition. 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

Definition. 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 information

CDs Bought at a Bank verses CD s Bought from a Brokerage. Floyd Vest

CDs 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 information

CHAPTER 3 DIGITAL CODING OF SIGNALS

CHAPTER 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 information

Confidence Intervals for One Mean

Confidence 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 information

BENEFIT-COST ANALYSIS Financial and Economic Appraisal using Spreadsheets

BENEFIT-COST ANALYSIS Financial and Economic Appraisal using Spreadsheets BENEIT-CST 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 information

INVESTMENT PERFORMANCE COUNCIL (IPC)

INVESTMENT 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 information

Amendments to employer debt Regulations

Amendments 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 information

I. Why is there a time value to money (TVM)?

I. 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 information

Rainbow options. A rainbow is an option on a basket that pays in its most common form, a nonequally

Rainbow 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 information

Solving Logarithms and Exponential Equations

Solving 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 information

Bond Mathematics & Valuation

Bond 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 information

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES

SECTION 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 information

THE ARITHMETIC OF INTEGERS. - multiplication, exponentiation, division, addition, and subtraction

THE 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 information

Subject CT5 Contingencies Core Technical Syllabus

Subject 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 information

Interest Rate Derivatives

Interest 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 information

Learning objectives. Duc K. Nguyen - Corporate Finance 21/10/2014

Learning 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 time-value

More information

where: 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

where: 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 information

Basic Elements of Arithmetic Sequences and Series

Basic Elements of Arithmetic Sequences and Series MA40S PRE-CALCULUS 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 information

This document contains a collection of formulas and constants useful for SPC chart construction. It assumes you are already familiar with SPC.

This 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 information

FI A CIAL MATHEMATICS

FI 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 information

INVESTMENT PERFORMANCE COUNCIL (IPC) Guidance Statement on Calculation Methodology

INVESTMENT 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 information

CHAPTER 4: NET PRESENT VALUE

CHAPTER 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 information

Pre-Suit Collection Strategies

Pre-Suit Collection Strategies Pre-Suit 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 information

Time Value of Money. First some technical stuff. HP10B II users

Time 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 information

Ground rules. Guide to Calculation Methods for the FTSE Fixed Income Indexes v1.3

Ground 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 information

Ground Rules. Guide to Calculation Methods for the Fixed Income Indexes v1.5

Ground 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 information

Dilution Example. Chapter 24 Warrants and Convertibles. Warrants. The Difference Between Warrants and Call Options. Warrants

Dilution 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 Black-Scholes Model Covertible Bods The Value of Covertible Bods Reasos for Issuig Warrats ad Covertibles

More information

Lesson 17 Pearson s Correlation Coefficient

Lesson 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 information

MMQ Problems Solutions with Calculators. Managerial Finance

MMQ 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 information

Working with numbers

Working 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 information

Example: Probability ($1 million in S&P 500 Index will decline by more than 20% within a

Example: Probability ($1 million in S&P 500 Index will decline by more than 20% within a Value at Risk For a give portfolio, Value-at-Risk (VAR) is defied as the umber VAR such that: Pr( Portfolio loses more tha VAR withi time period t)

More information

MainStay Funds IRA/SEP/Roth IRA Distribution Form

MainStay 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 information

Mathematical goals. Starting points. Materials required. Time needed

Mathematical 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 information

2 Time Value of Money

2 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 information

France caters to innovative companies and offers the best research tax credit in Europe

France 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 information

1. C. The formula for the confidence interval for a population mean is: x t, which was

1. 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 : p-value

More information

Swaps: Constant maturity swaps (CMS) and constant maturity. Treasury (CMT) swaps

Swaps: 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 information

THE TIME VALUE OF MONEY

THE 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.

*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 information

Forecasting. Forecasting Application. Practical Forecasting. Chapter 7 OVERVIEW KEY CONCEPTS. Chapter 7. Chapter 7

Forecasting. 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 information

Repeating Decimals are decimal numbers that have number(s) after the decimal point that repeat in a pattern.

Repeating 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 information

Present Value Factor To bring one dollar in the future back to present, one uses the Present Value Factor (PVF): Concept 9: Present Value

Present 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 information

Soving Recurrence Relations

Soving 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 information

In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008

In 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 information

For customers Key features of the Guaranteed Pension Annuity

For 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 information

Determining the sample size

Determining 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 information

Statement of cash flows

Statement 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 information

Baan Service Master Data Management

Baan 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 information

Information about Bankruptcy

Information 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 information

Present Value Tax Expenditure Estimate of Tax Assistance for Retirement Saving

Present 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 information

Example 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).

Example 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 information

DWS Investment GmbH. DWS Aktien Strategie Deutschland Sales Prospectus including Terms of Contract

DWS 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 information

Best of security and convenience

Best of security and convenience Get More with Additioal Cardholders. Importat iformatio. Add a co-applicat or authorized user to your accout ad you ca take advatage of the followig beefits: RBC Royal Bak Visa Customer Service Cosolidate

More information

CHAPTER 5: EQUITY MARKETS

CHAPTER 5: EQUITY MARKETS CHAPTER 5: EQUITY MARKETS Overview Whe we buy stock i a corporatio, we exchage cash for a share of hoped-for future profits of the compay. These profits ca come via capital appreciatio ad through receipt

More information

Valuing Firms in Distress

Valuing 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 information

Audit of Assumptions for the March 2001 Budget. REPORT BY THE COMPTROLLER AND AUDITOR GENERAL HC 304 Session 2000 2001: 7 March 2001

Audit 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 information

BCP ABSOLUTE RETURN BOND 16

BCP 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 information

Here 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.

Here 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 information

I apply to subscribe for a Stocks & Shares NISA for the tax year 2015/2016 and each subsequent year until further notice.

I 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 information

Enhance Your Financial Legacy Variable Annuity Death Benefits from Pacific Life

Enhance Your Financial Legacy Variable Annuity Death Benefits from Pacific Life Ehace Your Fiacial Legacy Variable Auity Death Beefits from Pacific Life 7/15 20172-15B As You Pla for Retiremet, Protect Your Loved Oes A Pacific Life variable auity ca offer three death beefits that

More information

TO: Users of the ACTEX Review Seminar on DVD for SOA Exam FM/CAS Exam 2

TO: 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 information

Introducing Your New Wells Fargo Trust and Investment Statement. Your Account Information Simply Stated.

Introducing 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 easy-to-read statemet. It provides a overview of your accout ad a complete

More information

5: Introduction to Estimation

5: 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 information

PENSION ANNUITY. Policy Conditions Document reference: PPAS1(7) This is an important document. Please keep it in a safe place.

PENSION 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 information

Investing in Stocks WHAT ARE THE DIFFERENT CLASSIFICATIONS OF STOCKS? WHY INVEST IN STOCKS? CAN YOU LOSE MONEY?

Investing 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 information

Guide to Calculation FTSE Global Equity Index Series v3.0

Guide 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 information

Simple Annuities Present Value.

Simple Annuities Present Value. Simple Auities Preset Value. OBJECTIVES (i) To uderstad the uderlyig priciple of a preset value auity. (ii) To use a CASIO CFX-9850GB PLUS to efficietly compute values associated with preset value auities.

More information

RISK TRANSFER FOR DESIGN-BUILD TEAMS

RISK TRANSFER FOR DESIGN-BUILD TEAMS WILLIS CONSTRUCTION PRACTICE I-BEAM Jauary 2010 www.willis.com RISK TRANSFER FOR DESIGN-BUILD TEAMS Desig-builD work is icreasig each quarter. cosequetly, we are fieldig more iquiries from cliets regardig

More information

Incremental calculation of weighted mean and variance

Incremental 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 information

How to read A Mutual Fund shareholder report

How 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 information

Edu-Risk International Financial Risk Management & Training Justin Clarke +353 87 901 4483 justin.clarke@edurisk.ie www.edurisk.ie

Edu-Risk International Financial Risk Management & Training Justin Clarke +353 87 901 4483 justin.clarke@edurisk.ie www.edurisk.ie Edu-Risk 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 information

A NOTE ON THE CALCULATION OF THE AFTER-TAX COST OF DEBT

A NOTE ON THE CALCULATION OF THE AFTER-TAX COST OF DEBT INTERNATIONAL JOURNAL OF BUSINESS, 1(1), 1996 ISSN:1083-4346 A NOTE ON THE CALCULATION OF THE AFTER-TAX COST OF DEBT Wm R McDaiel, Daiel E. McCarty, ad Keeth A. Jessell Whe oe examies stadard fiacial maagemet

More information

Learning Objectives. Chapter 2 Pricing of Bonds. Future Value (FV)

Learning 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 2-1 2-2 Leaig

More information

Biology 171L Environment and Ecology Lab Lab 2: Descriptive Statistics, Presenting Data and Graphing Relationships

Biology 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 information

GCSE STATISTICS. 4) How to calculate the range: The difference between the biggest number and the smallest number.

GCSE 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 information

CHAPTER 7: Central Limit Theorem: CLT for Averages (Means)

CHAPTER 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 information

BCP EQUITY INDEX BONDS

BCP 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 information

summary of cover CONTRACT WORKS INSURANCE

summary 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 information

Estimating Probability Distributions by Observing Betting Practices

Estimating 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 information

PAYG instalments how to complete your activity statement

PAYG 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 7393-11.2012 Our commitmet to you We are committed to providig you

More information

Annuities Under Random Rates of Interest II By Abraham Zaks. Technion I.I.T. Haifa ISRAEL and Haifa University Haifa ISRAEL.

Annuities 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 information

BLUE SKY SRA ALLIANCE FUND

BLUE 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 information

Chapter 7: Confidence Interval and Sample Size

Chapter 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 information

CS103X: Discrete Structures Homework 4 Solutions

CS103X: 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 six-figure salaries i whole dollar amouts are there that cotai at least

More information

Choosing a Mortgage FIXED-RATE MORTGAGES. ADJUSTABLE-RATE MORTGAGES (ARMs)

Choosing a Mortgage FIXED-RATE MORTGAGES. ADJUSTABLE-RATE MORTGAGES (ARMs) Choosig A Mortgage Like homes, home mortgages come i all shapes ad sizes: short-term, log-term, fixed, adjustable, jumbo, balloo these are all terms that will soo be familiar to you, if they re ot already.

More information

Option pricing. Elke Korn Ralf Korn 1. This publication is part of the book Mathematics and Economy, which is supported by the BertelsmannStiftung.

Option 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 information

Measures of Spread and Boxplots Discrete Math, Section 9.4

Measures 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 information

Section 3: Renters and Rental Units

Section 3: Renters and Rental Units Sectio 3: Reters ad Retal Uits About two millio New York City households roughly two-thirds ret their homes. Over the past decade retal housig has become less affordable to may New Yorkers. Give the dowtur

More information