Impact of High Variable Renewable Generation on Future Market Prices and Generator Revenue

Size: px
Start display at page:

Download "Impact of High Variable Renewable Generation on Future Market Prices and Generator Revenue"

Transcription

1 1 Impact of High Variable Reewable Geeratio o Future Market Prices ad Geerator Reveue P. Vithayasrichareo, Member, IEEE, J. Riesz, Member, IEEE ad I. MacGill, Member, IEEE Abstract This study assesses the potetial impact of high reewable geeratio o the spot electricity prices, geerator reveue ad profits i a -oly electricity market. I particular, it presets modellig outcomes for the Australia Natioal Electricity Market (NEM) with a rage of possible reewable peetratios i It is assumed that the curret reliability stadard is maitaied ad participats deploy short ru margial cost biddig. The study foud that icreasig the share of wid ad PV geeratio would likely result i lower average spot prices ad subsequetly reveue ad profit of geerators. The reveue impact o large-scale PV was foud to be very severe ad could lead to isufficiet reveue to cover the costs, particularly at higher reewable peetratios. Chages i market mechaisms, such as icreasig the Market Price, may be required to esure reveue sufficiecy ad log-term resource adequacy i a -oly market with high reewables. Idex Terms Reveue sufficiecy, oly market, reewable, Australia Natioal Electricity Market (NEM) I. INTRODUCTION ENEWABLE geeratio sources, particularly wid ad Rsolar photovoltaics (PV), are fast becomig major geeratio sources i a umber of electricity idustries. This is due to fallig solar ad wid techology costs ad growig cocers over climate chage ad security. Due to the variable availability ad somewhat upredictable ature of wid ad PV geeratio, there are cocers over the potetial impacts of such reewable sources o the electricity idustry. For restructured electricity idustries with competitive market arragemets, the high capital yet low operatig costs (short ru margial cost or SRMC) of these techologies poses some iterestig additioal challeges. I particular, growig peetratios of low SRMC reewable geeratio i -oly wholesale markets are likely to reduce spot electricity prices ad hece market returs to all geerators. The risk of isufficiet reveue to recover both fixed ad variable operatio costs is oe of the major cocers for geerators. Cocers over reveue sufficiecy are also shared by may policy makers ad market regulators give that this might lead to log-term resource adequacy challeges by promotig early retiremet ad deferred etry to the market, which ca reduce the reliability of the electricity supply [1, 2]. This work has bee supported i part by Australia Reewable Eergy Agecy (ARENA) ad the CSIRO Future Grid Project. The authors are with the Cetre for Eergy ad Evirometal Markets ad School of Electrical Egieerig ad Telecommuicatios, UNSW Australia, Sydey, Australia ( peerapat@usw.edu.au). The Australia Natioal Electricity Market (NEM) is a moderately sized market (aroud 35GW of peak demad ad 200TWh per year) with growig wid ad solar deploymet ad sigificat reewable resource potetial, It features a relatively trasparet -oly market with relatively few costraits imposed o geeratio offers, ad therefore provides a iterestig case study for aalysis of high reewable scearios, ad their reveue implicatios. Previous studies have explored the techical feasibility ad ecoomics of high reewable scearios i the NEM, icludig scearios of 100% reewable [3, 4]. However, these studies have ot directly quatified the reveue implicatios of these high reewable systems. Some observers have raised questios about the feasibility of the NEM s -oly market desig i high reewable scearios, icludig claims that a system composed of a majority of low SRMC geeratio may ot deliver appropriate commercial icetives for assured resource adequacy [5]. This study aims to examie the possible impact of high reewable peetratios o spot electricity prices, geerator reveues ad profits i a future Australia NEM i 2030, with a view to assessig the potetial viability of the preset -oly market ad its mechaisms to esure resource adequacy ad hece log-term reliability. The paper provides quatitative aalysis usig a log-term geeratio portfolio plaig ad ivestmet modellig tool first developed i [6]. A umber of high reewable peetratios are cosidered icludig ucertaities associated with these. The modellig assumes that the curret NEM reliability stadard is maitaied ad participats deploy SRMC biddig. II. METHODOLOGY This study uses a probabilistic geeratio portfolio modellig tool which exteds the commoly applied load duratio curve (LDC) based optimal geeratio mixes by usig Mote Carlo simulatio to icorporate key ucertaities ito the assessmet [6]. These ucertaities iclude future gas costs, carbo policies ad electricity demads. The tool determies a probability distributio of aual reveue, operatig costs ad profits/losses of each geeratio techology for differet possible geeratio portfolios. The expected aual reveue, operatig cost ad profit of each geeratio techology for a particular portfolio represet the average of all the simulated reveue, costs ad profits from every Mote Carlo ru. Geerators obtai reveue through a spot market based upo the spot electricity price (or market clearig price ) i each period.

2 2 Geerators are dispatched based o their SRMC with the objective of miimizig the total system operatig cost of meetig demad i a year subject to demad balacig costraits. SRMC is the sum of the fuel, variable operatios ad maiteace (O&M) ad greehouse emissios costs of each uit. The modellig assumes that geerators bid ito the market at their SRMCs ad the spot price is the cost to supply the last MW of electricity to meet demad. PV ad wid geeratio is icorporated ito the modellig through the use of a residual (et) load duratio curve (RLDC) approach to capture the chroology of PV ad wid resource variability ad its match to NEM electricity demad, based upo historical correlatios observed i As the lowest SRMC geeratio, PV ad wid geeratio is dispatched first i the merit order. With this approach, hourly simulated PV ad wid geeratio is subtracted from hourly demad over the year to obtai residual demad, which is the rearraged to obtai a RLDC. It is this curve which has to be met by covetioal techologies i the portfolio. A 15% miimum sychroous geeratio requiremet is applied i all dispatch periods to provide adequate system iertia, fault feed-i levels ad system stability [7]. This represets the miimum amout to which aggregate covetioal geerators ca be tured dow. This costrait is importat for high reewable scearios sice some of the most promisig kids of reewable geeratio (otably wid ad PV) are o-sychroous ad therefore do ot geerally provide iertia ad fault feed-i curret to the system [1]. For the purposes of this study, coal, gas ad hydro plats are assumed to provide sychroous geeratio (some types of reewable geeratio such as solar thermal, geothermal ad biomass are also sychroous, although these techology types have ot bee modelled i this study). I additio to the market reveue, covetioal geerators also receive a supplemetary paymet i periods i which they are dispatched out of merit order to satisfy the 15% sychroous requiremet costrait. This supplemetary paymet is referred to i this study as a costraied o paymet, ad is determied based upo the SRMC of the most expesive covetioal geerator that is dispatched to meet the sychroous requiremet. For each Mote Carlo ru, aual reveue, of each geeratio techology is calculated accordig to Eq. (1) (3). Spot market reveue Costraied o paymet REVSpot P MC (1) T t1 T t1 CP Pcov SRMC max Aual reveue REVTotal = REVSpot + CP (3) where P is the geeratio output of techology (MW), MC t is the market clearig price ($/MWh), Pcov is the output of covetioal geerator (MW) that is dispatched out of merit order to meet the sychroous requiremet, SRMCmax t is the SRMC of the most expesive geerator ($/MWh) that is dispatched to meet the sychroous requiremet i period t. Aual operatig cost ad profit of the geerator are determied based upo Eq. (4) (5) respectively. t t (2) OPEX P SRMC (4) T t1 OPProfit = REVTotal OPEX FOM (5) where SRMC is the SRMC ($/MWh) of techology i period t ad FOM is the aual fixed operatig ad maiteace (O&M) costs ($) of techology. III. THE AUSTRALIAN NATIONAL ELECTRICITY MARKET (NEM) CASE STUDY Six differet reewable peetratio scearios for the NEM i 2030 were cosidered: 15%, 30%, 40%, 60%, 75% ad 85% (by cotributio). Eight techologies were icluded: coal, combied cycle gas turbie (CCGT), ope cycle gas turbie (OCGT), co-geeratio, distillate, utilityscale PV (sigle axis trackig), wid (o shore) ad hydro. The reewable peetratio scearios ad the percetage of each reewable techology are summarised i TABLE I. Note that the proportio of PV ad wid for each reewable peetratio were selected based o assumptios o future ivestmet scearios, as explaied i [8]. Reewable peetratio scearios TABLE I DIFFERENT RENEWABLE PENETRATION SCENARIOS Achieved total reewable peetratio % PV % Wid % Hydro % Fossil 15% % % % % % The maximum spot price is set at $13,500/MWh, which is the curret Market Price Cap (MPC) for the NEM [9]. This price is triggered i periods whe demad exceeds available geeratio capacity. The istalled capacity was determied so that each geeratio portfolio will, o average, meet the preset NEM reliability stadard of 0.002% aual userved (USE). A. Hourly Demad ad Geeratio A hourly electricity demad profile for was obtaied from aalysis by the Australia Eergy Market Operator (AEMO) o a 100% reewables system uder a moderate ecoomic growth sceario. Hourly wid ad solar output profiles for 2030 were simulated from hourly traces of 1-MW o-shore wid ad solar PV (sigle axis trackig) geeratio i differet locatios across the NEM provided by AEMO [7]. For hydro geeratio a aual hydro dispatch limit of 13 TWh was applied, based upo the logterm average hydro geeratio estimated by AEMO [7]. Geeratio output of each thermal techology (coal, CCGT, OCGT, coge ad distillate) i each period was determied usig merit order dispatch based upo their SRMCs i Techical ad cost parameters of geeratig plats were based upo a previous study preseted i [8].

3 3 B. Modellig Ucertaities Key ucertai parameters cosidered i the modellig are gas prices, carbo prices ad electricity demad as they have experieced a higher degree of ucertaity tha other variables [10, 11]. Logormal distributios were applied to model future fuel ad carbo prices to reflect the asymmetric dowside risk associated with high price outcomes. Demad ucertaity was modelled assumig a ormal distributio of residual peak demad for each reewable peetratio sceario. Both logormal ad ormal distributios ca be characterized by their mea (expected value) ad stadard deviatio (SD). The mea ad SD of fuel prices ad carbo prices were determied based upo Australia Govermet estimates for 2030 [12, 13]. Correlated samples of coal, gas ad carbo prices were simulated from their margial logormal distributios 10,000 times usig Multivariate Mote Carlo simulatio techiques described i [6]. The mea ad SD of peak demad were estimated based o the Probability of Exceedace (POE) demad projectios i provided i [7], ad were explaied i detail i [8]. Residual peak demad were also simulated 10,000 times. I order to achieve the 0.002% USE reliability stadard o average, there were istaces where the simulated residual peak demads exceeded the istalled fossil-fuel geeratio capacity. IV. MODELLING RESULTS AND ANALYSIS With Mote Carlo simulatio techiques, the modellig calculated overall geeratio costs, emissios, reveue ad operatig profits for each techology withi each possible geeratio portfolio for 10,000 simulated future fuel prices, carbo prices ad electricity demads. The cost of USE is valued at the MPC ($13,500/MWh), ad is icluded i the overall geeratio cost. Fig. 1 illustrates the efficiet frotiers cosistig of optimal geeratio portfolios i terms of expected geeratio cost ad cost risk (SD of cost) for differet geeratig portfolios, ragig from 15% to 85% reewable geeratio. Each dot is a plot of a portfolio s expected costs (agaist the vertical axis) ad the cost risk (agaist the horizotal axis), calculated over 10,000 simulatios. 1 As illustrated i Fig. 1, the lowest cost geeratio portfolio features 60% reewable, with a expected cost of $92/MWh. The costs rise as reewable icreases to 75% ad 85%, ad are also higher for the reewable peetratio levels below 60%. For the purpose of this discussio, oly the reveue ad profits of each techology i the least cost portfolio for differet reewable peetratios are quoted. For example, the least cost portfolio for the 15% reewable portfolio is the oe that cosists of 41% coal, 21% CCGT, 7% OCGT, ad this lowest cost portfolio is used as the basis for aalysis. The average spot price duratio curve for the least cost portfolio i each reewable peetratio for the highest 2% price periods is show i Fig. 2. The figure also shows the correspodig PV ad wid geeratio outputs i those periods. The results suggest that the magitude of price spikes 1 For each reewable peetratio, the amout of distillate, cogeeratio, hydro, PV ad wid capacity was fixed for every possible thermal portfolio. icreases with higher reewable peetratios but the high price periods (e.g. greater tha $500/MWh) are less frequet. For example, the average highest spot price i the 85% reewables sceario is aroud $8,500/MWh compared to $1,500/MWh i the 15% reewables sceario. However the umber of periods where the spot prices are greater tha $500/MWh is less tha 0.4% of the time (35 hours per year) i the 85% reewables sceario compared to 2% of the time (75 hours per year) i the 15% reewables sceario. 2 Fig. 1. Efficiet frotiers cotaiig optimal geeratio portfolios for differet reewable peetratios i The capacity of fossil-fuel techologies i each portfolio is show i GW (i brackets) ad percetage share. The coloured boxes show the share of each techology by capacity istalled. Fig. 2. Average market price duratio curve for the top 2% of the price periods ad the correspodig PV ad wid geeratio. Sice the model does ot icorporate strategic biddig behaviour, high spot prices i the model are drive by periods where userved is occurrig. This meas that the price duratio curves illustrate that there are fewer periods of supply ad demad imbalace as the reewable peetratio icreases. However, the magitude of USE occurrig i each of those periods is higher (USE is cocetrated ito fewer periods as 2 Note that the figure shows the average spot price across 10,000 simulated fuel prices, carbo price ad electricity demad for each period. Without modellig the ucertaities, the highest spot price show o the graph would be $13,500/MWh.

4 4 the reewable percetage icreases, keepig i mid that the total USE for each geeratio portfolio is the same). Fig. 3 shows the expected aual geerator reveue ad operatig profit of each techology i the least cost portfolio for each reewable peetratio. The aual average spot prices are also show i Fig. 3(a). The impact of the carbo price o the reveue, operatig costs ad hece profits of the fossil fuel plats are apparet. Although the reveues of PV ad wid plats are relatively low, their operatig profits of PV ad wid plats are sigificatly higher tha those of coal ad CCGT, particularly at low to moderate reewable peetratios (i.e. from 15% to 60% reewable peetratio). This is due the low operatig cost of reewable geeratio ad the impact of carbo price o the high operatig costs of fossil fuel plats. The operatig profit of each techology geerally reduces as the amout of reewables icreases due to lower aual average spot prices iflueced by the low SRMCs of wid ad PV. However, fossil fuel geerators are able to make operatig profit eve at high reewable peetratio. This is likely iflueced by the 15% miimum sychroous geeratio requiremet applied i the modellig, which eforced thermal geeratig plats (most likely coal) to supply at least 15% of demad i every period. Hece they are able to ear reveue to most periods. This is particularly crucial durig scarcity or ear scarcity periods whe the spot prices are extremely high. (a) (b) Fig. 3. (a) Expected aual reveue of each techology ad aual average spot prices (b) Expected aual operatig profit of each techology for each reewable peetratio. The capacity (MW) of each techology is also show. O the other had, the profits of PV ad wid reduce far more sigificatly tha for thermal geeratio techologies. This is particularly the case for PV as show by its egligible operatig profit at a 85% reewable peetratio eve without takig ito accout aual capital repaymets. Sice PV, ad to a lesser extet wid, do ot ofte geerate durig high price periods (as show i Fig. 2), they were uable to beefit from the high spot prices. This result may due to the very large proportio of PV icluded i the 75% ad 85% reewable portfolios, which may be higher that ecoomically optimal, resultig i high costs ad almost egligible profits. These issues warrat further ivestigatio The modellig results suggest that, at high reewable peetratio levels ad give the curret market arragemets, PV ad wid plats might ot ear sufficiet reveue to cover their costs. I cotrast, coal ad CCGT plat appear to maitai operatig profitability followig a iitial declie. OCGT plat appear to maitai operatig profitability regardless of the reewable peetratio level, suggestig that peakig plat may be relatively immue to the reducig average wholesale price, ad able to flexibly adjust as required to access high priced periods. Oe of the optios for icreasig geerator reveue is to icrease the MPC from the curret $13,500/MWh, sice a higher MPC will lead to more reveue eared durig high demad periods ad hece higher profits for geerators [14]. This will be examied i future work. V. CONCLUSIONS This paper assesses the impact of variable reewable geeratio o spot market prices ad geerator reveues i a -oly electricity market. The Australia Natioal Electricity Market (NEM) with differet reewable peetratios i 2030 uder ucertai gas prices, carbo pricig policy ad electricity demad was used as a case study. Modellig results idicate that the aual average spot price geerally reduces as the amout of reewable geeratio icreases due to the low operatig costs of wid ad PV geeratio. Although there were fewer periods of demad ad supply imbalace as the reewable peetratio icreases, the magitude of the imbalace ad hece average price spikes were greater. Geerally, the reductio i the average spot price results i reduced reveues ad profitability of geerators ad potetially leads to isufficiet reveue to meet costs, particularly for large scale wid ad PV geerators. The reveue impacts o PV ad wid geeratio are very severe at the high reewable peetratios cosidered. Therefore, chages i market mechaisms such as icreasig market price cap may be required to esure reveue sufficiecy ad log-term resource adequacy i a oly market with high reewables. Further work is warrated to explore these issues. There are some limitatios i this study. The fidigs are highly depedet o modellig ad iput assumptios. For the reewable peetratio greater tha 60%, the proportio of PV ad wid geeratio chose i the modellig may ot be the most ecoomically optimal, resultig i higher idustry costs

5 5 ad almost egligible operatig profits for PV. Furthermore, there may be mechaisms other tha imposig a miimum sychroous geeratio costrait, which is a costly optio, to provide system iertia ad frequecy respose at times of high o-sychroous reewable peetratios. These limitatios represet areas for future work. VI. REFERENCES [1] E. Ela, M. Milliga, A. Bloom, A. Botterud, T. A., ad T. Levi, "Evolutio of Wholesale Electricity Market Desig with Icreasig Levels of Reewable Geeratio," Natioal Reewable Eergy Laboratory, [2] IEA, "The Power of Trasformatio: Wid, Su ad the Ecoomics of Flexible Power Systems," Iteratioal Eergy Agecy, [3] AEMO, "100 per cet Reewables Study - Modellig Outcomes," Australia Eergy Market Operator, [4] B. Ellisto, I. MacGill, ad M. Diesedorf, "Least cost 100% reewable electricity scearios i the Australia Natioal Electricity Market," Eergy Policy, vol. 59, 0, pp , 8// [5] J. Riesz ad M. Milliga, "Desigig electricity markets for a high peetratio of variable reewables," WIREs Eergy Eviromet doi: /wee.137, [6] P. Vithayasrichareo ad I. F. MacGill, "A Mote Carlo based decisiosupport tool for assessig geeratio portfolios i future carbo costraied electricity idustries," Eergy Policy, vol. 41, pp , [7] AEMO, "100 Per cet Reewables Study - Modellig Assumptios ad Iput," Australia Eergy Market Operator, [8] P. Vithayasrichareo, J. Riesz, ad I. F. MacGill, "Usig reewables to hedge agaist future electricity idustry ucertaities A Australia case study," Eergy Policy, vol. 76, pp , [9] AER, "State of the Eergy Market 2014," Australia Eergy Regulator, [10] S. Ji, S. Rya, J.-P. Watso, ad D. Woodruff, "Modelig ad solvig a large-scale geeratio expasio plaig problem uder ucertaity," Eergy Systems, vol. 2, 3-4, pp , 2011/11/ [11] F. A. Roques, D. M. Newbery, ad W. J. Nuttall, "Fuel mix diversificatio icetives i liberalized electricity markets: A Mea- Variace Portfolio theory approach," Eergy Ecoomics, vol. 30, 4, pp , [12] BREE, "Australia Eergy Techology Assessmet 2012," Bureau of Resources ad Eergy Ecoomics, Australia Govermet, [13] Australia Treasury, "Strog growth, low pollutio: Modellig a carbo price," Australia Govermet, Caberra, [14] J. Riesz ad I. MacGill, "100% Reewables i Australia: Will a Capacity Market be Required?," i 3rd Solar Itegratio Workshop Lodo, UK, 2013.

CAPITAL PROJECT SCREENING AND SELECTION

CAPITAL PROJECT SCREENING AND SELECTION CAPITAL PROJECT SCREEIG AD SELECTIO Before studyig the three measures of ivestmet attractiveess, we will review a simple method that is commoly used to scree capital ivestmets. Oe of the primary cocers

More information

Institute of Actuaries of India Subject CT5 General Insurance, Life and Health Contingencies

Institute of Actuaries of India Subject CT5 General Insurance, Life and Health Contingencies Istitute of Actuaries of Idia Subject CT5 Geeral Isurace, Life ad Health Cotigecies For 2017 Examiatios Aim The aim of the Cotigecies subject is to provide a groudig i the mathematical techiques which

More information

These characteristics are expressed in terms of statistical properties which are estimated from the sample data.

These characteristics are expressed in terms of statistical properties which are estimated from the sample data. 0. Key Statistical Measures of Data Four pricipal features which characterize a set of observatios o a radom variable are: (i) the cetral tedecy or the value aroud which all other values are buched, (ii)

More information

Economics of Generating Stations. - Definition - Factors affecting cost of generation - Methods of determining depreciation

Economics of Generating Stations. - Definition - Factors affecting cost of generation - Methods of determining depreciation Ecoomics of Geeratig Statios - Defiitio - Factors affectig cost of geeratio - Methods of determiig depreciatio Ecoomics of power geeratig statio is the art of determiig the per-uit cost of electric eergy

More information

The roll-out of the Jobcentre Plus Office network

The roll-out of the Jobcentre Plus Office network Departmet for Work ad Pesios The roll-out of the Jobcetre Plus Office etwork REPORT BY THE COMPTROLLER AND AUDITOR GENERAL HC 346 Sessio 2007-2008 22 February 2008 SummARy What is the Jobcetre Plus roll-out?

More information

EU ETS Hearing, European Parliament Xavier Labandeira, FSR Climate (EUI)

EU ETS Hearing, European Parliament Xavier Labandeira, FSR Climate (EUI) EU ETS Hearig, Europea Parliamet Xavier Labadeira, FSR Climate (EUI) 0. Thaks Chairma, MEPs. Thak you very much for ivitig me here today. I am hoored to participate i the work of a Committee whose previous

More information

Models of Asset Pricing

Models of Asset Pricing APPENDIX 1 TO CHAPTER 4 Models of Asset Pricig I this appedix, we first examie why diversificatio, the holdig of may risky assets i a portfolio, reduces the overall risk a ivestor faces. The we will see

More information

Models of Asset Pricing

Models of Asset Pricing APPENDIX 1 TO CHAPTER4 Models of Asset Pricig I this appedix, we first examie why diversificatio, the holdig of may risky assets i a portfolio, reduces the overall risk a ivestor faces. The we will see

More information

CAPITAL ASSET PRICING MODEL

CAPITAL ASSET PRICING MODEL CAPITAL ASSET PRICING MODEL RETURN. Retur i respect of a observatio is give by the followig formula R = (P P 0 ) + D P 0 Where R = Retur from the ivestmet durig this period P 0 = Curret market price P

More information

III. RESEARCH METHODS. Riau Province becomes the main area in this research on the role of pulp

III. RESEARCH METHODS. Riau Province becomes the main area in this research on the role of pulp III. RESEARCH METHODS 3.1 Research Locatio Riau Provice becomes the mai area i this research o the role of pulp ad paper idustry. The decisio o Riau Provice was supported by several facts: 1. The largest

More information

Cost-benefit analysis of plasma technologies

Cost-benefit analysis of plasma technologies Cost-beefit aalysis of plasma techologies Professor Adra Blumberga, Riga Techical uiversity Part-fiaced by the Europea Uio (Europea Regioal Developmet Fud Cost- beefit aalysis Part-fiaced by the Europea

More information

Economic Analysis and Optimization

Economic Analysis and Optimization Ecoomic Aalysis ad Optimizatio Assess ecoomic feasibility of eergy systems Idetify aticipated cost of eergy (COE) ad other measures of ecoomic performace usig cosistet methodologies Compare alteratives

More information

Productivity depending risk minimization of production activities

Productivity depending risk minimization of production activities Productivity depedig risk miimizatio of productio activities GEORGETTE KANARACHOU, VRASIDAS LEOPOULOS Productio Egieerig Sectio Natioal Techical Uiversity of Athes, Polytechioupolis Zografou, 15780 Athes

More information

Models of Asset Pricing

Models of Asset Pricing 4 Appedix 1 to Chapter Models of Asset Pricig I this appedix, we first examie why diversificatio, the holdig of may risky assets i a portfolio, reduces the overall risk a ivestor faces. The we will see

More information

Subject CT5 Contingencies Core Technical. Syllabus. for the 2011 Examinations. The Faculty of Actuaries and Institute of Actuaries.

Subject CT5 Contingencies Core Technical. Syllabus. for the 2011 Examinations. The Faculty of Actuaries and Institute of Actuaries. Subject CT5 Cotigecies Core Techical Syllabus for the 2011 Examiatios 1 Jue 2010 The Faculty of Actuaries ad Istitute of Actuaries Aim The aim of the Cotigecies subject is to provide a groudig i the mathematical

More information

Subject CT1 Financial Mathematics Core Technical Syllabus

Subject CT1 Financial Mathematics Core Technical Syllabus Subject CT1 Fiacial Mathematics Core Techical Syllabus for the 2018 exams 1 Jue 2017 Subject CT1 Fiacial Mathematics Core Techical Aim The aim of the Fiacial Mathematics subject is to provide a groudig

More information

This article is part of a series providing

This article is part of a series providing feature Bryce Millard ad Adrew Machi Characteristics of public sector workers SUMMARY This article presets aalysis of public sector employmet, ad makes comparisos with the private sector, usig data from

More information

Dr. Maddah ENMG 624 Financial Eng g I 03/22/06. Chapter 6 Mean-Variance Portfolio Theory

Dr. Maddah ENMG 624 Financial Eng g I 03/22/06. Chapter 6 Mean-Variance Portfolio Theory Dr Maddah ENMG 64 Fiacial Eg g I 03//06 Chapter 6 Mea-Variace Portfolio Theory Sigle Period Ivestmets Typically, i a ivestmet the iitial outlay of capital is kow but the retur is ucertai A sigle-period

More information

Binomial Model. Stock Price Dynamics. The Key Idea Riskless Hedge

Binomial Model. Stock Price Dynamics. The Key Idea Riskless Hedge Biomial Model Stock Price Dyamics The value of a optio at maturity depeds o the price of the uderlyig stock at maturity. The value of the optio today depeds o the expected value of the optio at maturity

More information

Appendix 1 to Chapter 5

Appendix 1 to Chapter 5 Appedix 1 to Chapter 5 Models of Asset Pricig I Chapter 4, we saw that the retur o a asset (such as a bod) measures how much we gai from holdig that asset. Whe we make a decisio to buy a asset, we are

More information

1 ECON4415: International Economics Problem Set 4 - Solutions

1 ECON4415: International Economics Problem Set 4 - Solutions ECON445: Iteratioal Ecoomics Problem Set 4 - Solutios. I Moopolistic competitio. Moopolistic competitio is a market form where May rms producig di eret varieties. Each rm has moopoly power over its ow

More information

Guide for. Plan Sponsors. Roth 401(k) get retirement right

Guide for. Plan Sponsors. Roth 401(k) get retirement right Uited of Omaha Life Isurace Compay Compaio Life Isurace Compay mutual of omaha retiremet services Roth 401(k) Guide for Pla Sposors MUGC8764_0210 get retiremet right roth 401(k) expads your optios Drive

More information

Methodology on setting the booking prices Project Development and expansion of Bulgartransgaz EAD gas transmission system

Methodology on setting the booking prices Project Development and expansion of Bulgartransgaz EAD gas transmission system Methodology o settig the bookig prices Project Developmet ad expasio of Bulgartrasgaz EAD gas trasmissio system Art.1. The preset Methodology determies the coditios, order, major requiremets ad model of

More information

43. A 000 par value 5-year bod with 8.0% semiaual coupos was bought to yield 7.5% covertible semiaually. Determie the amout of premium amortized i the 6 th coupo paymet. (A).00 (B).08 (C).5 (D).5 (E).34

More information

of Asset Pricing R e = expected return

of Asset Pricing R e = expected return Appedix 1 to Chapter 5 Models of Asset Pricig EXPECTED RETURN I Chapter 4, we saw that the retur o a asset (such as a bod) measures how much we gai from holdig that asset. Whe we make a decisio to buy

More information

of Asset Pricing APPENDIX 1 TO CHAPTER EXPECTED RETURN APPLICATION Expected Return

of Asset Pricing APPENDIX 1 TO CHAPTER EXPECTED RETURN APPLICATION Expected Return APPENDIX 1 TO CHAPTER 5 Models of Asset Pricig I Chapter 4, we saw that the retur o a asset (such as a bod) measures how much we gai from holdig that asset. Whe we make a decisio to buy a asset, we are

More information

Contents List of Files with Examples

Contents List of Files with Examples Paos Kostati Power ad Eergy Systems Egieerig Ecoomics Itroductio ad Istructios Cotets List of Files with Examples Frequetly used MS-Excel fuctios Add-Is developed by the Author Istallatio Istructio of

More information

Non-Inferiority Logrank Tests

Non-Inferiority Logrank Tests Chapter 706 No-Iferiority Lograk Tests Itroductio This module computes the sample size ad power for o-iferiority tests uder the assumptio of proportioal hazards. Accrual time ad follow-up time are icluded

More information

We learned: $100 cash today is preferred over $100 a year from now

We learned: $100 cash today is preferred over $100 a year from now Recap from Last Week Time Value of Moey We leared: $ cash today is preferred over $ a year from ow there is time value of moey i the form of willigess of baks, busiesses, ad people to pay iterest for its

More information

The ROI of Ellie Mae s Encompass All-In-One Mortgage Management Solution

The ROI of Ellie Mae s Encompass All-In-One Mortgage Management Solution The ROI of Ellie Mae s Ecompass All-I-Oe Mortgage Maagemet Solutio MAY 2017 Legal Disclaimer All iformatio cotaied withi this study is for iformatioal purposes oly. Neither Ellie Mae, Ic. or MarketWise

More information

Life Cycle Cost Analysis. Selection of Heating Equipment. By Henry Manczyk, CPE, CEM

Life Cycle Cost Analysis. Selection of Heating Equipment. By Henry Manczyk, CPE, CEM Life Cycle Cost Aalysis Selectio of Heatig Equipmet By Hery Maczyk, CE, CEM Life Cycle Cost Aalysis Selectio of Heatig Equipmet By Hery Maczyk, CE, CEM Maczyk Eergy Cosultig May 2003 Whe selectig equipmet

More information

Highest Daily Lifetime Seven SM Spousal Highest Daily Lifetime Seven SM

Highest Daily Lifetime Seven SM Spousal Highest Daily Lifetime Seven SM Optioal Icome beefits Highest Daily Lifetime Seve SM Spousal Highest Daily Lifetime Seve SM Daily Opportuities to Capture Greater Lifetime Icome HD Lifetime Seve ad Spousal HD Lifetime Seve Offer:» Miimum

More information

DESCRIPTION OF MATHEMATICAL MODELS USED IN RATING ACTIVITIES

DESCRIPTION OF MATHEMATICAL MODELS USED IN RATING ACTIVITIES July 2014, Frakfurt am Mai. DESCRIPTION OF MATHEMATICAL MODELS USED IN RATING ACTIVITIES This documet outlies priciples ad key assumptios uderlyig the ratig models ad methodologies of Ratig-Agetur Expert

More information

CHAPTER 2 PRICING OF BONDS

CHAPTER 2 PRICING OF BONDS CHAPTER 2 PRICING OF BONDS CHAPTER SUARY This chapter will focus o the time value of moey ad how to calculate the price of a bod. Whe pricig a bod it is ecessary to estimate the expected cash flows ad

More information

REINSURANCE ALLOCATING RISK

REINSURANCE ALLOCATING RISK 6REINSURANCE Reisurace is a risk maagemet tool used by isurers to spread risk ad maage capital. The isurer trasfers some or all of a isurace risk to aother isurer. The isurer trasferrig the risk is called

More information

Statistics for Economics & Business

Statistics for Economics & Business Statistics for Ecoomics & Busiess Cofidece Iterval Estimatio Learig Objectives I this chapter, you lear: To costruct ad iterpret cofidece iterval estimates for the mea ad the proportio How to determie

More information

Online appendices from Counterparty Risk and Credit Value Adjustment a continuing challenge for global financial markets by Jon Gregory

Online appendices from Counterparty Risk and Credit Value Adjustment a continuing challenge for global financial markets by Jon Gregory Olie appedices from Couterparty Risk ad Credit Value Adjustmet a APPENDIX 8A: Formulas for EE, PFE ad EPE for a ormal distributio Cosider a ormal distributio with mea (expected future value) ad stadard

More information

Quarterly Update First Quarter 2018

Quarterly Update First Quarter 2018 EDWARD JONES ADVISORY SOLUTIONS Quarterly Update First Quarter 2018 www.edwardjoes.com Member SIPC Key Steps to Fiacial Success We Use a Established Process 5 HOW CAN I STAY ON TRACK? 4 HOW DO I GET THERE?

More information

NPTEL DEPARTMENT OF INDUSTRIAL AND MANAGEMENT ENGINEERING IIT KANPUR QUANTITATIVE FINANCE END-TERM EXAMINATION (2015 JULY-AUG ONLINE COURSE)

NPTEL DEPARTMENT OF INDUSTRIAL AND MANAGEMENT ENGINEERING IIT KANPUR QUANTITATIVE FINANCE END-TERM EXAMINATION (2015 JULY-AUG ONLINE COURSE) NPTEL DEPARTMENT OF INDUSTRIAL AND MANAGEMENT ENGINEERING IIT KANPUR QUANTITATIVE FINANCE END-TERM EXAMINATION (2015 JULY-AUG ONLINE COURSE) READ THE INSTRUCTIONS VERY CAREFULLY 1) Time duratio is 2 hours

More information

Terms and conditions for the 28 - Day Interbank Equilibrium Interest Rate (TIIE) Futures Contract (Cash Settlement)

Terms and conditions for the 28 - Day Interbank Equilibrium Interest Rate (TIIE) Futures Contract (Cash Settlement) The Eglish versio of the Terms ad Coditios for Futures Cotracts is published for iformatio purposes oly ad does ot costitute legal advice. However, i case of ay Iterpretatio cotroversy, the Spaish versio

More information

Mine Closure Risk Assessment A living process during the operation

Mine Closure Risk Assessment A living process during the operation Tailigs ad Mie Waste 2017 Baff, Alberta, Caada Mie Closure Risk Assessmet A livig process durig the operatio Cristiá Marambio Golder Associates Closure chroology Chilea reality Gov. 1997 Evirometal basis

More information

An Empirical Study on the Contribution of Foreign Trade to the Economic Growth of Jiangxi Province, China

An Empirical Study on the Contribution of Foreign Trade to the Economic Growth of Jiangxi Province, China usiess, 21, 2, 183-187 doi:1.4236/ib.21.2222 Published Olie Jue 21 (http://www.scirp.org/joural/ib) 183 A Empirical Study o the Cotributio of Foreig Trade to the Ecoomic Growth of Jiagxi Provice, Chia

More information

Monopoly vs. Competition in Light of Extraction Norms. Abstract

Monopoly vs. Competition in Light of Extraction Norms. Abstract Moopoly vs. Competitio i Light of Extractio Norms By Arkadi Koziashvili, Shmuel Nitza ad Yossef Tobol Abstract This ote demostrates that whether the market is competitive or moopolistic eed ot be the result

More information

Optimizing of the Investment Structure of the Telecommunication Sector Company

Optimizing of the Investment Structure of the Telecommunication Sector Company Iteratioal Joural of Ecoomics ad Busiess Admiistratio Vol. 1, No. 2, 2015, pp. 59-70 http://www.aisciece.org/joural/ijeba Optimizig of the Ivestmet Structure of the Telecommuicatio Sector Compay P. N.

More information

Structuring the Selling Employee/ Shareholder Transition Period Payments after a Closely Held Company Acquisition

Structuring the Selling Employee/ Shareholder Transition Period Payments after a Closely Held Company Acquisition Icome Tax Isights Structurig the Sellig Employee/ Shareholder Trasitio Period Paymets after a Closely Held Compay Acquisitio Robert F. Reilly, CPA Corporate acquirers ofte acquire closely held target compaies.

More information

Risk Assessment for Project Plan Collapse

Risk Assessment for Project Plan Collapse 518 Proceedigs of the 8th Iteratioal Coferece o Iovatio & Maagemet Risk Assessmet for Project Pla Collapse Naoki Satoh 1, Hiromitsu Kumamoto 2, Norio Ohta 3 1. Wakayama Uiversity, Wakayama Uiv., Sakaedai

More information

Chapter Four Learning Objectives Valuing Monetary Payments Now and in the Future

Chapter Four Learning Objectives Valuing Monetary Payments Now and in the Future Chapter Four Future Value, Preset Value, ad Iterest Rates Chapter 4 Learig Objectives Develop a uderstadig of 1. Time ad the value of paymets 2. Preset value versus future value 3. Nomial versus real iterest

More information

Risk-Constrained Bidding Strategy with Stochastic Unit Commitment

Risk-Constrained Bidding Strategy with Stochastic Unit Commitment Risk-Costraied Biddig Strategy with Stochastic Uit Commitmet 1 Tao L Member, Mohammad Shahidehpour, Fellow, ad Zuyi L Member, IEEE Abstract This paper develops optimal biddig strategies based o hourly

More information

An Initiative to Minimise the Non- Technical Barriers to DG within Europe

An Initiative to Minimise the Non- Technical Barriers to DG within Europe Distributio Europe 2005, Sessio 4.3 Maagig for Growth i Distributed Geeratio A Iitiative to Miimise the No- Techical Barriers to DG withi Europe Richard Kight Rolls-Royce Strategic Research Cetre 2005

More information

Faculdade de Economia da Universidade de Coimbra

Faculdade de Economia da Universidade de Coimbra Faculdade de Ecoomia da Uiversidade de Coimbra Grupo de Estudos Moetários e Fiaceiros (GEMF) Av. Dias da Silva, 65 300-5 COIMBRA, PORTUGAL gemf@fe.uc.pt http://www.uc.pt/feuc/gemf PEDRO GODINHO Estimatig

More information

CreditRisk + Download document from CSFB web site:

CreditRisk + Download document from CSFB web site: CreditRis + Dowload documet from CSFB web site: http://www.csfb.com/creditris/ Features of CreditRis+ pplies a actuarial sciece framewor to the derivatio of the loss distributio of a bod/loa portfolio.

More information

A point estimate is the value of a statistic that estimates the value of a parameter.

A point estimate is the value of a statistic that estimates the value of a parameter. Chapter 9 Estimatig the Value of a Parameter Chapter 9.1 Estimatig a Populatio Proportio Objective A : Poit Estimate A poit estimate is the value of a statistic that estimates the value of a parameter.

More information

Summary of Benefits RRD

Summary of Benefits RRD Summary of Beefits RRD All Eligible Employees Basic Term Life, Optioal Term Life, Optioal Depedet Term Life ad Optioal Accidetal Death & Dismembermet Issued by The Prudetial Isurace Compay of America Effective:

More information

Proceedings of the 5th WSEAS Int. Conf. on SIMULATION, MODELING AND OPTIMIZATION, Corfu, Greece, August 17-19, 2005 (pp )

Proceedings of the 5th WSEAS Int. Conf. on SIMULATION, MODELING AND OPTIMIZATION, Corfu, Greece, August 17-19, 2005 (pp ) Proceedigs of the 5th WSEAS It. Cof. o SIMULATION, MODELING AND OPTIMIZATION, Corfu, Greece, August 7-9, 005 (pp488-49 Realized volatility estimatio: ew simulatio approach ad empirical study results JULIA

More information

BUSINESS PLAN IMMUNE TO RISKY SITUATIONS

BUSINESS PLAN IMMUNE TO RISKY SITUATIONS BUSINESS PLAN IMMUNE TO RISKY SITUATIONS JOANNA STARCZEWSKA, ADVISORY BUSINESS SOLUTIONS MANAGER RISK CENTER OF EXCELLENCE EMEA/AP ATHENS, 13TH OF MARCH 2015 FINANCE CHALLENGES OF MANY FINANCIAL DEPARTMENTS

More information

AY Term 2 Mock Examination

AY Term 2 Mock Examination AY 206-7 Term 2 Mock Examiatio Date / Start Time Course Group Istructor 24 March 207 / 2 PM to 3:00 PM QF302 Ivestmet ad Fiacial Data Aalysis G Christopher Tig INSTRUCTIONS TO STUDENTS. This mock examiatio

More information

Helping you reduce your family s tax burden

Helping you reduce your family s tax burden The RBC Do m i i o Se c u r i t i e s Family Trust Helpig you reduce your family s tax burde Professioal Wealth Maagemet Sice 1901 1 RBC Domiio Securities Charitable Gift Program Who should cosider a RBC

More information

EVIDENCE ON THE DISTRIBUTIONAL EFFECTS OF A LAND VALUE TAX ON RESIDENTIAL HOUSEHOLDS. Elizabeth Plummer

EVIDENCE ON THE DISTRIBUTIONAL EFFECTS OF A LAND VALUE TAX ON RESIDENTIAL HOUSEHOLDS. Elizabeth Plummer Natioal Tax Joural, March 2010, 63 (1), 63 92 EVIDENCE ON THE DISTRIBUTIONAL EFFECTS OF A LAND VALUE TAX ON RESIDENTIAL HOUSEHOLDS Elizabeth Plummer This study examies how replacig a uiform property tax

More information

Chapter 11 Appendices: Review of Topics from Foundations in Finance and Tables

Chapter 11 Appendices: Review of Topics from Foundations in Finance and Tables Chapter 11 Appedices: Review of Topics from Foudatios i Fiace ad Tables A: INTRODUCTION The expressio Time is moey certaily applies i fiace. People ad istitutios are impatiet; they wat moey ow ad are geerally

More information

Chapter Six. Bond Prices 1/15/2018. Chapter 4, Part 2 Bonds, Bond Prices, Interest Rates and Holding Period Return.

Chapter Six. Bond Prices 1/15/2018. Chapter 4, Part 2 Bonds, Bond Prices, Interest Rates and Holding Period Return. Chapter Six Chapter 4, Part Bods, Bod Prices, Iterest Rates ad Holdig Period Retur Bod Prices 1. Zero-coupo or discout bod Promise a sigle paymet o a future date Example: Treasury bill. Coupo bod periodic

More information

ENGINEERING ECONOMICS

ENGINEERING ECONOMICS ENGINEERING ECONOMICS Ref. Grat, Ireso & Leaveworth, "Priciples of Egieerig Ecoomy'','- Roald Press, 6th ed., New York, 1976. INTRODUCTION Choice Amogst Alteratives 1) Why do it at all? 2) Why do it ow?

More information

An Empirical Study of the Behaviour of the Sample Kurtosis in Samples from Symmetric Stable Distributions

An Empirical Study of the Behaviour of the Sample Kurtosis in Samples from Symmetric Stable Distributions A Empirical Study of the Behaviour of the Sample Kurtosis i Samples from Symmetric Stable Distributios J. Marti va Zyl Departmet of Actuarial Sciece ad Mathematical Statistics, Uiversity of the Free State,

More information

Osborne Books Update. Financial Statements of Limited Companies Tutorial

Osborne Books Update. Financial Statements of Limited Companies Tutorial Osbore Books Update Fiacial Statemets of Limited Compaies Tutorial Website update otes September 2018 2 f i a c i a l s t a t e m e t s o f l i m i t e d c o m p a i e s I N T R O D U C T I O N The followig

More information

Calculation of the Annual Equivalent Rate (AER)

Calculation of the Annual Equivalent Rate (AER) Appedix to Code of Coduct for the Advertisig of Iterest Bearig Accouts. (31/1/0) Calculatio of the Aual Equivalet Rate (AER) a) The most geeral case of the calculatio is the rate of iterest which, if applied

More information

2. The Time Value of Money

2. The Time Value of Money 2. The Time Value of Moey Problem 4 Suppose you deposit $100 i the bak today ad it ears iterest at a rate of 10% compouded aually. How much will be i the accout 50 years from today? I this case, $100 ivested

More information

1 + r. k=1. (1 + r) k = A r 1

1 + r. k=1. (1 + r) k = A r 1 Perpetual auity pays a fixed sum periodically forever. Suppose a amout A is paid at the ed of each period, ad suppose the per-period iterest rate is r. The the preset value of the perpetual auity is A

More information

PORTFOLIO THEORY FOR EARTHQUAKE INSURANCE RISK ASSESSMENT

PORTFOLIO THEORY FOR EARTHQUAKE INSURANCE RISK ASSESSMENT PORTFOLIO THEORY FOR EARTHQUAKE INSURANCE RISK ASSESSMENT 63 Weimi DONG Ad Felix S WONG SUMMARY This paper presets a approach to quatifyig portfolio risks that ackowledges the importace of correlatio betwee

More information

The material in this chapter is motivated by Experiment 9.

The material in this chapter is motivated by Experiment 9. Chapter 5 Optimal Auctios The material i this chapter is motivated by Experimet 9. We wish to aalyze the decisio of a seller who sets a reserve price whe auctioig off a item to a group of bidders. We begi

More information

Lecture 16 Investment, Time, and Risk (Basic issues in Finance)

Lecture 16 Investment, Time, and Risk (Basic issues in Finance) Lecture 16 Ivestmet, Time, ad Risk (Basic issues i Fiace) 1. Itertemporal Ivestmet Decisios: The Importace o Time ad Discoutig 1) Time as oe o the most importat actors aectig irm s ivestmet decisios: A

More information

FOUNDATION ACTED COURSE (FAC)

FOUNDATION ACTED COURSE (FAC) FOUNDATION ACTED COURSE (FAC) What is the Foudatio ActEd Course (FAC)? FAC is desiged to help studets improve their mathematical skills i preparatio for the Core Techical subjects. It is a referece documet

More information

REITInsight. In this month s REIT Insight:

REITInsight. In this month s REIT Insight: REITIsight Newsletter February 2014 REIT Isight is a mothly market commetary by Resource Real Estate's Global Portfolio Maager, Scott Crowe. It discusses our perspectives o major evets ad treds i real

More information

Online appendices from The xva Challenge by Jon Gregory. APPENDIX 10A: Exposure and swaption analogy.

Online appendices from The xva Challenge by Jon Gregory. APPENDIX 10A: Exposure and swaption analogy. APPENDIX 10A: Exposure ad swaptio aalogy. Sorese ad Bollier (1994), effectively calculate the CVA of a swap positio ad show this ca be writte as: CVA swap = LGD V swaptio (t; t i, T) PD(t i 1, t i ). i=1

More information

RAIPUR AS A NEW CAPITAL: IMPACT ON POPULATION

RAIPUR AS A NEW CAPITAL: IMPACT ON POPULATION It. J. Egg. Res. & Sci. & Tech. 2013 Vadaa Agrawal, 2013 Research Paper RAIPUR AS A NEW CAPITAL: IMPACT ON POPULATION ISSN 2319-5991 www.ijerst.com Vol. 2, No. 1, February 2013 2013 IJERST. All Rights

More information

First determine the payments under the payment system

First determine the payments under the payment system Corporate Fiace February 5, 2008 Problem Set # -- ANSWERS Klick. You wi a judgmet agaist a defedat worth $20,000,000. Uder state law, the defedat has the right to pay such a judgmet out over a 20 year

More information

Chapter Four 1/15/2018. Learning Objectives. The Meaning of Interest Rates Future Value, Present Value, and Interest Rates Chapter 4, Part 1.

Chapter Four 1/15/2018. Learning Objectives. The Meaning of Interest Rates Future Value, Present Value, and Interest Rates Chapter 4, Part 1. Chapter Four The Meaig of Iterest Rates Future Value, Preset Value, ad Iterest Rates Chapter 4, Part 1 Preview Develop uderstadig of exactly what the phrase iterest rates meas. I this chapter, we see that

More information

Financial Analysis of Public- Private Partnership (PPP) Projects in Highways

Financial Analysis of Public- Private Partnership (PPP) Projects in Highways Trasport Forum ad Learig Week 2006 Workshop o HDM-4 Fiacial Aalysis of Public- Private Partership (PPP) Projects i Highways Cesar Queiroz Highway Advisor TUDTR World Bak, 24 March 2006 Presetatio Outlie

More information

Standard Deviations for Normal Sampling Distributions are: For proportions For means _

Standard Deviations for Normal Sampling Distributions are: For proportions For means _ Sectio 9.2 Cofidece Itervals for Proportios We will lear to use a sample to say somethig about the world at large. This process (statistical iferece) is based o our uderstadig of samplig models, ad will

More information

Anomaly Correction by Optimal Trading Frequency

Anomaly Correction by Optimal Trading Frequency Aomaly Correctio by Optimal Tradig Frequecy Yiqiao Yi Columbia Uiversity September 9, 206 Abstract Uder the assumptio that security prices follow radom walk, we look at price versus differet movig averages.

More information

Assessment Feasibility of Construction a Small Hydropower Plant

Assessment Feasibility of Construction a Small Hydropower Plant Assessmet Feasibility of Costructio a Small Hydropower Plat Filip Stojkovski a), Prof.d-r Zvoimir Kostic b), Prof.d-r Valetio Stojkovski b) a) Post graduated studet at Uiversity St Kiril i Metodij, Faculty

More information

for a secure Retirement Foundation Gold (ICC11 IDX3)* *Form number and availability may vary by state.

for a secure Retirement Foundation Gold (ICC11 IDX3)* *Form number and availability may vary by state. for a secure Retiremet Foudatio Gold (ICC11 IDX3)* *Form umber ad availability may vary by state. Where Will Your Retiremet Dollars Take You? RETIREMENT PROTECTION ASSURING YOUR LIFESTYLE As Americas,

More information

Dr. Maddah ENMG 602 Intro to Financial Eng g 01/18/10. Fixed-Income Securities (2) (Chapter 3, Luenberger)

Dr. Maddah ENMG 602 Intro to Financial Eng g 01/18/10. Fixed-Income Securities (2) (Chapter 3, Luenberger) Dr Maddah ENMG 60 Itro to Fiacial Eg g 0/8/0 Fixed-Icome Securities () (Chapter 3 Lueberger) Other yield measures Curret yield is the ratio of aual coupo paymet to price C CY = For callable bods yield

More information

Economics Bulletin, 2014, Vol. 34 No. 3 pp Introduction

Economics Bulletin, 2014, Vol. 34 No. 3 pp Introduction 1. Itroductio Aroud the world, electricity geeratio is a major source of carbo emissios. May atios have begu employig policy istrumets capable of stimulatig ad supportig deploymet of reewable ( gree )

More information

Quantitative Analysis

Quantitative Analysis EduPristie www.edupristie.com Modellig Mea Variace Skewess Kurtosis Mea: X i = i Mode: Value that occurs most frequetly Media: Midpoit of data arraged i ascedig/ descedig order s Avg. of squared deviatios

More information

The Effect of Technological Improvement on Capacity Expansion for Uncertain Exponential Demand with Lead Times

The Effect of Technological Improvement on Capacity Expansion for Uncertain Exponential Demand with Lead Times The Effect of Techological Improvemet o Capacity Expasio for Ucertai Expoetial Demad with Lead Times Dohyu Pak Departmet of Idustrial & Operatios Egieerig 205 Beal Aveue The Uiversity of Michiga A Arbor,

More information

STRAND: FINANCE. Unit 3 Loans and Mortgages TEXT. Contents. Section. 3.1 Annual Percentage Rate (APR) 3.2 APR for Repayment of Loans

STRAND: FINANCE. Unit 3 Loans and Mortgages TEXT. Contents. Section. 3.1 Annual Percentage Rate (APR) 3.2 APR for Repayment of Loans CMM Subject Support Strad: FINANCE Uit 3 Loas ad Mortgages: Text m e p STRAND: FINANCE Uit 3 Loas ad Mortgages TEXT Cotets Sectio 3.1 Aual Percetage Rate (APR) 3.2 APR for Repaymet of Loas 3.3 Credit Purchases

More information

Life Products Bulletin

Life Products Bulletin Life Products Bulleti Tredsetter Super Series Tredsetter Super Series: 2009 Chages Effective September 1, 2009, Trasamerica Life Isurace Compay is releasig ew rates for Tredsetter Super Series level premium

More information

Introduction to Financial Derivatives

Introduction to Financial Derivatives 550.444 Itroductio to Fiacial Derivatives Determiig Prices for Forwards ad Futures Week of October 1, 01 Where we are Last week: Itroductio to Iterest Rates, Future Value, Preset Value ad FRAs (Chapter

More information

Linear Programming for Portfolio Selection Based on Fuzzy Decision-Making Theory

Linear Programming for Portfolio Selection Based on Fuzzy Decision-Making Theory The Teth Iteratioal Symposium o Operatios Research ad Its Applicatios (ISORA 2011 Duhuag, Chia, August 28 31, 2011 Copyright 2011 ORSC & APORC, pp. 195 202 Liear Programmig for Portfolio Selectio Based

More information

Combining imperfect data, and an introduction to data assimilation Ross Bannister, NCEO, September 2010

Combining imperfect data, and an introduction to data assimilation Ross Bannister, NCEO, September 2010 Combiig imperfect data, ad a itroductio to data assimilatio Ross Baister, NCEO, September 00 rbaister@readigacuk The probability desity fuctio (PDF prob that x lies betwee x ad x + dx p (x restrictio o

More information

1 Random Variables and Key Statistics

1 Random Variables and Key Statistics Review of Statistics 1 Radom Variables ad Key Statistics Radom Variable: A radom variable is a variable that takes o differet umerical values from a sample space determied by chace (probability distributio,

More information

A Direct Finance Deposit and Borrowing Method Built Upon the Web Implemented Bidding ROSCA Model

A Direct Finance Deposit and Borrowing Method Built Upon the Web Implemented Bidding ROSCA Model A Direct Fiace Deposit ad Borrowig Method Built Upo the Web Implemeted Biddig ROSCA Model Adjuct Professor Kue-Bao (Frak) Lig, Natioal Taiwa Uiversity, Taiwa Presidet Yug-Sug Chie, SHACOM.COM INC., Taiwa

More information

Section 3.3 Exercises Part A Simplify the following. 1. (3m 2 ) 5 2. x 7 x 11

Section 3.3 Exercises Part A Simplify the following. 1. (3m 2 ) 5 2. x 7 x 11 123 Sectio 3.3 Exercises Part A Simplify the followig. 1. (3m 2 ) 5 2. x 7 x 11 3. f 12 4. t 8 t 5 f 5 5. 3-4 6. 3x 7 4x 7. 3z 5 12z 3 8. 17 0 9. (g 8 ) -2 10. 14d 3 21d 7 11. (2m 2 5 g 8 ) 7 12. 5x 2

More information

Estimating Proportions with Confidence

Estimating Proportions with Confidence Aoucemets: Discussio today is review for midterm, o credit. You may atted more tha oe discussio sectio. Brig sheets of otes ad calculator to midterm. We will provide Scatro form. Homework: (Due Wed Chapter

More information

Chapter 8: Estimation of Mean & Proportion. Introduction

Chapter 8: Estimation of Mean & Proportion. Introduction Chapter 8: Estimatio of Mea & Proportio 8.1 Estimatio, Poit Estimate, ad Iterval Estimate 8.2 Estimatio of a Populatio Mea: σ Kow 8.3 Estimatio of a Populatio Mea: σ Not Kow 8.4 Estimatio of a Populatio

More information

A random variable is a variable whose value is a numerical outcome of a random phenomenon.

A random variable is a variable whose value is a numerical outcome of a random phenomenon. The Practice of Statistics, d ed ates, Moore, ad Stares Itroductio We are ofte more iterested i the umber of times a give outcome ca occur tha i the possible outcomes themselves For example, if we toss

More information

T4032-ON, Payroll Deductions Tables CPP, EI, and income tax deductions Ontario Effective January 1, 2016

T4032-ON, Payroll Deductions Tables CPP, EI, and income tax deductions Ontario Effective January 1, 2016 T4032-ON, Payroll Deductios Tables CPP, EI, ad icome tax deductios Otario Effective Jauary 1, 2016 T4032-ON What s ew as of Jauary 1, 2016 The major chages made to this guide sice the last editio are outlied.

More information

REITInsight. In this month s REIT Insight:

REITInsight. In this month s REIT Insight: REITIsight Newsletter March 2014 REIT Isight is a mothly market commetary by Resource Real Estate's Global Portfolio Maager, Scott Crowe. It discusses our perspectives o major evets ad treds i real estate

More information

Chapter 5: Sequences and Series

Chapter 5: Sequences and Series Chapter 5: Sequeces ad Series 1. Sequeces 2. Arithmetic ad Geometric Sequeces 3. Summatio Notatio 4. Arithmetic Series 5. Geometric Series 6. Mortgage Paymets LESSON 1 SEQUENCES I Commo Core Algebra I,

More information

APPLICATION OF GEOMETRIC SEQUENCES AND SERIES: COMPOUND INTEREST AND ANNUITIES

APPLICATION OF GEOMETRIC SEQUENCES AND SERIES: COMPOUND INTEREST AND ANNUITIES APPLICATION OF GEOMETRIC SEQUENCES AND SERIES: COMPOUND INTEREST AND ANNUITIES Example: Brado s Problem Brado, who is ow sixtee, would like to be a poker champio some day. At the age of twety-oe, he would

More information

living well in retirement Adjusting Your Annuity Income Your Payment Flexibilities

living well in retirement Adjusting Your Annuity Income Your Payment Flexibilities livig well i retiremet Adjustig Your Auity Icome Your Paymet Flexibilities what s iside 2 TIAA Traditioal auity Icome 4 TIAA ad CREF Variable Auity Icome 7 Choices for Adjustig Your Auity Icome 7 Auity

More information