Overhaul Overdraft Fees: Creating Pricing and Product Design Strategies with Big Data


 Olivia Caldwell
 2 years ago
 Views:
Transcription
1 Overhaul Overdraft Fees: Creatng Prcng and Product Desgn Strateges wth Bg Data Xao Lu, Alan Montgomery, Kannan Srnvasan September 30, 2014 Abstract In 2012, consumers pad an enormous $32 bllon overdraft fees. Consumer attrton and potental government regulatons to shut down the overdraft servce urge banks to come up wth fnancal nnovatons to overhaul the overdraft fees. However, no emprcal research has been done to explan consumers overdraft ncentves and evaluate alternatve prcng and product strateges. In ths paper, we buld a dynamc structural model wth consumer montorng cost and dssatsfacton. We fnd that on one hand, consumers heavly dscount the future and overdraw because of mpulsve spendng. On the other hand, a hgh montorng cost makes t hard for consumers to track ther fnances therefore they overdraw because of ratonal nattenton. In addton, consumers are dssatsfed by the overly hgh overdraft fee and close ther accounts. We apply the model to a bg dataset of more than 500,000 accounts for a span of 450 days. Our polcy smulatons show that alternatve prcng strateges may ncrease the bank s revenue. Sendng targeted and dynamc alerts to consumers can not only help consumers avod overdraft fees but mprove bank profts from hgher nterchange fees and less consumer attrton. To allevate the computatonal burden of solvng dynamc programmng problems on a large scale, we combne parallel computng technques wth a Bayesan Markov Chan Monte Carlo algorthm. The Bg Data allow us to detect the rare event of overdraft and reduce the samplng error wth mnmal computatonal costs. 1 Introducton An overdraft occurs when a consumer attempts to spend or wthdraw funds from her checkng accounts n an amount exceedng the account s avalable funds. In the US, banks allow consumers to overdraw ther accounts (subject to some restrctons at banks dscreton and charge an overdraft fee. Overdraft fees have become a major source of bank revenues snce banks started to offer free checkng accounts to attract consumers. In 2012, the total amount of overdraft fees n the US reached $32 bllon, accordng to Moebs Servces 1. Ths s equvalent to an average of $178 for each checkng account annually 2. Accordng to the Center for Responsble Lendng, US households spent more on overdraft fees than on fresh vegetables, postage and books n We acknowledge support from the Dpankar and Sharmla Chakravart Fellowshp. All errors are our own Accordng to Evans, Ltan, and Schmalensee 2011, there are 180 mllon checkng accounts n the US. 3 1
2 The unfarly hgh overdraft fee has provoked a storm of consumer outrage and therefore caused many consumers to close the account. The US government has taken actons to regulate these overdraft fees through the Consumer Fnancal Protecton Agency 4 and may potentally shut down the overdraft servce 5. Wthout overhaulng the current overdraft fee, banks encounter the problem of losng valuable customers and possbly totally losng the revenue source from overdrafts. Fnancal nsttutons store massve amounts of nformaton about consumers. The advantages of technology and Bg Data enable banks to reverse the nformaton asymmetry (Kamenca, Mullanathan, and Thaler 2011 as they may be able to generate better forecasts about a consumer s fnancal state than consumers themselves can. In ths paper, we extract the valuable nformaton embedded n the Bg Data and harness t wth structural economc theores to explan consumers overdraft behavor. The large scale fnancal transacton panel data allows us to sort through consumers fnancal decson makng processes and dscover rch consumer heterogenety. As a consequence, we come up wth ndvdually customzed strateges that can ncrease both consumer welfare and bank revenue. In ths paper, we am to acheve two substantve goals. Frst, we leverage rch data about consumer spendng and balance checkng to understand the decson process for consumers to overdraw. We address the followng research questons. Are consumers fully attentve n montorng ther checkng account balances? How great s the montorng cost? Why do attentve consumers also overdraw? Are consumers dssatsfed because the overdraft fee? Second, we nvestgate prcng and new product desgn strateges that overhaul overdraft fees. Specfcally, we tackle these questons. Is the current overdraft fee structure optmal? How wll the bank revenue change under alternatve prcng strateges? More mportantly, what new revenue model can make the ncentves of the bank and consumers better algned? Can the bank beneft from helpng consumers make more nformed fnancal decsons, lke sendng alerts to consumers? If so, what s the optmal alert strategy? How can the bank leverage ts rch data about consumer fnancal behavors to reverse nformaton asymmetry and create targeted strateges? We estmate the dynamc structural model usng data from a large commercal bank n the US. The sample sze s over 500,000 accounts and the sample length s up to 450 days. We fnd that some consumers are nattentve n montorng ther fnances because of a substantally hgh montorng cost. In contrast, attentve consumers overdraw because they heavly dscount future utltes and are subject to mpulsve spendng. Consumers are dssatsfed to leave the bank after beng charged the unfarly hgh overdraft fees. In our counterfactual analyss, we show that a percentage fee or a quantty premum fee strategy can acheve hgher bank revenue compared to the current flat pertransacton fee strategy. Enabled by Bg Data, we also propose an optmal targeted alert strategy. The bank can beneft from sendng alerts to let consumers spend ther unused balances so that the bank can earn more nterchange fees. Helpng consumers make more nformed decsons wll also sgnfcantly reduce consumer attrton. The targeted dynamc alerts should be sent to consumers wth hgher montorng costs and both when they are underspendng and overspendng. Methodologcally, our paper makes two key contrbutons. Frst, we buld a dynamc structural model that ncorporates nattenton and dssatsfacton nto the lfetme consumpton model. Although we apply t to the overdraft context, the model framework can be generalzed to ana
3 lyze other marketng problems regardng consumer dynamc budget allocaton, lke electrcty and cellphone usage. Second, we estmate the model on Bg Data wth the help of parallel computng technques. Structural models have the mert of producng polcy nvarate parameters that allow us to conduct counterfactual analyss. However, the nherent computatonal burden prevents t from beng wdely adopted by ndustres. Moreover, the data sze n a real settng s typcally much larger than what s used for research purposes. Companes, n our case a large bank, need to have methods that are easly scalable to generate targeted solutons for each consumer. Our proposed algorthm takes advantage of stateoftheart parallel computng technques and estmaton methods that allevate computatonal burden and reduce the curse of dmensonalty. The rest of the paper s organzed as follows. In secton 2 we frst revew related lterature. Then we show summary statstcs n secton 3 whch motvate our model setup. Secton 4 descrbes our structural model and we provde detals of dentfcaton and estmaton procedures n secton 5. Then n sectons 6 and 7 we show estmaton results and counterfactual analyss. Secton 8 concludes and summarzes our lmtatons. 2 Related Lterature A varety of economc and psychologcal models can explan overdrafts, ncludng fullnformaton pure ratonal models and lmted attenton, as summarzed by Stango and Znman (2014. However, no emprcal paper has appled these theores to real consumer spendng data. Although Stango and Znman (2014 had a smlar dataset to ours, ther focus was on testng whether takng related surveys can reduce overdrafts. We develop a dynamc structural model that ncorporates theores of heavy dscountng, nattenton and dssatsfacton n a comprehensve framework. The model s flexble to address varous overdraft scenaros, thus t can be used by polcy makers and the bank to desgn targeted strateges to ncrease consumer welfare and bank revenue. Our model nherts from the tradtonal lfetme consumpton model but adds two novel features, nattenton and dssatsfacton. Frst of all, a large body of lterature n psychology and economcs has found that consumers pay lmted attenton to relevant nformaton. In the revew paper by Card, DellaVgna and Malmender (2011, they summarze fndngs ndcatng that consumers pay lmted attenton to 1 shppng costs, 2 tax (Chetty et. al and 3 rankng (Pope Gabax and Labson (2006 fnd that consumers don t pay enough attenton to addon prcng and Grubb (2014 shows consumers nattenton to ther cellphone mnute balances. Many papers n the fnance and accountng doman have documented that nvestors and fnancal analysts are nattentve to varous fnancal nformaton (e.g., Hrshlefer and Teoh 2003, Peng and Xong We follow Stango and Znman (2014 to defne nattenton as ncomplete consderaton of account balances (realzed balance and avalable balance net of comng blls that would nform choces. We further explan nattenton wth a structural parameter, montorng cost, whch represents the tme and effort to know the exact amount of money n the checkng account. Wth ths parameter estmated, we are able to quantfy the economc value of sendng alerts to consumers and provde gudance for the bank to set ts prcng strategy. We also come up wth polcy smulatons about alerts because we thnk a drect remedy for consumers lmted attenton s to make nformaton more salent (Card, DellaVgna and Malmender Past lterature also fnds that remnders (Karlan et. al. 2010, mandatory dsclosure (Fshman and Hagerty 2003, and penal 3
4 tes (Haselhuhn et al all serve the purpose of ncreasng salence and thus mtgatng the negatve consequences of nattenton. Second, as documented n prevous lterature, unfarly hgh prce may cause consumer dssatsfacton whch s one of the man causes of customer swtchng behavor (Keaveney 1995, Bolton We notce that consumers are more lkely to close the account after payng the overdraft fee and when the rato of the overdraft fee over the overdraft transacton amount s hgh. Ths s because gven the current bankng ndustry practce, a consumer pays a flat pertransacton fee regardless of the transacton amount. Therefore, the mpled nterest rate for an overdraft orgnated by a small transacton amount s much hgher than the socally accepted nterest rate (Matzler, Wurtele and Renzl 2006, leadng to prce dssatsfacton. We am to estmate ths nfnte horzon dynamc structural model on a large scale of data and obtan heterogeneous best response for each consumer to prepare targeted marketng strateges. After searchng among dfferent estmaton methods, ncludng the nested fxed pont algorthm (Rust 1987, the condtonal choce probablty estmaton (Arcdacono and Mller 2011 and the Bayesan estmaton method developed n Ima, Jan and Chng (2009 (IJC, we fnally choose the IJC method for the followng reasons. Frst of all, the herarchcal Bayes framework fts our goal of obtanng heterogeneous parameters. Second, n order to apply our model to a large scale of data, we need to estmate the model wth Bayesan MCMC so that we can mplement a parallel computng technque. Thrd, IJC s the stateofthe art Bayesan estmaton algorthm for nfnte horzon dynamc programmng models. It provdes two addtonal benefts n tacklng the computatonal challenges. One s that t allevates the computatonal burden by only evaluatng the value functon once n each MC teraton. Essentally, the algorthm solves the value functon and estmates the structural parameters smultaneously. So the computatonal burden of a dynamc problem s reduced by an order of magntude smlar to those computatonal costs of a statc model. The other s that the method reduces the curse of dmensonalty by allowng state space grd ponts to vary between estmaton teratons. On the other hand, as our sample sze s huge, tradtonal MCMC estmaton may take a prohbtvely, f not mpossbly, long tme, snce for N data ponts, most methods must perform O(N operatons to draw a sample. A natural way to reduce the computaton tme s to run the chan n parallel. Past methods of Parallel MCMC duplcate the data on multple machnes and cannot reduce the tme of burnn. We nstead use a new technque developed by Neswanger, Wang and Xng (2014 to solve ths problem. The key dea of ths algorthm s that we can dstrbute data nto multple machnes and perform IJC estmaton n parallel. Once we obtan the posteror Markov Chans from each machne, we can algorthmcally combne these ndvdual chans to get the posteror chan of the whole sample. 3 Background and Model Free Evdence We obtaned data from a major commercal bank n the US. Durng our sample perod n 2012 and 2013, overdraft fees accounted for 47% of the revenue from depost account servce charges and 9.8% of the operatng revenue. The bank provdes a comprehensve overdraft soluton to consumers. (For general overdraft practces n the US, please refer to Stango and Znman (2014 for a good revew. Appendx A.1 tabulates current fee settngs n top US banks. In the standard overdraft servce, f the consumer 4
5 overdraws her account, the bank mght cover the transacton and charge $31 6 Overdraft Fee (OD or declne the transacton and charge a $31 NonSuffcentFund Fee (NSF. Whether the transacton s accepted or declned s at the bank s dscreton. The OD/NSF fee s at a pertem level. If a consumer performs several transactons when the account s already overdrawn, each transacton tem wll ncur a fee of 31 dollars. Wthn a day, a maxmum of four pertem fees can be charged. If the account remans overdrawn for fve or more consecutve calendar days, a Contnuous Overdraft Fee of $6 wll be assessed up to a maxmum of $84. The bank also provdes an Overdraft Protecton Servce where the checkng account can lnk to another checkng account, a credt card or a lne of credt. In ths case, when the focal account s overdrawn, funds can be transferred to cover the negatve balance. The Overdraft Transfer Balance Fee s $9 for each transfer. As you can see, the fee structure for the bank s qute complcated. In the emprcal analyss below, we don t dstngush between dfferent types of overdraft fees and assume that money s fungble so that the consumer only cares about the total amount of overdraft fee rather than the underlyng prcng structure. The bank also provdes balance checkng servces through branch, automated teller machne (ATM, call center and onlne/moble bankng. Consumers can nqure about ther avalable balances and recent actvtes. There s also a notfcaton servce to consumers va emal or text message, named alerts. Consumers can set alerts when certan events take place, lke overdrafts, nsuffcent funds, transfers, deposts, etc. Unfortunately, our dataset only ncludes the balance checkng data but not the alert data. We ll dscuss ths lmtaton n secton 8. In 2009, the Federal Reserve Board made an amendment to Regulaton E (subsequently recodfed by the Consumer Fnancal Protecton Bureau (CFPB whch requres account holders to provde affrmatve consent (opt n for overdraft coverage of ATM and nonrecurrng pont of sale (POS debt card transactons before banks can charge for payng such transactons 7. Ths Regulaton E amed to protect consumers aganst the heavy overdraft fees. The change became effectve for new accounts on July 1, 2010, and for exstng accounts on August 15, Our sample contans both optn and optout accounts. However, we don t know whch accounts have opted n unless we observe an ATM/POS ntated overdraft occason. We also dscuss ths data lmtaton n secton Summary Statstcs Our data can be dvded nto two categores, checkng account transactons and balance nqury actvtes. In our sample, there are between 500,000 and 1,000,000 8 accounts, among whch 15.8% had at least one overdraft ncdence durng the sample perod between June 2012 and Aug The proporton of accounts wth overdraft s lower than the 27% (across all banks and credt unons reported by the CFPB n In total, all the counts performed more than 200 mllon transactons, ncludng deposts, wthdrawals, transfers, and payments etc. For each transacton, we know the account number, transacton date, transacton amount, and transacton descrpton. The transac 6 All dollar values n the paper have been rescaled by a number between.85 and 1.15 to help obfuscate the exact amounts wthout changng the substantve mplcatons. The bank also sets the frst tme overdraft fee for each consumer at $22. All the rest overdraft fees are set at $ For the sake of prvacy, we can t dsclose the exact number. 9 5
6 ton descrpton tells us the type of transacton (e.g., ATM wthdrawal or debt card purchase and locaton/assocated nsttuton of the transacton, lke merchant name or branch locaton. The descrpton helps us dentfy the cause of the overdraft, for nstance whether t s due to an electrcty bll or due to a grocery purchase. Table 1: Overdraft Frequency and Fee Dstrbuton Mean Std Medan Mn Percentle OD Frequency >100 OD Fee >2730 As shown n Table 1, consumers who pad overdraft fees, on average, overdrew nearly 10 tmes and pad $245 durng the 15 month sample perod. Ths s consstent wth the fndng from the CFPB that the average overdraft and NSFrelated fees pad by all accounts that had one or more overdraft transactons n 2011 were $ There s sgnfcant heterogenety n consumers overdraft frequency and the dstrbuton of overdraft frequency s qute skewed. The medan overdraft frequency s three and more than 25% of consumers overdrew only once. In contrast, the top 0.15% of heavy overdrafters overdrew more than 100 tmes. A smlar skewed pattern apples to the dstrbuton of overdraft fees. Whle the medan overdraft fee s $77, the top 0.15% of heavest overdrafters pad more than $2,730 n fees. Fgure 1: Overdraft Frequency and Fee Dstrbuton Now let s zoom n to take a look at the behavor of the majorty overdrafters that have overdrawn less than 40 tmes. The frst panel n Fgure 1 depcts the dstrbuton of overdraft frequency for those accounts. Notce that most consumers (> 50% only overdrew less than three tmes. The second panel shows the dstrbuton of the pad overdraft fee for accounts that have overdrawn less than $300. Consstent wth the fee structure where the standard pertem overdraft fee s $22 or $31, we see spkes on these two numbers and ther multples
7 Table 2: Types of Transactons That Cause Overdraft Type Frequency Percentage Amount Debt Card Purchase 946, % ACH Transacton 267, % Check 227, % ATM Wthdrawal 68, % What types of transactons cause overdraft? We fnd that nearly 50% of overdrafts are caused by debt card purchases wth mean transacton amounts around $30. On the other hand, ACH (Automated Clearng House and Check transactons account for 13.77% and 11.68% of overdraft occasons. These transactons are generally for larger amounts, $ and $417.78, respectvely. ATM wthdrawals lead to another 3.51% of the overdraft transactons wth an average amount of around $ Model Free Evdence Ths secton presents some patterns n the data that suggest the causes and effects of overdrafts. We show that heavy dscountng and nattenton may drve consumers overdraft behavors. And consumers are dssatsfed because of the overdraft fees. The model free evdence also hghlghts the varaton n the data that wll allow for the dentfcaton of the dscount factor, montorng cost and dssatsfacton senstvty Heavy Dscountng Frst of all, we argue that a consumer may overdraw because she prefers current consumpton much more than future consumpton,.e. she heavly dscounts future consumpton utlty. At the pont of sale, the consumer sharply dscounts the future cost of the overdraft fee to satsfy mmedate gratfcaton 11. If that s the case, then we should observe a steep downward slopng trend n the spendng pattern wthn a pay perod. That s, the consumer wll spend a lot rght after gettng a pay check and then reduce spendng durng the course of the month. But because of overspendng at the begnnng, the consumer s gong to run out of budget at the end of the pay perod and has to overdraw. We test ths hypothess wth the followng model specfcaton. We assume that the spendng for consumer at tme t Spendng t can be modeled as Spendng t = β LapsedTmeA fterincome t + µ + v t + ε t where LapsedTmeA fterincome t s the number of days after the consumer receved ncome (salary, µ s the ndvdual fxed effect and v t s the tme (day fxed effect. To control for the 11 We also consdered hyperbolc dscountng wth two dscount factors, a short term present bas parameter and a long term dscount factor. Wth more than three perods of data wthn a pay perod, hyperbolc dscount factors can be dentfed (Fang and Slverman However, our estmaton results show that the present bas parameter s not sgnfcantly dfferent from 1. Therefore we only keep one dscount factor n the current model. Estmaton results wth hyperbolc dscount factors are avalable upon requests. 7
8 effect that consumers usually pay for ther blls (utltes, phone blls, credt card blls, etc after gettng the pay check, we exclude checks and ACH transactons whch are the common choces for bll payments from the daly spendngs and only keep debt card purchases, ATM wthdrawals and persontoperson transfers. We run ths OLS regresson for heavy overdrafters (whose overdraft frequency s n the top 20 percentle among all overdrafters, lght overdrafters (whose overdraft frequency s not n the top 20 percentle among all overdrafters and nonoverdrafters (who ddn t overdraw durng the 15 months sample perod separately. The results are reported n column (1 (2 and (3 of Table 3. Table 3: Spendng Decreases wth Tme n a Pay Cycle (1 (2 (3 Heavy Overdrafters Lght Overdrafters Non Overdrafters Lapsed Tme after Income (β ( ( ( Fxed Effect Yes Yes Yes Number of Observatons 17, 810, , 845, , 598, 851 R Note: *p<0.01;**p<0.001;***p< We fnd that the coeffcent of LapsedTmeA fterincome t s negatve and sgnfcant for heavy overdrafters but not lght overdrafters or nonoverdrafters. Ths suggests that heavy overdrafters have a steep downward slopng spendng pattern durng a pay perod whle lght overdrafters or nonoverdrafters have a relatvely stable spendng stream. The heavy overdrafters are lkely to overdraw because they heavly dscount ther future consumptons Inattenton Next we explan the overdraft ncentves for the lght overdrafters wth nattenton. The dea s that consumers mght be nattentvely montorng ther checkng accounts so that they are uncertan about the exact balance amount. Sometmes the perceved balance can be hgher than the true balance and ths mght cause an overdraft. We frst present a representatve example of consumer nattenton. The example s based upon our data, but to protect the prvacy of the consumer and the merchants, amounts have been changed. However, the example remans representatve of the underlyng data. 8
9 Fgure 2: Overdraft due to Balance Percepton Error As shown n fgure 2, the consumer frst receved her salary on August 17th. After a seres of expenses she was left wth $21.16 on August 20th. As she had never checked her balance, she contnued spendng and overdrew her account for several small purchases, ncludng a $25 restaurant bll, a $17.12 beauty purchase, a $6.31 game and a $4.95 coffee purchase. These four transactons added up to $53.38 but caused her to pay four overdraft tem fees, a total of $124. We speculate that ths consumer was careless n montorng her account and overestmated her balance. Beyond ths example, we fnd more evdence of nattenton n the data. Intutvely, a drect support of nattenton s that the less frequent a consumer checks her balance, the more overdraft fee she pays. To test ths hypothess, we estmate the followng specfcaton: TotODPmt t =β 0 + β 1 BCFreq t + µ + v t + ε t where for consumer at tme t (month, TotODPmt t s the total overdraft payment, BCFreq t s the balance checkng frequency. We estmate ths model on lght overdrafters (whose overdraft frequency s not n the top 20 percentle and heavy overdrafters (whose overdraft frequency s n the top 20 percentle separately and report the result n the column (1 and (2 n Table 4. 9
10 Table 4: Frequent Balance Checkng Reduces Overdrafts for Lght Overdrafters (1 (2 (3 Lght Overdrafters Heavy Overdrafters All Overdrafters Balance Checkng Frequency (BCFreq, β 1 Overdraft Frequency (ODFreq, β 2 BCFreq ODFreq (β ( ( ( ( ( Number of Observatons 53, 845, , 810, , 655, 315 R Note: Fxed effects at ndvdual and day level; Robust standard errors, clustered at ndvdual level.*p<0.01;**p<0.001;***p< The result suggests that more balance checkng decreases overdraft payment for lght overdrafters but not for heavy overdrafters. We further test ths effect by ncludng overdraft frequency (ODFreq t and an nteracton term of balance checkng frequency and overdraft frequency BCFreq t ODFreq t n the equaton below. The dea s that f the coeffcent for ths nteracton term s postve whle the coeffcent for balance checkng frequency (BCFreq t s negatve, then t mples that checkng balances more often only decreases the overdraft payment for consumers who overdraw nfrequently but not for those who do t wth hgh frequency. TotODPmt t =β 0 + β 1 BCFreq t + β 2 ODFreq t + β 3 BCFreq t ODFreq t + µ + v t + ε t The result n column (3 of Table 4 confrms our hypothess. Interestngly, we fnd that a consumer s balance percepton error accumulates overtme n the sense that the longer a consumer hasn t check balances, the more lkely that she s gong to overdraw and pay hgher amount of overdraft fees. Fgure 3 below exhbts the overdraft probablty across number of days snce a consumer checked balance last tme for lght overdrafters (whose overdraft frequency s not n the top 20 percentle. It suggests that the overdraft probablty ncreases moderately wth the number of days snce the last balance check. Fgure 3: Overdraft Lkelhood Increases wth Lapsed Tme Snce Last Balance Check 10
11 We confrm ths relatonshp wth the followng two specfcatons. We assume that overdraft ncdence I(OD t (where I(OD t = 1 denotes overdraft and I(OD t = 0 denotes no overdraft and overdraft fee payment amount ODFee t for consumer at tme t can be modeled as: I(OD t = Φ(ρ 0 + ρ 1 DaysSnceLastBalanceCheck t + ρ 2 BegnBal t + µ + v t ODFee t = ρ 0 + ρ 1 DaysSnceLastBalanceCheck t + ρ 2 BegnBal t + µ + v t + ε t where Φ s the cumulatve dstrbuton functon for standard normal dstrbuton. The term DaysSnceLastBalanceCheck t denotes the number of days consumer hasn t checked her balance untl tme t and BegnBal t s the begnnng balance at tme t. We control for the begnnng balance because t can be negatvely correlated wth the days snce last balance check due to the fact that consumers tend to check when the balance s low and a lower balance usually leads to an overdraft. Table 5: Reduced Form Evdence of Exstance of Montorng Cost I (OD ODFee Days Snce Last Balance Check (ρ ( ( Begnnng Balance (ρ ( ( Indvdual Fxed Effect Yes Yes Tme Fxed Effect Yes Yes Number of Observatons 53, 845, , 845, 039 R Note: The estmaton sample only ncludes overdrafters. Margnal effects for the Probt model; Fxed effects at ndvdual and day level; robust standard errors, clustered at ndvdual level.*p<0.01;**p<0.001;***p< Table 5 reports the estmaton results whch support our hypothess that the longer a consumer hasn t checked balance, the more lkely she overdraws and the hgher overdraft fee she pays. Snce checkng balances can effectvely help prevent overdrafts, why don t consumers do t often enough to avod overdraft fees? We argue that t s because montorng the account s costly n terms of tme, effort and mental resources. Therefore, a natural consequence s that f there s a means to save consumers tme, effort or mental resources, the consumer wll ndeed check balances more frequently. We fnd such support from the data about onlne bankng ownershp. Specfcally, for consumer we estmate the followng specfcaton: CheckBalFreq = β 0 + β 1 OnlneBankng +β 2 LowIncome + β 3 Age + ε where CheckBalFreq s the balance checkng frequency, OnlneBankng s onlne bankng ownershp (1 denotes the consumer has onlne bankng whle 0 denotes otherwse, LowIncome s whether the consumer belongs to the low ncome group (1 denotes yes and 0 denotes no and Age s age (n years. 11
12 Table 6: Reduced Form Evdence of Exstance of Montorng Cost Dependent varable Check Balance Frequency Onlne Bankng (β ( Low Income (β ( Age (β ( Number of Observatons 602,481 R *p<0.01;**p<0.001;***p< Table 6 shows that after controllng for ncome and age, consumers wth onlne bankng accounts check the balance more frequently than those wthout, whch suggests that montorng costs exst and when they are reduced, consumers montor more frequently Dssatsfacton Table 7: Account Closure Frequency for Overdrafters vs NonOverdrafters Total % Closed Heavy Overdrafters 23.36% Lght Overdrafters 10.56% NonOverdrafters 7.87% We also fnd that overdrafters are more lkely to close ther accounts (Table 7. Among nonoverdrafters, 7.87% closed ther accounts durng the sample perod. Ths rato s much hgher for overdrafters. Specfcally, 23.36% of heavy overdrafters (whose overdraft frequency s n the top 20 percentle closed ther accounts, whle 10.56% of lght overdrafters (whose overdraft frequency s not n the top 20 percentle closed ther accounts. Table 8: Closure Reasons Overdraft Overdraft No Overdraft Forced Closure Voluntary Closure Voluntary Closure Heavy Overdrafters 86.34% 13.66% Lght Overdrafters 52.58% 47.42% NonOverdrafters % From the descrpton feld n the data, we can dstngush the cause of account closure: forced closure by the bank because the consumer s unable or unwllng to pay back the negatve balances and the fee (chargeoff or voluntary closure by the consumer. Among heavy overdrafters, 13.66% closed voluntarly and the rest (86.34% were forced to close by the bank (Table 8. In contrast, 47.42% of the lght overdrafters closed ther accounts voluntarly. We conjecture that the hgher 12
13 voluntary closures may be due to customer dssatsfacton wth the bank, wth evdence shown below. Fgure 4: Days to Closure After Last Overdraft Frst, we fnd that overdrafters who closed voluntarly were very lkely to close soon after the overdraft. In Fgure 4 we plot the hstogram of number of days t took the account to close after ts last overdraft occason. It shows that more than 60% of accounts closed wthn 30 days after the overdraft occason. Fgure 5: Percentage of Accounts Closed Increases wth Fee/Transacton Amount Rato Second, lght overdrafters are also more lkely to close ther accounts when the rato of overdraft fee over the transacton amount that caused the overdraft fee s hgher. In other words, the more unfar the overdraft fee (hgher rato of overdraft fee over the transacton amount that caused the overdraft fee, the more lkely t s that she wll close the account. We show ths pattern n the left panel of Fgure 5. However, ths effect doesn t seem to be present for heavy overdrafters (rght panel of Fgure 5. The model free evdence ndcate that consumer heavy dscountng and nattenton can help explan consumers overdraft behavors as consumers mght be dssatsfed after beng charged the overdraft fees. Below we ll buld a structural model that ncorporates consumer heavy dscountng, nattenton and dssatsfacton. 4 Model We model a consumer s daly decson about nonpreauthorzed spendng n her checkng account. Alternatvely we could descrbe ths nonpreauthorzed spendng as mmedate or dscretonary; not dscretonary n the sense that economsts tradtonally use the term, but n the sense that mmedate spendng lkely could have been delayed. To focus on ratonalzng the consumer s overdraft 13
14 behavor, we make the followng assumptons. Frst, we abstract away from the complexty assocated wth our data and assume that the consumer s ncome and preauthorzed spendngs are exogenously gven. We refer to preauthorzed spendng to mean those expenses for whch the spendng decson was made pror to payment. For example, a telephone bll or a mortgage due are usually arranged before the date that the actual payment occurs. We assume that decsons for preauthorzed spendng are hard to change on a daly bass after they are authorzed and more lkely to be related to consumpton that has medum or longrun consequences. In contrast, nonpreauthorzed spendng nvolves a consumer s frequent daytoday decsons and the consumer can adjust the spendng amount flexbly. We make ths dstncton because nonpreauthorzed spendng s at the consumer s dscreton and thus affects the overdraft outcome drectly. To ease explanaton, we use comng blls to represent preauthorzed spendng for the rest of the paper. Second, we allow the consumer to be nattentve to montorng her account balance and comng blls. But she can decde whether to check her balance. When a consumer hasn t checked the balance, she comes up wth an estmate of the avalable balance and forms an expectaton about comng blls. If she makes a wrong estmate or expectaton, she faces the rsk of overdrawng her account. Last, as consumpton s not observed n the data, we make a bold assumpton that spendng s equvalent to consumpton n terms of generatng utlty. That s, the more a consumer spends, the more she consumes, the hgher utlty she obtans. In what follows, we use consumpton and spendng nterchangeably. We ll descrbe the model n the next four parts: (1 tmng, (2 basc model (3 nattenton and balance checkng and (4 dssatsfacton and account closng. 4.1 Tmng The tmng of the model s as follows (Fgure 6. On each day: 1. The consumer receves ncome, f there s any. 2. Her blls arrve f there s any. 3. Balance checkng stage (CB: She decdes whether to check her balance. If she checks, she ncurs a cost and knows today s begnnng balance and the bll amount. If not, she recalls an estmate of the balance and bll amount. 4. Spendng stage (SP: She makes the dscretonary spendng decson (Choose C to maxmze total dscounted utlty V (or expected total dscounted utlty EV f she ddn t check balancefor today and spends the money. 5. Overdraft fee s charged f the endng balance s below zero. 6. Account closng stage (AC: She decdes whether to close the account (after payng the overdraft fee f there s any. If she closes the account, she receves an outsde opton. If she doesn t chose the account, she goes to Balance updates and the next day comes. 14
15 Fgure 6: Model Tmng 4.2 Basc Model We assume the consumer s perperod consumpton utlty at tme t s a constant relatve rsk averse utlty (Arrow 1963: u C (C t = C1 θ t t (1 1 θ t where θ t s the relatve rsk averse coeffcent whch represents the consumer s preference about consumpton. The hgher θ t, the hgher utlty the consumer can derve from a margnal unt of consumpton. θ t = exp(θ + ε t ε t N ( 0,ς 2 As consumers preference for consumpton mght change over tme and the relatve rsk averse coeffcent s always postve, we allow θ t to follow a lognormal dstrbuton. Essentally, θ t s the exponental of the sum of a tmenvarant mean θ and a random shock ε t. The shocks capture unexpected needs for consumpton and follow a normal dstrbuton wth mean 0 and varance ς 2 (Yao et. al Notce that the consumpton plan C t depends on the consumer s budget constrant, whch further depends on her current balance B t, ncome Y t and future blls Ψ t. For example, when the comng bll s for a small amount, the consumpton can be hgher than when the bll s for a large amount. 4.3 Inattenton and Balance Checkng In practce, the consumer may not be fully attentve to her fnancal wellbeng. Because montorng her account balance takes tme and effort, she may not check her balance frequently. As a 15
16 consequence, nstead of knowng the exact (avalable balance B t 12, she recalls a perceved balance B t. Followng Mehta, Rajv and Srnvasan (2003, we allow the perceved balance B t to be the sum of the true balance B t and a percepton error η t ω t. The frst component of the percepton error η t s a random draw from the standard normal dstrbuton 13 and the second component s the standard devaton of the percepton error, ω t. So B t follows a normal dstrbuton B t N ( B t + η t ω t,ωt 2 The varance of the percepton error ωt 2 measures the extent of uncertanty. Based on the evdence from secton 3.2.2, we allow ths extent of uncertanty to accumulate through tme whch mples that the longer the consumer goes wthout checkng her balance, the more naccurate her perceved balance s. That s, ω 2 t = ργ t (2 where Γ t denotes the lapsed tme snce the consumer last checked her balance, and ρ denotes the senstvty to lapsed tme as shown n the equaton (2 above 14. Notce that the expected utlty s decreasng n the varance of the percepton error ω 2 t. Ths s true because the larger the varance of the percepton error, the less accurate the consumer s estmate of her true balance, and the more lkely she s gong to mstakenly overdraw, whch lowers her utlty. We further assume that the consumer s sophstcated nattentve 15 n the sense that she s aware of her own nattenton (Grubb Sophstcated nattentve consumers are ratonal n that they choose to be nattentve due to the hgh cost of montorng her balances from daytoday. We also model the consumer s balance checkng behavor. We denote the balance checkng choce as Q t {1,0} where 1 means check and 0 otherwse. If a consumer checks her balance, she ncurs a montorng cost but knows exactly what her balance s. So the percepton error s reduced to zero and she can make her optmal spendng decson wth all nformaton. In mathematcs form, her consumpton utlty functon changes to u t = C1 θ t t Q t ξ + χ tqt (3 1 θ t where ξ s her balance checkng cost and χ Qt s the dosyncratc shock that affects her balance checkng cost. The shock χ tqt can come from random events lke a consumer checks balance because she s also performng other types of transactons (lke onlne bll payments or she s on vacaton wthout access to any bank channels so t s hard for her to check balances. The equaton 12 Avalable balance means the ntal balance plus ncome mnus blls. For the ease of exposton, we omt the word "avalable" and only use "balance". 13 The mean balance percepton error η cannot be separately dentfed from the varance parameters ρ because the dentfcaton sources both come from consumers overdraft fee payment. Specfcally, the hgh overdraft payment for a consumer can be ether explaned by a postve balance percepton error or large percepton error varance caused by large ρ. So we fx η at zero,.e. the percepton error s assumed to be unbased. 14 We consdered other specfcatons for the relatonshp between percepton error varance and lapsed tme snce last balance check. Results reman qualtatvely unchanged 15 Consumers can also be navely nattentve, but we don t allow t here. See dscusson n Grubb
17 1 mples that f the consumer checks her balance, then her utlty decreases by a monetary equvalence of [(1 θ t ξ ] 1 θt. We assume that χ tqt are d and follow a type I extreme value dstrbuton. If she doesn t check, she recalls her balance B t wth the percepton error η t. So her perceved balance s B t Q t B t + (1 Q t N ( B t + η t ω t,ωt 2 She forms an expected utlty based on her knowledge about the dstrbuton of her percepton error. The optmal spendng wll maxmze her expected utlty after ntegratng out the balance percepton error, whch s ˆ ˆ ( u t = (C t ; B t df (η t df B t B t η t u t 4.4 Dssatsfacton and Account Closng We assume that the consumer also has the opton of closng the account (e.g., an outsde opton. If she chooses to close the account, she mght swtch to other competng banks or become unbanked. Wth support from secton 3.1, we make an assumpton that consumers are senstve to the rato of the overdraft fee to the overdraft transacton amount and we useξ t to denote ths rato as a state varable. We assume that the hgher the rato, the more lkely t s that the consumer wll be dssatsfed to close the account because the forwardlookng consumer antcpates that she s gong to accumulate more dssatsfacton (as well as lost consumpton utlty due to overdrafts n the future so that t s not benefcal for her to keep the account open any more. Furthermore, we assume that consumers keep updatng her belef of the rato and only remembers the hghest rato that has ever ncurred. That s f we use t to denote the perperod rato then and t = OD t B t C t E [Ξ t+1 Ξ t ] = max(ξ t, t. Ths assumpton reflects a consumer s learnng behavor over tme n the sense that after experencng many overdrafts, a consumer realzes how costly (or dssatsfed t could be for her to keep the account open. When she learns that the rato can be hgh enough so that t s not benefcal for her to keep the account open any more, she ll choose to close the account. Once she chooses to close the account, she receves an outsde opton wth a value normalzed to 0 for dentfcaton purposes 16. More specfcally, let W denote the choce to close the account, where W = 1 s closng the account and W = 0 s keepng the account open. Then the perperod utlty functon for the consumer becomes { u t ϒ t I[B t C t < 0] + ϖ t0 f W t = 0 U t = ϖ t1 f W t = 1 16 Although the outsde opton s normalzed to zero for all consumers, the mplct assumpton s that we allow for heterogeneous utlty of the outsde opton. The heterogenety s reflected by the other structural parameters, ncludng the dssatsfacton senstvty. 17
18 whereu t s defned n equaton 3. We use ϒ to model the dssatsfacton senstvty,.e., the mpact of chargng an overdraft fee on a consumer s decson to close the account. ϖ 0 and ϖ 1 are the dosyncratc shocks that determne a consumer s account closng decson. Sources of the shocks may nclude (1 the consumer moved address; (2 competng bank entered the market, and so on. We assume these shocks follow a type I extreme value dstrbuton. 4.5 State Varables and the Transton Process We have explaned the followng state varables n the model: (begnnng balance B t, ncome Y t, comng bll ψ t, lapsed tme snce last balance check Γ t, overdraft fee OD t, rato of overdraft fee to the overdraft transacton amount Ξ t, preference shock ε t, balance checkng cost shock χ t and account closure utlty shock ϖ t. The other state varable to be ntroduced later, DL t, s nvolved n the transton process. For (avalable balance B t, the transton process satsfes the consumer s budget constrant, whch s B t+1 = B t C t OD t I (B t C t < 0 +Y t+1 ψ t+1 where OD t s the overdraft fee. As we model the consumer s spendng decson at the daly level rather than transacton level, we aggregate all overdraft fees pad and assume the consumer knows the pertem fee structure stated n secton 3. Ths assumpton s realstc n our settng because we have already dstngushed between nattentve and attentve consumers. The argument that a consumer mght not be fully aware of the pertem fee s ndrectly captured by the balance percepton error n the sense that the uncertan overdraft fee s equvalent to the uncertan balance because they both tghten the consumer s budget constrant. As for the attentve consumer who overdraws because of heavy dscountng, she should be fully aware of the potental cost of overdraft. So n both cases we argue that the assumpton of a known total overdraft fee s reasonable. The state varable OD t s assumed to be d over tme and to follow a dscrete dstrbuton wth support vector and probablty vector {X, p}. The support vector contans multples of the pertem overdraft fee. Consstent wth our data, we assume an ncome dstrbuton as follows Y t = Y I (DL t = PC where Y s the stable perodc (monthly/weekly/bweekly ncome, DL t s the number of days left untl the next payday and PC s the length of the pay cycle. The transton process of DL s determnstc DL t+1 = DL t 1 + PC I (DL t = 1 where t decreases by one for each perod ahead and goes back to the full length when one pay cycle ends. The comng blls are assumed to be d draws from a compound Posson dstrbuton wth arrval rate φ and jump sze dstrbuton G, Ψ t CP(φ,G. Ths dstrbuton can capture the pattern of blls arrvng randomly accordng to a Posson process and bll szes are sums of fxed components (each separate bll. The tme snce last checkng the balance also evolves determnstcally based on the balance checkng behavor. Formally, we have 18
19 Γ t+1 = 1 + Γ t (1 Q t whch means that f the consumer checks her balance n the current perod, then the lapsed tme goes back to 1 but f she doesn t check, the lapsed tme accumulates by one more perod. The rato of the overdraft fee to the overdraft transacton amount evolves by keepng the maxmum amount over tme. E [Ξ t+1 Ξ t ] = max(ξ t, t The shocks ε t, χ t and ϖ t are all assumed to be d over tme. { } In summary, the whole state space for consumer s S t = B t,ψ t,y t,dl t,od t,γ t,ξ t,ε t, χ t,ϖ t. In our dataset, { we observe } Ŝ t = {B t,ψ t,y t,dl t,od t,γ t,ξ t } and our unobservable state varables are S t = B t,η t,ε t, χ t,ϖ t. S t = Ŝ t S t {B t,ψ t }. Notce here that consumers also have unobserved states B t and ψ t due to nattenton, whch means that the consumer doesn t know the true balance (B t or the bll amount (ψ t f she doesn t check her balance but only the perceved balance ( B t and expected bll (Ψ t. 4.6 The Dynamc Optmzaton Problem and Intertemporal Tradeoff The consumer chooses an nfnte sequence of decson rules {C t,q t,w t } t=1 n order to maxmze the expected total dscounted utlty: { where U t (C t,q t,w t ;S t =. max {C t,q t,w t } t=0 E {St } t=1 [ˆ Let V (S t denote the value functon: B t V (S t = ˆ η t U 0 (C 0,Q 0,W 0 ;S 0 + t=1 β t U t (C t,q t,w t ;S t S 0 } { } C 1 θ t ( t Q t ξ + χ tqt df (η t df B t ϒ OD t I[B t C t < 0] + ϖ t0 ](1 W t +W t ϖ t1 1 θ t B t C t max {C τ,q τ,w τ } τ=t E {{Sτ } τ=t+1} { U t (S t + τ=t+1 β τ t U τ (S τ S t } accordng to Bellman (1957, ths nfnte perod dynamc optmzaton problem can be solved through the Bellman Equaton V (S t = max C,Q,W E S t+1 {U (C,Q,W;S t + βv (S t+1 S t } (5 In the nfnte horzon dynamc programmng problem, the polcy functon doesn t depend on tme. So we can elmnate the tme subscrpt. Then we have the followng choce specfc value functon: (4 19
20 v ( C,Q,W; B,Ψ,Y,DL,OD,Γ,Ξ,ε, χ,ϖ u C (C ξ + χ 1 ϒ OD I[B C<0] B C + ϖ ( 0 ] +βe S+1 [V B +1,Ψ +1,Y +1,DL +1,OD +1,1,Ξ +1 ε +1, χ +1,ϖ +1 f Q = 1&W = 0 ( = B t η t [u C (C + χ 0 ]df (η t df B t ϒ OD I[B C<0] B C + ϖ 0 ( ] +βe S+1 [V B +1,Ψ +1,Y +1,DL +1,OD +1,Γ + 1,Ξ +1,ε +1, χ +1,ϖ +1 f Q = 0&W = 0 ϖ 1 f W = 1 (6 where subscrpt+1 denotes the next tme perod. So the optmal polcy s gven by the followng soluton {C,Q,W } = argmaxv ( C,Q,W; B,Ψ,Y,DL,OD,Γ,Ξ,ε, χ,ϖ One thng that s worth notcng s that there s a dstncton between ths dynamc programmng problem and tradtonal ones. Because of the percepton error, the consumer observes B t = B t + η t ω t but doesn t know B t or η t. She only knows the dstrbuton N(B t + η t ω t,ω 2 t. The consumer makes a decson C ( B t based on the perceved balance B t. But as researchers, we don t know the realzed percepton error η t. We observe the true balance B t and the consumer s spendng C ( B t. So we can only assume C ( B t maxmzes the expected exante value functon. Later we look for parameters such that the lkelhood for C ( B t maxmzes the expected exante value functon attans maxmum. Followng Rust (1987, we obtan the exante value functon whch ntegrates out the cost shocks, preference shocks, account closng shocks and unobserved mean balance error. ˆ EV (B,ψ,Y,DL,OD,Γ,Ξ = ϖ ˆ ˆ χ ε ˆ η v ( C,Q,W ; B,Ψ,Y,DL,OD,Γ,Ξ,ε, χ,ϖ dηdεdχdϖ Consumers ntertemporal tradeoffs are assocated wth the three dynamc decsons. Frst of all, gven the budget constrant, a consumer wll evaluate the utlty of spendng (or consumng today versus tomorrow. The hgher amount she spends today, the lower amount she can spend tomorrow. So spendng s essentally a dynamc decson and the optmal choce for the consumer s to smooth out consumpton over the tme. Second, when decdng when to check balance, the consumer wll compare the montorng cost wth the expected gan from avodng the overdraft fee. She ll only check when the expected overdraft fee s hgher than her montorng cost. As the consumer s balance percepton error mght accumulate wth tme, the consumer s overdraft probablty also ncreases wth the lapse tme snce the last balance check. As a result, the consumer wll wat untl the overdraft probablty reaches the certan threshold (when the expected overdraft fee equals the montorng cost to check the balance. Fnally, the decson to close the account s an optmal stoppng problem. The consumer wll compare the total dscounted utlty of keepng the account wth the utlty from the outsde opton to decde when to close the account. When expectng too much overdraft fees as well as the accompaned dssatsfacton, the consumer wll fnd t more attractve to take the outsde opton and close the account. 20
Overhaul Overdraft Fees: Creating Pricing and Product Design Strategies with Big Data
Overhaul Overdraft Fees: Creatng Prcng and Product Desgn Strateges wth Bg Data Xao Lu, Alan Montgomery, Kannan Srnvasan October 12, 2014 Abstract In 2012, consumers pad an enormous $32 bllon overdraft
More informationAn Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationChapter 4 Financial Markets
Chapter 4 Fnancal Markets ECON2123 (Sprng 2012) 14 & 15.3.2012 (Tutoral 5) The demand for money Assumptons: There are only two assets n the fnancal market: money and bonds Prce s fxed and s gven, that
More informationThe OC Curve of Attribute Acceptance Plans
The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4
More informationbenefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationCan Auto Liability Insurance Purchases Signal Risk Attitude?
Internatonal Journal of Busness and Economcs, 2011, Vol. 10, No. 2, 159164 Can Auto Lablty Insurance Purchases Sgnal Rsk Atttude? ChuShu L Department of Internatonal Busness, Asa Unversty, Tawan ShengChang
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 MultpleChoce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multplechoce questons. For each queston, only one of the answers s correct.
More information9.1 The Cumulative Sum Control Chart
Learnng Objectves 9.1 The Cumulatve Sum Control Chart 9.1.1 Basc Prncples: Cusum Control Chart for Montorng the Process Mean If s the target for the process mean, then the cumulatve sum control chart s
More informationSmall pots lump sum payment instruction
For customers Small pots lump sum payment nstructon Please read these notes before completng ths nstructon About ths nstructon Use ths nstructon f you re an ndvdual wth Aegon Retrement Choces Self Invested
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMISP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationWhen Talk is Free : The Effect of Tariff Structure on Usage under Two and ThreePart Tariffs
0 When Talk s Free : The Effect of Tarff Structure on Usage under Two and ThreePart Tarffs Eva Ascarza Ana Lambrecht Naufel Vlcassm July 2012 (Forthcomng at Journal of Marketng Research) Eva Ascarza
More informationCommunication Networks II Contents
8 / 1  Communcaton Networs II (Görg)  www.comnets.unbremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP
More informationDO LOSS FIRMS MANAGE EARNINGS AROUND SEASONED EQUITY OFFERINGS?
DO LOSS FIRMS MANAGE EARNINGS AROUND SEASONED EQUITY OFFERINGS? Fernando Comran, Unversty of San Francsco, School of Management, 2130 Fulton Street, CA 94117, Unted States, fcomran@usfca.edu Tatana Fedyk,
More informationSimple Interest Loans (Section 5.1) :
Chapter 5 Fnance The frst part of ths revew wll explan the dfferent nterest and nvestment equatons you learned n secton 5.1 through 5.4 of your textbook and go through several examples. The second part
More informationChapter 11 Practice Problems Answers
Chapter 11 Practce Problems Answers 1. Would you be more wllng to lend to a frend f she put all of her lfe savngs nto her busness than you would f she had not done so? Why? Ths problem s ntended to make
More informationNasdaq Iceland Bond Indices 01 April 2015
Nasdaq Iceland Bond Indces 01 Aprl 2015 Fxed duraton Indces Introducton Nasdaq Iceland (the Exchange) began calculatng ts current bond ndces n the begnnng of 2005. They were a response to recent changes
More informationForecasting the Direction and Strength of Stock Market Movement
Forecastng the Drecton and Strength of Stock Market Movement Jngwe Chen Mng Chen Nan Ye cjngwe@stanford.edu mchen5@stanford.edu nanye@stanford.edu Abstract  Stock market s one of the most complcated systems
More informationWhat is Candidate Sampling
What s Canddate Samplng Say we have a multclass or mult label problem where each tranng example ( x, T ) conssts of a context x a small (mult)set of target classes T out of a large unverse L of possble
More informationOn the Optimal Control of a Cascade of HydroElectric Power Stations
On the Optmal Control of a Cascade of HydroElectrc Power Statons M.C.M. Guedes a, A.F. Rbero a, G.V. Smrnov b and S. Vlela c a Department of Mathematcs, School of Scences, Unversty of Porto, Portugal;
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationInstitute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic
Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange
More informationCredit Limit Optimization (CLO) for Credit Cards
Credt Lmt Optmzaton (CLO) for Credt Cards Vay S. Desa CSCC IX, Ednburgh September 8, 2005 Copyrght 2003, SAS Insttute Inc. All rghts reserved. SAS Propretary Agenda Background Tradtonal approaches to credt
More informationIDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS
IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS Chrs Deeley* Last revsed: September 22, 200 * Chrs Deeley s a Senor Lecturer n the School of Accountng, Charles Sturt Unversty,
More information7.5. Present Value of an Annuity. Investigate
7.5 Present Value of an Annuty Owen and Anna are approachng retrement and are puttng ther fnances n order. They have worked hard and nvested ther earnngs so that they now have a large amount of money on
More informationAn Empirical Study of Search Engine Advertising Effectiveness
An Emprcal Study of Search Engne Advertsng Effectveness Sanjog Msra, Smon School of Busness Unversty of Rochester Edeal Pnker, Smon School of Busness Unversty of Rochester Alan RmmKaufman, RmmKaufman
More informationPRIVATE SCHOOL CHOICE: THE EFFECTS OF RELIGIOUS AFFILIATION AND PARTICIPATION
PRIVATE SCHOOL CHOICE: THE EFFECTS OF RELIIOUS AFFILIATION AND PARTICIPATION Danny CohenZada Department of Economcs, Benuron Unversty, BeerSheva 84105, Israel Wllam Sander Department of Economcs, DePaul
More informationAn InterestOriented Network Evolution Mechanism for Online Communities
An InterestOrented Network Evoluton Mechansm for Onlne Communtes Cahong Sun and Xaopng Yang School of Informaton, Renmn Unversty of Chna, Bejng 100872, P.R. Chna {chsun,yang}@ruc.edu.cn Abstract. Onlne
More informationMultivariate EWMA Control Chart
Multvarate EWMA Control Chart Summary The Multvarate EWMA Control Chart procedure creates control charts for two or more numerc varables. Examnng the varables n a multvarate sense s extremely mportant
More informationUsing Series to Analyze Financial Situations: Present Value
2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated
More informationTHE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek
HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo
More informationRobust Design of Public Storage Warehouses. Yeming (Yale) Gong EMLYON Business School
Robust Desgn of Publc Storage Warehouses Yemng (Yale) Gong EMLYON Busness School Rene de Koster Rotterdam school of management, Erasmus Unversty Abstract We apply robust optmzaton and revenue management
More informationSection 5.4 Annuities, Present Value, and Amortization
Secton 5.4 Annutes, Present Value, and Amortzaton Present Value In Secton 5.2, we saw that the present value of A dollars at nterest rate per perod for n perods s the amount that must be deposted today
More informationCapital asset pricing model, arbitrage pricing theory and portfolio management
Captal asset prcng model, arbtrage prcng theory and portfolo management Vnod Kothar The captal asset prcng model (CAPM) s great n terms of ts understandng of rsk decomposton of rsk nto securtyspecfc rsk
More informationThe Choice of Direct Dealing or Electronic Brokerage in Foreign Exchange Trading
The Choce of Drect Dealng or Electronc Brokerage n Foregn Exchange Tradng Mchael Melvn Arzona State Unversty & Ln Wen Unversty of Redlands MARKET PARTICIPANTS: Customers Endusers Multnatonal frms Central
More information10.2 Future Value and Present Value of an Ordinary Simple Annuity
348 Chapter 10 Annutes 10.2 Future Value and Present Value of an Ordnary Smple Annuty In compound nterest, 'n' s the number of compoundng perods durng the term. In an ordnary smple annuty, payments are
More informationLecture 3: Force of Interest, Real Interest Rate, Annuity
Lecture 3: Force of Interest, Real Interest Rate, Annuty Goals: Study contnuous compoundng and force of nterest Dscuss real nterest rate Learn annutymmedate, and ts present value Study annutydue, and
More informationANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING
ANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING Matthew J. Lberatore, Department of Management and Operatons, Vllanova Unversty, Vllanova, PA 19085, 6105194390,
More informationStaff Paper. Farm Savings Accounts: Examining Income Variability, Eligibility, and Benefits. Brent Gloy, Eddy LaDue, and Charles Cuykendall
SP 200502 August 2005 Staff Paper Department of Appled Economcs and Management Cornell Unversty, Ithaca, New York 148537801 USA Farm Savngs Accounts: Examnng Income Varablty, Elgblty, and Benefts Brent
More informationWeek 6 Market Failure due to Externalities
Week 6 Market Falure due to Externaltes 1. Externaltes n externalty exsts when the acton of one agent unavodably affects the welfare of another agent. The affected agent may be a consumer, gvng rse to
More informationI. SCOPE, APPLICABILITY AND PARAMETERS Scope
D Executve Board Annex 9 Page A/R ethodologcal Tool alculaton of the number of sample plots for measurements wthn A/R D project actvtes (Verson 0) I. SOPE, PIABIITY AD PARAETERS Scope. Ths tool s applcable
More informationTrade Adjustment and Productivity in Large Crises. Online Appendix May 2013. Appendix A: Derivation of Equations for Productivity
Trade Adjustment Productvty n Large Crses Gta Gopnath Department of Economcs Harvard Unversty NBER Brent Neman Booth School of Busness Unversty of Chcago NBER Onlne Appendx May 2013 Appendx A: Dervaton
More informationInequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001.
Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.
More informationStudy on CET4 Marks in China s Graded English Teaching
Study on CET4 Marks n Chna s Graded Englsh Teachng CHE We College of Foregn Studes, Shandong Insttute of Busness and Technology, P.R.Chna, 264005 Abstract: Ths paper deploys Logt model, and decomposes
More informationCriminal Justice System on Crime *
On the Impact of the NSW Crmnal Justce System on Crme * Dr Vasls Sarafds, Dscplne of Operatons Management and Econometrcs Unversty of Sydney * Ths presentaton s based on jont work wth Rchard Kelaher 1
More informationThe Development of Web Log Mining Based on ImproveKMeans Clustering Analysis
The Development of Web Log Mnng Based on ImproveKMeans Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.
More informationCausal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting
Causal, Explanatory Forecastng Assumes causeandeffect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of
More informationKiel Institute for World Economics Duesternbrooker Weg 120 24105 Kiel (Germany) Kiel Working Paper No. 1120
Kel Insttute for World Economcs Duesternbrooker Weg 45 Kel (Germany) Kel Workng Paper No. Path Dependences n enture Captal Markets by Andrea Schertler July The responsblty for the contents of the workng
More informationSolutions to First Midterm
rofessor Chrstano Economcs 3, Wnter 2004 Solutons to Frst Mdterm. Multple Choce. 2. (a) v. (b). (c) v. (d) v. (e). (f). (g) v. (a) The goods market s n equlbrum when total demand equals total producton,.e.
More informationLecture 3: Annuity. Study annuities whose payments form a geometric progression or a arithmetic progression.
Lecture 3: Annuty Goals: Learn contnuous annuty and perpetuty. Study annutes whose payments form a geometrc progresson or a arthmetc progresson. Dscuss yeld rates. Introduce Amortzaton Suggested Textbook
More informationThe Choice of Direct Dealing or Electronic Brokerage in Foreign Exchange Trading
The Choce of Drect Dealng or Electronc Brokerage n Foregn Exchange Tradng Mchael Melvn & Ln Wen Arzona State Unversty Introducton Electronc Brokerage n Foregn Exchange Start from a base of zero n 1992
More informationUnderstanding the Impact of Marketing Actions in Traditional Channels on the Internet: Evidence from a Large Scale Field Experiment
A research and educaton ntatve at the MT Sloan School of Management Understandng the mpact of Marketng Actons n Tradtonal Channels on the nternet: Evdence from a Large Scale Feld Experment Paper 216 Erc
More informationSolution: Let i = 10% and d = 5%. By definition, the respective forces of interest on funds A and B are. i 1 + it. S A (t) = d (1 dt) 2 1. = d 1 dt.
Chapter 9 Revew problems 9.1 Interest rate measurement Example 9.1. Fund A accumulates at a smple nterest rate of 10%. Fund B accumulates at a smple dscount rate of 5%. Fnd the pont n tme at whch the forces
More informationNumber of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000
Problem Set 5 Solutons 1 MIT s consderng buldng a new car park near Kendall Square. o unversty funds are avalable (overhead rates are under pressure and the new faclty would have to pay for tself from
More informationAwellknown result in the Bayesian inventory management literature is: If lost sales are not observed, the
MANUFACTURING & SERVICE OPERATIONS MANAGEMENT Vol. 10, No. 2, Sprng 2008, pp. 236 256 ssn 15234614 essn 15265498 08 1002 0236 nforms do 10.1287/msom.1070.0165 2008 INFORMS Dynamc Inventory Management
More informationIntrayear Cash Flow Patterns: A Simple Solution for an Unnecessary Appraisal Error
Intrayear Cash Flow Patterns: A Smple Soluton for an Unnecessary Apprasal Error By C. Donald Wggns (Professor of Accountng and Fnance, the Unversty of North Florda), B. Perry Woodsde (Assocate Professor
More information1. Math 210 Finite Mathematics
1. ath 210 Fnte athematcs Chapter 5.2 and 5.3 Annutes ortgages Amortzaton Professor Rchard Blecksmth Dept. of athematcal Scences Northern Illnos Unversty ath 210 Webste: http://math.nu.edu/courses/math210
More informationTime Value of Money Module
Tme Value of Money Module O BJECTIVES After readng ths Module, you wll be able to: Understand smple nterest and compound nterest. 2 Compute and use the future value of a sngle sum. 3 Compute and use the
More informationFinancial Mathemetics
Fnancal Mathemetcs 15 Mathematcs Grade 12 Teacher Gude Fnancal Maths Seres Overvew In ths seres we am to show how Mathematcs can be used to support personal fnancal decsons. In ths seres we jon Tebogo,
More informationFeature selection for intrusion detection. Slobodan Petrović NISlab, Gjøvik University College
Feature selecton for ntruson detecton Slobodan Petrovć NISlab, Gjøvk Unversty College Contents The feature selecton problem Intruson detecton Traffc features relevant for IDS The CFS measure The mrmr measure
More informationECONOMICS OF PLANT ENERGY SAVINGS PROJECTS IN A CHANGING MARKET Douglas C White Emerson Process Management
ECONOMICS OF PLANT ENERGY SAVINGS PROJECTS IN A CHANGING MARKET Douglas C Whte Emerson Process Management Abstract Energy prces have exhbted sgnfcant volatlty n recent years. For example, natural gas prces
More informationDescribing Communities. Species Diversity Concepts. Species Richness. Species Richness. SpeciesArea Curve. SpeciesArea Curve
peces versty Concepts peces Rchness pecesarea Curves versty Indces  mpson's Index  hannonwener Index  rlloun Index peces Abundance Models escrbng Communtes There are two mportant descrptors of a communty:
More informationOnLine Fault Detection in Wind Turbine Transmission System using Adaptive Filter and Robust Statistical Features
OnLne Fault Detecton n Wnd Turbne Transmsson System usng Adaptve Flter and Robust Statstcal Features Ruoyu L Remote Dagnostcs Center SKF USA Inc. 3443 N. Sam Houston Pkwy., Houston TX 77086 Emal: ruoyu.l@skf.com
More informationStress test for measuring insurance risks in nonlife insurance
PROMEMORIA Datum June 01 Fnansnspektonen Författare Bengt von Bahr, Younes Elonq and Erk Elvers Stress test for measurng nsurance rsks n nonlfe nsurance Summary Ths memo descrbes stress testng of nsurance
More informationCourse outline. Financial Time Series Analysis. Overview. Data analysis. Predictive signal. Trading strategy
Fnancal Tme Seres Analyss Patrck McSharry patrck@mcsharry.net www.mcsharry.net Trnty Term 2014 Mathematcal Insttute Unversty of Oxford Course outlne 1. Data analyss, probablty, correlatons, vsualsaton
More informationHealth Insurance and Household Savings
Health Insurance and Household Savngs Mnchung Hsu Job Market Paper Last Updated: November, 2006 Abstract Recent emprcal studes have documented a puzzlng pattern of household savngs n the U.S.: households
More informationSPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background:
SPEE Recommended Evaluaton Practce #6 efnton of eclne Curve Parameters Background: The producton hstores of ol and gas wells can be analyzed to estmate reserves and future ol and gas producton rates and
More informationThis study examines whether the framing mode (narrow versus broad) influences the stock investment decisions
MANAGEMENT SCIENCE Vol. 54, No. 6, June 2008, pp. 1052 1064 ssn 00251909 essn 15265501 08 5406 1052 nforms do 10.1287/mnsc.1070.0845 2008 INFORMS How Do Decson Frames Influence the Stock Investment Choces
More informationSearching and Switching: Empirical estimates of consumer behaviour in regulated markets
Searchng and Swtchng: Emprcal estmates of consumer behavour n regulated markets Catherne Waddams Prce Centre for Competton Polcy, Unversty of East Angla Catherne Webster Centre for Competton Polcy, Unversty
More informationQuestions that we may have about the variables
Antono Olmos, 01 Multple Regresson Problem: we want to determne the effect of Desre for control, Famly support, Number of frends, and Score on the BDI test on Perceved Support of Latno women. Dependent
More informationGender differences in revealed risk taking: evidence from mutual fund investors
Economcs Letters 76 (2002) 151 158 www.elsever.com/ locate/ econbase Gender dfferences n revealed rsk takng: evdence from mutual fund nvestors a b c, * Peggy D. Dwyer, James H. Glkeson, John A. Lst a Unversty
More informationApplication of Quasi Monte Carlo methods and Global Sensitivity Analysis in finance
Applcaton of Quas Monte Carlo methods and Global Senstvty Analyss n fnance Serge Kucherenko, Nlay Shah Imperal College London, UK skucherenko@mperalacuk Daro Czraky Barclays Captal DaroCzraky@barclayscaptalcom
More informationPortfolio Loss Distribution
Portfolo Loss Dstrbuton Rsky assets n loan ortfolo hghly llqud assets holdtomaturty n the bank s balance sheet Outstandngs The orton of the bank asset that has already been extended to borrowers. Commtment
More informationDISCLOSURES I. ELECTRONIC FUND TRANSFER DISCLOSURE (REGULATION E)... 2 ELECTRONIC DISCLOSURE AND ELECTRONIC SIGNATURE CONSENT... 7
DISCLOSURES The Dsclosures set forth below may affect the accounts you have selected wth Bank Leum USA. Read these dsclosures carefully as they descrbe your rghts and oblgatons for the accounts and/or
More informationHollinger Canadian Publishing Holdings Co. ( HCPH ) proceeding under the Companies Creditors Arrangement Act ( CCAA )
February 17, 2011 Andrew J. Hatnay ahatnay@kmlaw.ca Dear Sr/Madam: Re: Re: Hollnger Canadan Publshng Holdngs Co. ( HCPH ) proceedng under the Companes Credtors Arrangement Act ( CCAA ) Update on CCAA Proceedngs
More informationCHAPTER 14 MORE ABOUT REGRESSION
CHAPTER 14 MORE ABOUT REGRESSION We learned n Chapter 5 that often a straght lne descrbes the pattern of a relatonshp between two quanttatve varables. For nstance, n Example 5.1 we explored the relatonshp
More informationStatistical Methods to Develop Rating Models
Statstcal Methods to Develop Ratng Models [Evelyn Hayden and Danel Porath, Österrechsche Natonalbank and Unversty of Appled Scences at Manz] Source: The Basel II Rsk Parameters Estmaton, Valdaton, and
More informationTrafficlight a stress test for life insurance provisions
MEMORANDUM Date 006097 Authors Bengt von Bahr, Göran Ronge Traffclght a stress test for lfe nsurance provsons Fnansnspetonen P.O. Box 6750 SE113 85 Stocholm [Sveavägen 167] Tel +46 8 787 80 00 Fax
More informationStudent Performance in Online Quizzes as a Function of Time in Undergraduate Financial Management Courses
Student Performance n Onlne Quzzes as a Functon of Tme n Undergraduate Fnancal Management Courses Olver Schnusenberg The Unversty of North Florda ABSTRACT An nterestng research queston n lght of recent
More informationUncrystallised funds pension lump sum payment instruction
For customers Uncrystallsed funds penson lump sum payment nstructon Don t complete ths form f your wrapper s derved from a penson credt receved followng a dvorce where your ex spouse or cvl partner had
More informationTime Value of Money. Types of Interest. Compounding and Discounting Single Sums. Page 1. Ch. 6  The Time Value of Money. The Time Value of Money
Ch. 6  The Tme Value of Money Tme Value of Money The Interest Rate Smple Interest Compound Interest Amortzng a Loan FIN21 Ahmed Y, Dasht TIME VALUE OF MONEY OR DISCOUNTED CASH FLOW ANALYSIS Very Important
More informationFinite Math Chapter 10: Study Guide and Solution to Problems
Fnte Math Chapter 10: Study Gude and Soluton to Problems Basc Formulas and Concepts 10.1 Interest Basc Concepts Interest A fee a bank pays you for money you depost nto a savngs account. Prncpal P The amount
More informationA Model of Private Equity Fund Compensation
A Model of Prvate Equty Fund Compensaton Wonho Wlson Cho Andrew Metrck Ayako Yasuda KAIST Yale School of Management Unversty of Calforna at Davs June 26, 2011 Abstract: Ths paper analyzes the economcs
More informationPSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 12
14 The Chsquared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More informationThursday, December 10, 2009 Noon  1:50 pm Faraday 143
1. ath 210 Fnte athematcs Chapter 5.2 and 4.3 Annutes ortgages Amortzaton Professor Rchard Blecksmth Dept. of athematcal Scences Northern Illnos Unversty ath 210 Webste: http://math.nu.edu/courses/math210
More informationLIFETIME INCOME OPTIONS
LIFETIME INCOME OPTIONS May 2011 by: Marca S. Wagner, Esq. The Wagner Law Group A Professonal Corporaton 99 Summer Street, 13 th Floor Boston, MA 02110 Tel: (617) 3575200 Fax: (617) 3575250 www.ersalawyers.com
More informationExhaustive Regression. An Exploration of RegressionBased Data Mining Techniques Using Super Computation
Exhaustve Regresson An Exploraton of RegressonBased Data Mnng Technques Usng Super Computaton Antony Daves, Ph.D. Assocate Professor of Economcs Duquesne Unversty Pttsburgh, PA 58 Research Fellow The
More informationMARKET SHARE CONSTRAINTS AND THE LOSS FUNCTION IN CHOICE BASED CONJOINT ANALYSIS
MARKET SHARE CONSTRAINTS AND THE LOSS FUNCTION IN CHOICE BASED CONJOINT ANALYSIS Tmothy J. Glbrde Assstant Professor of Marketng 315 Mendoza College of Busness Unversty of Notre Dame Notre Dame, IN 46556
More informationTHE EFFECT OF PREPAYMENT PENALTIES ON THE PRICING OF SUBPRIME MORTGAGES
THE EFFECT OF PREPAYMENT PENALTIES ON THE PRICING OF SUBPRIME MORTGAGES Gregory Ellehausen, Fnancal Servces Research Program George Washngton Unversty Mchael E. Staten, Fnancal Servces Research Program
More informationHOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA*
HOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA* Luísa Farnha** 1. INTRODUCTION The rapd growth n Portuguese households ndebtedness n the past few years ncreased the concerns that debt
More informationThe Current Employment Statistics (CES) survey,
Busness Brths and Deaths Impact of busness brths and deaths n the payroll survey The CES probabltybased sample redesgn accounts for most busness brth employment through the mputaton of busness deaths,
More informationScale Dependence of Overconfidence in Stock Market Volatility Forecasts
Scale Dependence of Overconfdence n Stoc Maret Volatlty Forecasts Marus Glaser, Thomas Langer, Jens Reynders, Martn Weber* June 7, 007 Abstract In ths study, we analyze whether volatlty forecasts (judgmental
More informationReturn decomposing of absoluteperformance multiasset class portfolios. Working Paper  Nummer: 16
Return decomposng of absoluteperformance multasset class portfolos Workng Paper  Nummer: 16 2007 by Dr. Stefan J. Illmer und Wolfgang Marty; n: Fnancal Markets and Portfolo Management; March 2007; Volume
More informationIn some supply chains, materials are ordered periodically according to local information. This paper investigates
MANUFACTURING & SRVIC OPRATIONS MANAGMNT Vol. 12, No. 3, Summer 2010, pp. 430 448 ssn 15234614 essn 15265498 10 1203 0430 nforms do 10.1287/msom.1090.0277 2010 INFORMS Improvng Supply Chan Performance:
More informationStudy on Model of Risks Assessment of Standard Operation in Rural Power Network
Study on Model of Rsks Assessment of Standard Operaton n Rural Power Network Qngj L 1, Tao Yang 2 1 Qngj L, College of Informaton and Electrcal Engneerng, Shenyang Agrculture Unversty, Shenyang 110866,
More informationChapter 7. RandomVariate Generation 7.1. Prof. Dr. Mesut Güneş Ch. 7 RandomVariate Generation
Chapter 7 RandomVarate Generaton 7. Contents Inversetransform Technque AcceptanceRejecton Technque Specal Propertes 7. Purpose & Overvew Develop understandng of generatng samples from a specfed dstrbuton
More informationA Computer Technique for Solving LP Problems with Bounded Variables
Dhaka Unv. J. Sc. 60(2): 163168, 2012 (July) A Computer Technque for Solvng LP Problems wth Bounded Varables S. M. Atqur Rahman Chowdhury * and Sanwar Uddn Ahmad Department of Mathematcs; Unversty of
More informationTHE DETERMINANTS OF THE TUNISIAN BANKING INDUSTRY PROFITABILITY: PANEL EVIDENCE
THE DETERMINANTS OF THE TUNISIAN BANKING INDUSTRY PROFITABILITY: PANEL EVIDENCE Samy Ben Naceur ERF Research Fellow Department of Fnance Unversté Lbre de Tuns Avenue Khéreddne Pacha, 002 Tuns Emal : sbennaceur@eudoramal.com
More informationThe Shortterm and Longterm Market
A Presentaton on Market Effcences to Northfeld Informaton Servces Annual Conference he Shortterm and Longterm Market Effcences en Post Offce Square Boston, MA 0209 www.acadanasset.com Charles H. Wang,
More informationCapacity Reservation for TimeSensitive Service Providers: An Application in Seaport Management
Capacty Reservaton for TmeSenstve Servce Provders: An Applcaton n Seaport Management L. Jeff Hong Department of Industral Engneerng and Logstcs Management The Hong Kong Unversty of Scence and Technology
More information