scispace - formally typeset
Search or ask a question

Showing papers on "Credit risk published in 2010"


Reference EntryDOI
15 May 2010
TL;DR: Merton's most notable works include the intertemporal capital asset pricing model, the Black-Scholes-Merton option pricing formula, and the Merton structural model for credit risk.
Abstract: Robert C Merton is John and Natty McArthur University Professor at Harvard Business School He shared the Nobel Prize in Economic Sciences in 1997 He introduced Ito calculus to finance and economics and made significant contributions in asset pricing, corporate finance, empirical finance, and financial systems His most notable works include the intertemporal capital asset pricing model, the Black–Scholes–Merton option pricing formula, the Merton jump-diffusion model, and the Merton structural model for credit risk Keywords: Robert Merton; continuous-time finance; intertemporal capital asset pricing model; derivatives; options; Merton model; credit risk; institutions; financial systems

1,715 citations


Posted Content
TL;DR: In this article, the authors provide a model of competition among credit ratings Agencies (CRAs) in which there are three possible sources of conflicts: 1) the CRA conflict of interest of understating credit risk to attract more business; 2) the ability of issuers to purchase only the most favorable ratings; and 3) the trusting nature of some investor clienteles who may take ratings at face value.
Abstract: The collapse of so many AAA-rated structured finance products in 2007-2008 has brought renewed attention to the causes of ratings failures and the conflicts of interest in the Credit Ratings Industry. We provide a model of competition among Credit Ratings Agencies (CRAs) in which there are three possible sources of conflicts: 1) the CRA conflict of interest of understating credit risk to attract more business; 2) the ability of issuers to purchase only the most favorable ratings; and 3) the trusting nature of some investor clienteles who may take ratings at face value. We show that when combined, these give rise to three fundamental equilibrium distortions. First, competition among CRAs can reduce market efficiency, as competition facilitates ratings shopping by issuers. Second, CRAs are more prone to inflate ratings in boom times, when there are more trusting investors, and when the risks of failure which could damage CRA reputation are lower. Third, the industry practice of tranching of structured products distorts market efficiency as its role is to deceive trusting investors. We argue that regulatory intervention requiring: i) upfront payments for rating services (before CRAs propose a rating to the issuer), ii) mandatory disclosure of any rating produced by CRAs, and iii) oversight of ratings methodology can substantially mitigate ratings inflation and promote efficiency.

749 citations


Journal ArticleDOI
TL;DR: In this paper, the relative financial strength of Islamic banks is assessed empirically based on evidence covering individual Islamic and commercial banks in 19 banking systems with a substantial presence of Islamic banking.
Abstract: The relative financial strength of Islamic banks is assessed empirically based on evidence covering individual Islamic and commercial banks in 19 banking systems with a substantial presence of Islamic banking. We find that (a) small Islamic banks tend to be financially stronger than small commercial banks; (b) large commercial banks tend to be financially stronger than large Islamic banks; and (c) small Islamic banks tend to be financially stronger than large Islamic banks, which may reflect challenges of credit risk management in large Islamic banks. We also find that the market share of Islamic banks does not have a significant impact on the financial strength of other banks.

568 citations


Journal ArticleDOI
TL;DR: In this article, the authors used a unique dataset to study how firms managed liquidity during the 2008-09 financial crisis and found that companies substitute between credit lines and internal liquidity (cash and profits) when facing a severe credit shortage.
Abstract: This paper uses a unique dataset to study how firms managed liquidity during the 2008-09 financial crisis. Our analysis provides new insights on interactions between internal liquidity, external funds, and real corporate decisions, such as investment and employment. We first describe how companies used credit lines during the crisis (access, size of facilities, and drawdown activity), the characteristics of these facilities (fees, markups, maturity, and collateral), and whether managers had difficulties in renewing or initiating lines. We also describe the dynamics of credit line violations and the outcome of subsequent renegotiations. We show how companies substitute between credit lines and internal liquidity (cash and profits) when facing a severe credit shortage. Looking at real-side decisions, we find that credit lines are associated with greater spending when companies are not cash-strapped. Firms with limited access to credit lines, on the other hand, appear to choose between saving and investing during the crisis. Our evidence indicates that credit lines eased the impact of the financial crisis on corporate spending.

546 citations


01 Nov 2010
TL;DR: In this article, a dynamic capital structure model that demonstrates how business-cycle variations in expected growth rates, economic uncertainty, and risk premia influence firms' financing and default policies is presented.
Abstract: I build a dynamic capital structure model that demonstrates how business-cycle variations in expected growth rates, economic uncertainty, and risk premia influence firms' financing and default policies. Countercyclical fluctuations in risk prices, default probabilities, and default losses arise endogenously through firms' responses to the macroeconomic conditions. These comovements generate large credit risk premia for investment grade firms, which helps address the "credit spread puzzle" and "under-leverage puzzle" in a unified framework. The model generates interesting dynamics for financing and defaults, including "credit contagion" and market timing of debt issuance. It also provides a novel procedure to estimate state-dependent default losses.

514 citations


Journal ArticleDOI
TL;DR: In this paper, the authors identify an important channel through which excess control rights affect firm value and find that the cost of debt financing is significantly higher for companies with a wider divergence between the largest ultimate owner's control rights and cash-flow rights.
Abstract: This article identifies an important channel through which excess control rights affect firm value. Using a new, hand-collected data set on corporate ownership and control of 3,468 firms in 22 countries during the 1996–2008 period, we find that the cost of debt financing is significantly higher for companies with a wider divergence between the largest ultimate owner’s control rights and cash-flow rights and investigate factors that affect this relation. Our results suggest that potential tunneling and other moral hazard activities by large shareholders are facilitated by their excess control rights. These activities increase the monitoring costs and the credit risk faced by banks and, in turn, raise the cost of debt for the borrower.

456 citations


Journal ArticleDOI
TL;DR: This paper applied machine learning techniques to construct nonlinear nonparametric forecasting models of consumer credit risk, which significantly improved the classification rates of credit-card-holder delinquencies and defaults with linear regression R-squared's of forecasted/realized delinquencies of 85%.
Abstract: We apply machine-learning techniques to construct nonlinear nonparametric forecasting models of consumer credit risk. By combining customer transactions and credit bureau data from January 2005 to April 2009 for a sample of a major commercial bank's customers, we are able to construct out-of-sample forecasts that significantly improve the classification rates of credit-card-holder delinquencies and defaults, with linear regression R-squared's of forecasted/realized delinquencies of 85%. Using conservative assumptions for the costs and benefits of cutting credit lines based on machine-learning forecasts, we estimate the cost savings to range from 6% to 25% of total losses. Moreover, the time-series patterns of estimated delinquency rates from this model over the course of the recent financial crisis suggests that aggregated consumer-credit risk analytics may have important applications in forecasting systemic risk.

428 citations


Journal ArticleDOI
TL;DR: In this paper, a dynamic capital structure model that demonstrates how business cycle variation in expected growth rates, economic uncertainty, and risk premia influences firms' financing policies is presented. But the model is not suitable for the analysis of credit spreads.
Abstract: I build a dynamic capital structure model that demonstrates how business cycle variation in expected growth rates, economic uncertainty, and risk premia influences firms' financing policies. Countercyclical fluctuations in risk prices, default probabilities, and default losses arise endogenously through firms' responses to macroeconomic conditions. These comovements generate large credit risk premia for investment grade firms, which helps address the credit spread puzzle and the under-leverage puzzle in a unified framework. The model generates interesting dynamics for financing and defaults, including market timing in debt issuance and credit contagion. It also provides a novel procedure to estimate state-dependent default losses.

425 citations


Journal ArticleDOI
TL;DR: This article applied machine learning techniques to construct nonlinear nonparametric forecasting models of consumer credit risk, which significantly improved the classification rates of credit-card-holder delinquencies and defaults, with linear regression R2's of forecasted/realized delinquencies of 85%.
Abstract: We apply machine-learning techniques to construct nonlinear nonparametric forecasting models of consumer credit risk. By combining customer transactions and credit bureau data from January 2005 to April 2009 for a sample of a major commercial bank’s customers, we are able to construct out-of-sample forecasts that significantly improve the classification rates of credit-card-holder delinquencies and defaults, with linear regression R2’s of forecasted/realized delinquencies of 85%. Using conservative assumptions for the costs and benefits of cutting credit lines based on machine-learning forecasts, we estimate the cost savings to range from 6% to 25% of total losses. Moreover, the time-series patterns of estimated delinquency rates from this model over the course of the recent financial crisis suggest that aggregated consumer credit-risk analytics may have important applications in forecasting systemic risk.

390 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigate whether loan growth affects the riskiness of individual banks in 16 major countries using bankscope data from more than 16,000 individual banks during 1997-2007.
Abstract: We investigate whether loan growth affects the riskiness of individual banks in 16 major countries. Using Bankscope data from more than 16,000 individual banks during 1997-2007, we test three hypotheses on the relation between abnormal loan growth and asset risk, bank profitability, and bank solvency. We find that loan growth leads to an increase in loan loss provisions during the subsequent three years, to a decrease in relative interest income, and to lower capital ratios. Further analyses show that loan growth also has a negative impact on the risk-adjusted interest income. These results suggest that loan growth represents an important driver of the riskiness of banks.

346 citations


Journal ArticleDOI
TL;DR: In this paper, the role of supply and demand factors in credit developments, with a focus on the sharp slowdown of 2008-09, was analyzed. But the authors did not consider the effect of supply factors on the growth of lending to firms.
Abstract: This paper combines qualitative information from the Eurosystem Bank Lending Survey with micro-data on loan prices and quantities for the participating Italian banks to assess the role of supply and demand factors in credit developments, with a focus on the sharp slowdown of 2008-09. Both demand and supply have played a relevant role, especially for lending to enterprises, in the whole sample period and during the financial crisis. A counterfactual exercise shows that the effect of supply factors on the growth of lending to firms was strongest after the Lehman collapse. On average, over the crisis period (2007q3-2009q4) the negative effect on the annualized quarter-on-quarter growth rate of the panel banks’ lending to enterprises can be estimated in a range of 2.2 to 3.1 percentage points, depending on the specification. About one fourth of the total supply effect can be attributed to costs related to the banks’ balance sheet position, the rest to their perception of credit risk.

Journal ArticleDOI
TL;DR: This article investigated the effects of macroeconomic fundamentals on emerging market sovereign credit spreads and found that the volatility of terms of trade in particular has a statistically and economically significant effect on spreads, even controlling for global factors and credit ratings.
Abstract: This paper investigates the effects of macroeconomic fundamentals on emerging market sovereign credit spreads. We find that the volatility of terms of trade in particular has a statistically and economically significant effect on spreads. This is robust to instrumenting terms of trade with a country-specific commodity price index. Our measures of country fundamentals have substantial explanatory power, even controlling for global factors and credit ratings. We also estimate default probabilities in a hazard model and find that model implied spreads capture a significant part of the variation in observed spreads out-of-sample. The fit is better for lower credit quality borrowers.

Posted Content
TL;DR: This paper studied the determinants of euro area sovereign bond spreads since the introduction of the euro and found that an aggregate risk factor is a main driver of spreads, both directly and indirectly by interacting with the size and structure of national banking sectors, suggesting that financial markets perceive a larger risk that governments will have to rescue banks, increasing public debt and therefore sovereign risk.
Abstract: We study the determinants of euro area sovereign bond spreads since the introduction of the euro. An aggregate risk factor is a main driver of spreads, both directly and indirectly by interacting with the size and structure of national banking sectors. When aggregate risk increases, countries with large banking sectors with low equity ratios experience greater widening in yield spreads, suggesting that financial markets perceive a larger risk that governments will have to rescue banks, increasing public debt and therefore sovereign risk. Moreover, government debt levels and forecasts of future fiscal deficits are also significant determinants of sovereign spreads.

Posted Content
TL;DR: This paper explored how much of these large movements reflected shifts in (i) global risk aversion (ii) country-specific risks, directly from worsening fundamentals, or indirectly from spillovers originating in other sovereigns.
Abstract: Over the past year, euro area sovereign spreads have exhibited an unprecedented degree of volatility. This paper explores how much of these large movements reflected shifts in (i) global risk aversion (ii) country-specific risks, directly from worsening fundamentals, or indirectly from spillovers originating in other sovereigns. The analysis shows that earlier in the crisis, the surge in global risk aversion was a significant factor influencing sovereign spreads, while recently country-specific factors have started playing a more important role. The perceived source of contagion itself has changed: previously, it could be found among those sovereigns hit hard by the financial crisis, such as Austria, the Netherlands, and Ireland, whereas lately the countries putting pressure on euro area government bonds have been primarily Greece, Portugal, and Spain, as the emphasis has shifted towards short-term refinancing risk and long-term fiscal sustainability. The paper concludes that debt sustainability and appropriate management of sovereign balance sheets are necessary conditions for preventing sovereign risk from feeding back into broader financial stability concerns.

Journal ArticleDOI
TL;DR: In this paper, the authors find evidence of a bank lending channel operating in the euro area via bank risk and show that banks characterized by lower expected default frequency are able to offer a larger amount of credit and to better insulate their loan supply from monetary policy changes.

Journal ArticleDOI
TL;DR: In this article, the determinants of credit default swap spread changes for a large sample of US non-financial companies over the period between January 2002 and March 2009 were analyzed using variables that the literature has found have an impact on CDS spreads and, in order to account for possible non-linear effects, the theoretical CDS spread predicted by the Merton model.
Abstract: This paper analyzes the determinants of credit default swap spread changes for a large sample of US non-financial companies over the period between January 2002 and March 2009. In our analysis we use variables that the literature has found have an impact on CDS spreads and, in order to account for possible non-linear effects, the theoretical CDS spreads predicted by the Merton model. We show that our set of variables is able to explain more than 50% of CDS spread variations both before and after July 2007, when the current financial turmoil began. We also document that since the onset of the crisis CDS spreads have become much more sensitive to the level of leverage while volatility has lost its importance. Using a principal component analysis we also show that since the beginning of the crisis CDS spread changes have been increasingly driven by a common factor, which cannot be explained by indicators of economic activity, uncertainty, and risk aversion.

Posted Content
TL;DR: This article showed that firms with high exposure to systematic risk have a higher ratio of cash to credit lines and face higher spreads on their lines and that exposure to undrawn credit lines increases bank specific risks in times of high aggregate volatility.
Abstract: We model corporate liquidity policy and show that aggregate risk exposure is a key determinant of how firms choose between cash and bank credit lines. Banks create liquidity for firms by pooling their idiosyncratic risks. As a result, firms with high aggregate risk find it costly to get credit lines and opt for cash in spite of higher opportunity costs and liquidity premium. Likewise, in times when aggregate risk is high, firms rely more on cash than on credit lines. We verify these predictions empirically. Cross-sectional analyses show that firms with high exposure to systematic risk have a higher ratio of cash to credit lines and face higher spreads on their lines. Time-series analyses show that firms' cash reserves rise in times of high aggregate volatility and in such times credit lines initiations fall, their spreads widen, and maturities shorten. Also consistent with the mechanism in the model, we find that exposure to undrawn credit lines increases bank-specific risks in times of high aggregate volatility.

Journal ArticleDOI
TL;DR: In this paper, the authors used a novel and unique dataset on almost 30,000 supplier contracts for 56 large buyers and more than 24,000 suppliers in Europe and North America and found that the largest and most creditworthy buyers receive contracts with the longest maturities, as measured by net days, from smaller, investment grade suppliers.
Abstract: This paper provides new evidence on the unique role of trade credit and contracting terms as a way for both sellers and buyers to mange business risk The authors use a novel and unique dataset on almost 30,000 supplier contracts for 56 large buyers and more than 24,000 suppliers in Europe and North America The sample of buyers and suppliers includes firms of varying size, investment grade, and sectors The paper finds evidence in support of four important, and not mutually exclusive, reasons for trade credit: 1) as a method of financing; 2) as a means of price discrimination; 3) as a bond assuring buyers of product quality; and 4) as a screening mechanism to gauge buyer default risk In particular, the analysis finds that the largest and most creditworthy buyers receive contracts with the longest maturities, as measured by net days, from smaller, investment grade suppliers In comparison, early payment discounts seem to be used as a risk management tool to limit the potential nonpayment risk of trade credit Early payment discounts are generally offered to smaller, non-investment grade buyers The results suggest that contract terms are jointly determined by supplier and buyer characteristics

Journal ArticleDOI
TL;DR: In this paper, credit ratings on subprime and Alt-A mortgage-backed-securities (MBS) deals issued between 2001 and 2007, the period leading up to the subprime crisis were studied.
Abstract: We study credit ratings on subprime and Alt-A mortgage-backed-securities (MBS) deals issued between 2001 and 2007, the period leading up to the subprime crisis. The fraction of highly rated securities in each deal is decreasing in mortgage credit risk (measured either ex ante or ex post), suggesting that ratings contain useful information for investors. However, we also find evidence of significant time variation in risk-adjusted credit ratings, including a progressive decline in standards around the MBS market peak between the start of 2005 and mid-2007. Conditional on initial ratings, we observe underperformance (high mortgage defaults and losses and large rating downgrades) among deals with observably higher risk mortgages based on a simple ex ante model and deals with a high fraction of opaque low-documentation loans. These findings hold over the entire sample period, not just for deal cohorts most affected by the crisis.

Journal ArticleDOI
TL;DR: The authors empirically examined the impact of the interaction between market and default risk on corporate credit spreads using credit default swap (CDS) spreads, and found that average credit spreads decrease in GDP growth rate, but increase in nominal GDP growth volatility and jump risk in the equity market.
Abstract: This study empirically examines the impact of the interaction between market and default risk on corporate credit spreads. Using credit default swap (CDS) spreads, we find that average credit spreads decrease in GDP growth rate, but increase in GDP growth volatility and jump risk in the equity market. At the market level, investor sentiment is the most important determinant of credit spreads. At the firm level, credit spreads generally rise with cash flow volatility and beta, with the effect of cash flow beta varying with market conditions. We identify implied volatility as the most significant determinant of default risk among firm-level characteristics. Overall, a major portion of individual credit spreads is accounted for by firm-level determinants of default risk, while macroeconomic variables are directly responsible for a lesser portion.

Journal ArticleDOI
TL;DR: A credit risk evaluation system that uses supervised neural network models based on the back propagation learning algorithm to decide whether to approve or reject a credit application is described.
Abstract: This paper describes a credit risk evaluation system that uses supervised neural network models based on the back propagation learning algorithm. We train and implement three neural networks to decide whether to approve or reject a credit application. Credit scoring and evaluation is one of the key analytical techniques in credit risk evaluation which has been an active research area in financial risk management. The neural networks are trained using real world credit application cases from the German credit approval datasets which has 1000 cases; each case with 24 numerical attributes; based on which an application is accepted or rejected. Nine learning schemes with different training-to-validation data ratios have been investigated, and a comparison between their implementation results has been provided. Experimental results will suggest which neural network model, and under which learning scheme, can the proposed credit risk evaluation system deliver optimum performance; where it may be used efficiently, and quickly in automatic processing of credit applications.


Journal ArticleDOI
TL;DR: Estimating binary and ordered logit regression models find that productive efficiency has significant explanatory power in predicting the likelihood of default over and above the effect of standard financial indicators.

Journal ArticleDOI
TL;DR: In this paper, the authors present a model that can explain a sudden drop in the amount of money that can be borrowed against an asset, even in the absence of asymmetric information or fears about the value of the collateral.
Abstract: We present a model that can explain a sudden drop in the amount of money that can be borrowed against an asset, even in the absence of asymmetric information or fears about the value of the collateral. Three features of the model are essential: (i) the debt has a much shorter tenor than the assets and needs to rolled over frequently; (ii) in the event of default by the borrower, the collateral is sold by the creditors and there is a (small) liquidation cost; (iii) a significant fraction of the potential buyers of the collateral also relies on short-term debt finance. Under these conditions, the debt capacity of the assets (the maximum amount that can be borrowed using the securities as collateral) can be much less than the fundamental value, and in fact, equal the minimum possible value of the asset. This is true even if the fundamental value of the assets is currently high. In particular, a small change in the fundamental value of the assets can be associated with a sudden collapse in the debt capacity. The crisis of 2007-09 was characterized by just such a sudden freeze in the market for short-term, asset-backed financing.

Journal ArticleDOI
TL;DR: In this article, the authors analyze the impact of environmental management on the credit standing of borrowing firms through legal, reputational, and regulatory risks associated with environmental incidents and find that firms with environmental concerns pay a premium on their cost of debt financing and are assigned lower credit ratings.
Abstract: This study analyzes environmental management and its implications for bond investors. Poor environmental practices influence the credit standing of borrowing firms through the legal, reputational, and regulatory risks associated with environmental incidents. We devise environmental performance measures based on information from an independent rating agency, and provide evidence that these measures explain the cross-sectional variation in credit risk for a sample of 582 U.S. public corporations between 1995 and 2006. Our findings suggest that firms with environmental concerns pay a premium on their cost of debt financing and are assigned lower credit ratings. In contrast, firms with proactive environmental engagement benefit from a lower cost of debt financing. The results are robust to numerous controls for company and bond specific characteristics, alternative model specifications, and industry membership.

Journal ArticleDOI
TL;DR: In this article, the authors show that branching deregulations in the U.S have significantly affected the supply of mortgage credit, and ultimately house prices, and show that house prices rise with branching deregulation, particularly so in Metropolitan Areas where construction is inelastic for topographic reasons.
Abstract: We show that since 1994, branching deregulations in the U.S have significantly affected the supply of mortgage credit, and ultimately house prices. With deregulation, the number and volume of originated mortgage loans increase, while denial rates fall. But the deregulation has no effect on a placebo sample, formed of independent mortgage companies that should not be affected by the regulatory change. This sharpens the causal interpretation of our results. Deregulation boosts the supply of mortgage credit, which has significant end effects on house prices. We find evidence house prices rise with branching deregulation, particularly so in Metropolitan Areas where construction is inelastic for topographic reasons. There is also evidence the fall in house prices after 2006 is most pronounced in least regulated states. We document these results in a large sample of counties across the U.S. We also focus on a reduced cross-section formed by counties on each side of a state border, where a regression discontinuity approach is possible. Our conclusions are strengthened.

Journal ArticleDOI
TL;DR: In this article, the authors examined the effects of government guarantee schemes for bank bonds adopted in the aftermath of the Lehman Brothers demise to help banks retain access to wholesale funding and found that they mainly reflect the characteristics of the guarantor (credit risk, size of rescue measures, timeliness of repayments) and not those of the issuing bank or of the bond itself.
Abstract: We examine the effects of the government guarantee schemes for bank bonds adopted in the aftermath of the Lehman Brothers demise to help banks retain access to wholesale funding. We describe the evolution and the pattern of bond issuance across countries to assess the effect of the schemes. Then we propose an econometric analysis of one striking feature of this new market, namely the significant “tiering” of the spreads paid by banks at issuance, finding that they mainly reflect the characteristics of the guarantor (credit risk, size of rescue measures, timeliness of repayments) and not those of the issuing bank or of the bond itself.

Posted Content
TL;DR: The results suggest that banks whose government guarantee was removed reduced credit risk by cutting off the riskiest borrowers from credit, and banks that ex ante benefitted more from the guarantee increased interest rates on their remaining borrowers.
Abstract: In 2001, government guarantees for savings banks in Germany were removed following a law suit. We use this natural experiment to examine the effect of government guarantees on bank risk taking, using a large data set of matched bank/borrower information. The results suggest that banks whose government guarantee was removed reduced credit risk by cutting off the riskiest borrowers from credit. At the same time, the banks also increased interest rates on their remaining borrowers. The effects are economically large: the Z-Score of average borrowers increased by 7.5% and the average loan size declined by 17.2%. Remaining borrowers paid 46 basis points higher interest rates, despite their higher quality. Using a difference-in-differences approach we show that the effect is larger for banks that ex ante benefited more from the guarantee and that none of these effects are present in a control group of German banks to whom the guarantee was not applicable. Furthermore, savings banks adjusted their liabilities away from risk-sensitive debt instruments after the removal of the guarantee, while we do not observe this for the control group. We also document in an event study that yield spreads of savings banks’ bonds increased significantly right after the announcement of the decision to remove guarantees, while the yield spread of a sample of bonds issued by the control group remained unchanged. The results suggest that public guarantees may be associated with substantial moral hazard effects. JEL Classification: G21, G28, G32

Journal ArticleDOI
TL;DR: The authors examined how government ownership and government involvement in a country's banking system affect bank performance from 1989 through 2004 and found that state-owned banks operated less profitably, held less core capital, and had higher credit risk than privately-owned ones.

Journal ArticleDOI
TL;DR: A missing data imputation method is defined and an ensemble classification technique, subagging, is proposed, particularly suitable for highly unbalanced data, such as credit scoring data, to build and validate robust models, able to handle missing information, class unbalancedness and non-iid data points.