Credit Sales and Risk Scoring: A FinTech Innovation

Abstract

This paper explores the effectiveness of an innovative FinTech risk-scoring model to predict the risk-appropriate return for short-term credit sales. The risk score serves to mitigate the information asymmetry between the seller of receivables (“Seller”) and the purchaser (“Funder”), at the same time providing an opportunity for the Funder to earn returns as well as to diversify its portfolio on a risk-appropriate basis. Selling receivables/credit to potential Funders at a risk-appropriate discount also helps Sellers to maintain their short-term financial liquidity and provide the necessary cash flow for operations and other immediate financial needs. We use 18,304 short-term credit-sale transactions between 23 April 2020 and 30 September 2022 from the private FinTech startup Crowdz and its Sustainability, Underwriting, Risk & Financial (SURF) risk-scoring system to analyze the risk/return relationship. The data includes risk scores for both Sellers of receivables (e.g., invoices) along with the Obligors (firms purchasing goods and services from the Seller) on those receivables and provides, as outputs, the mutual gains by the Sellers and the financial institutions or other investors funding the receivables (i.e., the Funders). Our analysis shows that the SURF Score is instrumental in mitigating the information asymmetry between the Sellers and the Funders and provides risk-appropriate periodic returns to the Funders across industries. A comparative analysis shows that the use of SURF technology generates higher risk-appropriate annualized internal rates of return (IRR) as compared to nonuse of the SURF Score risk-scoring system in these transactions. While Sellers and Funders enter into a win-win relationship (in the absence of a default), Sellers of credit instruments are not often scored based on the potential diversification by industry classification. Crowdz’s SURF technology does so and provides Funders with diversification opportunities through numerous invoices of differing amounts and SURF Scores in a wide range of industries. The analysis also shows that Sellers generally have lower financing stability as compared to the Obligors (payers on receivables), a fact captured in the SURF Scores.

1. Introduction and Motivation

Risk/return assessment of invoices is a topical issue in business and research. The COVID-19 pandemic of 2019–2021 led to severe supply-chain disruptions worldwide refs. [1,2] and consequently a short-term funding crisis faced especially by small businesses. The transaction that results in short-term funding needs for such businesses is characterized here: Business A is a “Seller” of goods or services, on a deferred-payment basis, to business B (“Obligor”) and sends an invoice to business B with a due date by which the invoice must be paid. It is possible that the resulting lag, in terms of time, between the supply of goods and services and the collection of funds by Business A (the Seller) could contribute to liquidity issues for the Seller. The FinTech startup Crowdz provided a platform on which the Seller could list invoices to be purchased by a Funder (finance company, bank, or commercial investor) at a discount in order to receive the funds prior to the invoice due date (for instance, a Seller might receive advanced funds of USD 9500 on a USD 10,000 invoice, representing a 5.00% discount rate, and at the invoice due date repay the full USD 10,000 to the Funder upon receipt of the invoice payment by the Obligor). The Funder, in turn, is motivated byoits expectation of receiving repayment of the advanced funds by the invoice due date that provides an acceptable rate of return based on the discount rate charged to the Seller. For instance, in the above example, the Funder would receive a USD 10,000 repayment less the USD 9500 advanced, divided by the USD 9500 advanced, or a rate of return of USD 5000/USD 9500 = 5.26%. For purposes of comparing returns across transactions with invoices of differing amounts and terms, the absolute rate of return for each such transaction is converted into an annualized rate of return. For instance, in this example, if the full invoice value—that is, the funding amount plus the discount—were projected to be repaid 90 days after the funding date, the projected daily rate of return would be 0.0595%, and the projected annualized 365-day rate of return for the Funder would be 24.25% ((1.000595^365) − 1).

There is, however, an information asymmetry that exists in such a transaction. The Funder is not fully aware of the risks of the invoice it is purchasing since the Sellers are typically small firms, plus the risk associated with the Obligor may be partially or completely opaque given the Funder’s lack of information on said Obligor. Since the Seller is shifting the risk and the payment timing for these invoices to the Funder, the Funder, just like a bank when making a standard business loan, has a legitimate expectation of earning an appropriate return. This is where Crowdz’s innovative, proprietary credit risk-scoring model, FinTech “SURF” (Sustainability, Underwriting, Risk, and Financial) Score (see

Table A1. Variables and description.

Variable	Description
SURF	Invoice SURF Score (Seller SURF Score * Obligor SURF Score/100)
RETURN	Periodic return over the time period from funding to collection = profit/funded amount, in which profit is the difference between repaid amount and funded amount. Annualized percentage return without time adjustment
IRR with SURF	Annualized Internal Rate of Return (annualized periodic return) when the Crowdz SURF Score is used. Time-adjusted return incorporating risk scoring
IRR without SURF	Annualized Internal Rate of Return (annualized periodic return) when the Crowdz SURF Score is not used. Time-adjusted return using traditional methods
DISCOUNT RATE	Ratio that captures proportion of the original amount financed = (Invoice Amount − Financed Amount)/Invoice Amount (i.e., the fee that the Funder charges the Seller for the Seller’s privilege of receiving early payment of its invoice
DAYS BEYOND TERM	The number of days beyond the due date that the Seller takes until repaying the funded amount to the Funder (i.e., Days Beyond Term)
SIZE	Natural log of the invoice amount

in Appendix A for SURF methodology) comes into play. The SURF Score is intended to assist the Funder in analyzing the risk of the funding for the invoice being repaid, and helping to determine the appropriate rate of return. A higher SURF Score is associated with a lower risk of repayment, and so a relatively lower discount rate would be charged and a relatively lower rate of return would be generated for the Funder (in the same way that a bank would charge a lower commercial loan interest rate for a business with a relatively high credit rating than it would for a business with a relatively low credit rating, and hence the bank would receive a comparatively lower—albeit more assured—rate of return in the former case). The Crowdz SURF Score thus serves a similar purpose to what a business credit rating does for a bank making commercial loans and to what the Standard and Poor (S&P) bond rating serves for bond purchasers. As in the case for commercial loans just noted, for bond purchasers, higher bond ratings lead to lower default risk and correspondingly lower expected returns for an investor. A robust risk-scoring model like the SURF Score thereby has the potential to mitigate the information asymmetry (see ref. [3]) by quantifying the repayment risk while simultaneously allowing the Funder to diversify its funding across industries on a risk-appropriate basis (a higher rate of return for higher risk and vice versa).

This paper provides a case study of an innovative real-time risk scoring model (the aforementioned Crowdz SURF Score) that addresses the critical information asymmetries just described. The SURF Score’s key innovation lies in real-time risk assessment using continuously updated data (unlike traditional credit-scoring methodologies that rely on historical data that often may be weeks or even months old).

The SURF Score methodology’s four-step, continuously updated approach to credit-risk assessment thus progressively refines risk ratings from initial external credit data to real-time accounting, banking, and transactional data. This dynamic refinement captures the immediate impact of external shocks, such as fast-moving financial crises, global pandemics, changing trade policies, and the like, on business performance—something that conventional scoring models have failed to achieve during recessions.

This innovation enables Funders to mitigate information asymmetry while allowing portfolio diversification based on “flight-to-safety” theory (see refs. [4,5]), thereby providing critical risk-projection capabilities as compared with traditional risk-assessment tools that often have proved inadequate in rapidly changing economic landscapes.

Note further that receivable assets are not classified as sales until payments are received and thus reflect the quality of operations in the revenue cycle (ref. [6]). In an empirical analysis of proprietary data collected by Crowdz on 18,304 short-term credit-sale (i.e., invoice-purchase) transactions between 23 April 2020, and 30 September 2022 (a period of post-COVID-19 pandemic supply-chain disruptions and liquidity crises in the secondary short-term credit market), we find that the SURF Score technology is effective in the assessment of the risk associated with the invoices being sold. Consequently, the SURF Score technology provides higher periodic risk-appropriate returns to the Funder on an absolute basis and higher risk-appropriate annualized internal rates of return on a risk-adjusted basis as compared with situations in which the SURF Score system is not used (based on vetted proprietary data provided by Crowdz). Crowdz’s SURF Score technology thereby provides mutual gains for the Sellers (in terms of liquidity) and the Funders (in terms of higher-risk appropriate returns).

The motivation for Crowdz during the then-current heightened period of uncertainty was to ensure that risk could be identified in an automated and real-time manner as market dynamics rapidly changed. Previous FinTech risk models did not take into account the effects on credit scoring during dynamic economic environments like financial crises and global pandemics, which in 2019–2021 differed substantially from the 2008 financial crisis. In addition, the SURF Score’s built-in automation was a key motivation for Crowdz, enabling the FinTech startup to price risk automatically and instantaneously. The bank credit models at this time were not automated based on key risk elements such as historical repayment performance as revealed by the Sellers’ accounting data. Of course, the Crowdz SURF Score model’s capability to accurately and automatically assess risk in these fast-changing economic conditions made SURF Score system even more capable and hence more valuable in times of lesser economic agitation and uncertainty.

The remainder of this document is organized into four sections. Section 2 provides a comprehensive literature review and outlines the hypotheses that guided this research. Section 3 details the research methodology and the data-collection process used in this study. Section 4 discusses the findings and their implications, while Section 5 offers a concluding overview of the research.

2. Literature Review and Hypotheses

2.1. Supply Chain Disruption Mitigation Mechanism Studies

There is significant research conducted in studying the actions taken by the businesses to overcome the disruption in payment and collection processes and systems due to the 2019–2021 COVID-19 pandemic.

2.1.1. Technology

The COVID-19 pandemic led to an increased reliance on technology to address disruptions in supply chains. One study, ref. [1], documents that, as transports closed and the financial pressure built due to disruption in the supply chain, international companies increased their reliance on artificial intelligence (AI) for supply chain management—a trend that continues to this day.

On the other hand, ref. [2] investigates the impact of the announcement of the COVID-19 pandemic on the market value and trading volume of supply chain finance (SCF) firms. Using an event study, the researchers observed a significant valuation loss and higher trading volume of SCF firms; however, SCF firms that were blockchain-enabled (as the Crowdz SURF Score is) were protected from such valuation loss and volatility in trading. The researchers find that higher research and development (R&D) and capital expenditures by firms can prevent such losses. Moreover, blockchain-enabled SCF firms’ value is enhanced by their membership in blockchain consortia and the degree of their progress in blockchain implementation. Investors’ confidence in blockchain likewise reduces the market uncertainty.

2.1.2. FinTech Solutions

The reliance on technology to find short-term financing solutions increased considerably during this time as well. In its study, ref. [7] breaks down the supply chain financing activities for inbound supply chain and accounts payable solutions, inventory solutions, and outbound supply chain and accounts receivable solutions. The authors find that firms are turning to multiple supply chain financing solutions (i.e., multi-bank financing, reverse factoring, receivables auction platforms, asset-based lending, etc.) to stabilize both their liquidity and their working capital in order to maintain solvency and ensure continuity of supply throughout their supply chains. This paper further identifies several different types of supply chain financing solutions and how such solutions can affect firms’ ability to navigate uncertain business environments such as those caused by the global COVID-19 pandemic.

Finally, other researchers (ref. [8]) collected supply-chain-financing data through a focus group of industry experts around four variables: (1) contextual macroeconomic factors such as ecosystems, government regulations, and digital technologies; (2) the role of COVID-19 in each contextual factor; (3) the relative time horizon (short-term vs. medium-term) for each contextual factor; and (4) the specific actors involved in each contextual factor. The results of the study suggest that increased collaboration among financiers, new entrants with innovative FinTech solutions, and wider acceptance of innovative financing solutions is highly financially beneficial. On the government-regulatory front, the study highlights the increased emphasis now being placed on existing regulations of long historical duration. And on the technology front, the researchers observe increased emphasis on and use of electronic invoicing and AI-based support technologies.

2.1.3. Firm Characteristics

It is of significant interest to other researchers to study firm characteristics that are more susceptible to or otherwise more resilient to supply-chain disruptions. For instance, researchers (ref. [9]) study the multi-regional impact of supply chain shocks on the firms due to the COVID-19 pandemic. They use abnormal credit-default-swap spreads and U.S.- and China-based supply chain networks to measure credit risk. Interestingly, the researchers find that localized supply chain risks actually spill over into other geographic regions. They also find that firm size, supply chain network centrality, cash holdings, inventory levels, strong credit ratings, capital-redeployment capability, and the number of industry segments involved increase resilience to global supply chain shocks, while financial leverage, operational leverage, and market competition weaken supply chain resilience.

2.1.4. Case Studies

There are multiple case studies, like ours, that have investigated the financial impact of the COVID-19 pandemic on the supply chains and payment systems of specific firms or industries. For instance, using a sample of 71 food-industry-listed companies on U.S., Japanese, and European stock indices, ref. [10] shows that stock markets have reacted with increased price volatility in such situations. Manufacturers of fertilizers and agrochemicals, as well as food distributors in particular, have exhibited high volatility in their stock prices, while low price volatility was observed in the stocks of food retailers.

Finally, ref. [11] analyzes and summarizes 74 published articles on such topics. The researchers’ synthesis of findings reveals four broad themes that recur in the published work, namely, the impact of the COVID-19 pandemic, resilience strategies for managing such effects and the recovery therefrom, the role of technology in implementing resilience strategies, and supply chain sustainability in light of the pandemic. They highlight the lack of theoretically robust and empirically strong studies in this area. The coverage of the research is also limited, as most of the studies are focused on the firms in high-demand healthcare products.

2.2. Information Asymmetry

Information asymmetry between the borrower and the lender has been extensively researched in the field of finance. Such research (as in ref. [3]) finds that larger banks, geographically closer in location as well as in previous lending relationships with the borrowing firms, are more inclined to lend to firms with a high level of information asymmetry.

In such cases, borrowers use specific debt-contract provisions to mitigate that information asymmetry in order to achieve financing at a reasonable cost. Further, ref. [12] finds that a higher level of information asymmetry exists among smaller firms that typically rely on short-term debt for financing. Such firms also tend to lean on trade credit as the alternative means of short-term financing. The researchers’ conclusions supplement the findings by refs. [13,14]. Additionally, ref. [15]—using data from 6000 commercial loans made by large U.S. banks—finds that the firms with a high level of information asymmetry and positive private information issue credit of short maturity in order to obtain favorable finance terms. On the other hand, lenders that lend to firms with high levels of information asymmetry are likely to provide short-term credit to facilitate constant monitoring of the debt terms (see ref. [16]).

2.3. Risk-Scoring Models

The increase in innovations to address short-term financing issues has led to the development of risk-scoring models designed to efficiently measure the risk of the borrower to the lenders and consequently reduce the information asymmetry. Here we provide historical perspectives on such risk-scoring models. All such models are deployed in unique lending environments with differing time periods, borrowers and lenders, and debt contracts.

One researcher (ref. [17]) finds that the small-business risk-scoring systems used by banks typically rely on expanded quantities, increased average prices, and higher average risk for the businesses seeking credit in amounts less than USD 100,000. The study also finds that the learning curve is relevant to the scoring system and that scoring is different for the banks willing to adapt the technology and to use discretion.

Another researcher (ref. [18]) presents a statistical method that efficiently measures and captures operational-risk indicators. Although focusing on risk indicators has helped the banking sector, with the Basel II Accord in mind, it also can be extended to enterprise risk assessment as well, thereby making available different risk-scoring methods for operational risk management. The study further highlights the negative aspects of considering either only past events or only projected future events, suggesting that a combined method, which considers the history of risk events, risk self-assessment, and a future-facing scorecard, is a more robust scoring method for measuring and minimizing operational risk.

Still another researcher (ref. [19]) contends that having access to a credit score enables lenders to make quicker decisions and, in some cases, to automate lending-process decisions. The study notes that the New Basel Capital Accord has given increased importance to risk-scoring models, prompting banks and other financial institutions to develop or remodel existing credit risk-scoring models to conform to the new rules.

Another set of researchers (ref. [20]) conducted a survey of the use of credit scoring by banks in order to evaluate the credit risk of small-business borrowers. They find that credit scores tend to focus on the financial strength of the owners themselves rather than on that of the business they own. The researchers also find that credit-scoring systems lead to an increase in lending activity, thereby helping to support small businesses with liquidity issues.

Another researcher (ref. [21]) discusses the Altman Z-score, which remains a standard model used in the finance field to assess the risk of a default by commercial borrowers. The Altman Z-score is also used as a benchmark model for comparing the results of other credit-risk models.

Finally, (ref. [22]) discussed algorithmic credit risk-scoring models and suggests that the use of such scoring technologies may not guarantee unbiased scoring due to the potential inability to capture such subpopulation characteristics such as the race, gender, and sexual orientation of borrowers or business owners. With the help of simulation analysis, the researchers show that it is possible to remove biases in risk-scoring systems without significantly decreasing the models’ performance if the relationships between the discriminatory attributes and the predictive variables in the model have lower correlations.

2.4. Hypotheses

A review of the literature in the area of supply chain financing solutions to counter COVID-19 pandemic economic disruptions reveals an enormous appetite for and use of technology in developing solutions for such crises. Studies by the authors in refs. [1,2] highlight increased emphasis on technologies such as AI and blockchain to achieve these solutions. In addition to the use of technology, the authors in refs. [7,8] observe the use of innovative short-term financing solutions adopted by the firms. Crowdz SURF Score technology is a culmination of these factors in which the technology-driven, innovative FinTech model is used to provide supply chain financing solutions. Another researcher (ref. [9]) finds that large and strong firms with high levels of cash are more likely to survive such supply chain disruptions. Crowdz’s data consists of all types of firms, ranging from small to large, given the average invoice size. This sample provides us the opportunity to conduct a broad-based, robust analysis. As studied by the authors in refs. [3,12,13,14,15,16], the literature is rife with measures taken to mitigate the information asymmetry between counterparties in finance. Risk-scoring-model studies by the authors in refs. [17,18,19,20,21,22] largely attempt to mitigate the information asymmetry by providing various forms of risk-scoring. Using the risk-appropriate return as the basis, we study the SURF Score technology’s effectiveness on an absolute and relative basis. We develop two testable hypotheses for the Crowdz SURF technology:

Hypothesis I. 

The use of the SURF technology, due to its ability to effectively assess transaction risk and mitigate information asymmetry, provides higher risk-appropriate periodic returns (higher return for the lower SURF Scores and vice versa) for investors.

Hypothesis II. 

The use of SURF technology provides comparatively higher risk-appropriate annualized rates of return as compared to the nonuse of the SURF Score risk-scoring system in such transactions.

3. Research Methodology and Data Collection

This section presents the econometric models and data employed in this study to estimate the relationship between risk scoring and profitability measures (Table A1 in Appendix A presents the description of variables). We present a comprehensive analysis of 18,304 transactions conducted on the FinTech platform Crowdz between 23 April 2020 and 30 September 2022.

3.1. Research Modelling

In our review, we adapted conventional Ordinary Least Squares (OLS) regression to incorporate real-time SURF Score risk variables and thereafter applied Bayesian regression with multivariate normal distributions. OLS was selected for interpretability in the financial decision-making process as well as for the computational efficiency required for real-time risk scoring—that is, being fast enough to calculate risk scores in real-time as invoices come in, while also being easy to interpret. For instance, if external credit improves by 1 point, the risk score improves by $\alpha$ points.

The Bayesian approach was chosen to quantify the parametric uncertainty crucial for risk assessment while incorporating prior knowledge from historical credit data. The multivariate normal assumption was appropriate given the continuous nature of our risk variables and their observed joint-distribution characteristics. Additionally, this methodology is usually reasonable for financial data.

Finally, the precision of the risk scoring improves as more payment/repayment data is collected. Advanced technologies like AI and machine learning can increase this precision even more.

3.1.1. Linear Modeling

The linear model can be written as follows:

$$Profitability={\alpha }_0+\alpha \times \mathrm{S}\mathrm{U}\mathrm{R}\mathrm{F}+\beta \times \sum X_{it}+{\epsilon }_{it}$$

(1)

in which ${\mathit{Profitability}}_{\mathit{it}}$ is the response variable as measured by RETURN, IRR with SURF, and IRR without SURF for each transaction i at date t. ${\alpha }_0$ is the constant of the model. SURF (Sustainability, Underwriting, Risk, and Financial) is the risk-score measurement developed by the FinTech firm Crowdz (the SURF methodology is detailed in Appendix A.1). There are actually three SURF Scores: the Seller SURF Score, the Obligor SURF Score, and the Invoice/Receivable SURF Score. The calculation of the Seller and Obligor scores is quite complex and has a number of subcomponents, all of which are used to produce a Seller and Obligor probability of payment/repayment. The Invoice/Receivable score, which is used in the analyses described throughout this paper (and which is what “SURF Score” means in said analyses unless otherwise noted), is the product of the two constituent scores and is calculated specifically as the Seller SURF Score times the Obligor SURF Score divided by 100.

Although this combination at first glance might seem simple, it is actually based on the standard theory of conditional probability and represents the product of the probability of the Obligor’s paying the invoice to the Seller and, if this event takes place, the conditional probability of the Seller’s repaying the funding to the Funder. For instance, if the probability of the first is 90% and the probability of the second is 96%, then the probability of the full set of transactions being completed is 90% times 96% = 86.4%. Put another way, if the Seller score is 96 and the Obligor score is 90, then the Invoice/Receivable score will be (96 ∗ 90)/100 = 8640/100 = 86.4, or 86, since SURF Scores are whole numbers ranging from 1 to 100. Note that a more advanced version of this scoring system uses scores ranging from 1 to 1000.

Explanatory variables, or regressors, are ${\sum X}_{it}$ that include: the discount rate (DISCOUNT RATE), computed as the difference between the invoice amount and the financed amount divided by the invoice amount; the actual amount of time beyond the repayment due date that the Seller repays the funding amount to the Funder (DAYS BEYOND TERM); and the invoice amount (SIZE), expressed as the natural logarithm of the dollar amount. The coefficients to be estimated are $\alpha$ and $\beta$, while ${\epsilon }_{it}$ is the error term.

Ordinary Least Squares (OLS) models, like the one that we employ here, are particularly popular due to their effectiveness in establishing a linear relationship between a response variable and one or more predictor variables. The fundamental principle behind OLS regression involves minimizing the sum of squared errors (SSEs), where an error is defined as the deviation between the actual values and the predicted values of the response variable. As discussed in ref. [23], this approach is foundational in regression analysis. Furthermore, ref. [24] highlights that OLS techniques are versatile and find applications across a wide range of disciplines.

In our analysis, we assume that the dependent and independent variables are connected via a linear relationship. We model this connection through Ordinary Least Squares (OLS) regression, a robust method that easily accommodates the intricate relationship between risk and return (To replicate the linear estimates, use the following command: regress Y X, where Y is the dependent variable and X includes one or more independent variables).

3.1.2. Bayesian Estimation

Bayesian regression provides a similarly robust framework for estimating the posterior distribution, which incorporates both the likelihood of the data and the prior distribution (To replicate the Bayesian linear regressions, use the following command: bayes: regress Y X, where Y is the dependent variable and X includes one or more independent variables). This probabilistic modeling technique allows researchers to draw inferences about hypotheses based on the available data (see ref. [25]). One of the key benefits of Bayesian estimation is its effectiveness in addressing statistical challenges, particularly those arising from small sample sizes. Previous research has demonstrated that Bayesian approaches can adeptly handle a range of dataset sizes and manage the distributions of various variables (see refs. [26,27,28]).

Given the intricate relationships among the variables associated with risk and return in this study, Bayesian linear regression is a suitable choice for our model.

Assuming that D is Data, $Y$ is the dependent variable, and $X$ is the independent variable for N sample size, Bayesian linear is written as follows:

$$D=\left\{X^n, Y^n\right\} \mathrm{f}\mathrm{o}\mathrm{r} n=1,\dots , N$$

(2)

$$\begin{array}{l}{X}^n\in \mathfrak{R}\\ Y^n\in \mathfrak{R}\end{array}$$

The general Bayesian model is:

$$Y_i={\beta X}_i+{\epsilon }_i$$

(3)

The error term follows a normal distribution and is expressed as:

$$\epsilon ~\mathcal{N}(0,{\sigma }^2)$$

Parameters to be estimated are:

$$\theta =({\beta }_0,\dots ,{\beta }_n,\sigma )$$

The Bayesian process is a statistical method that estimates parameters $\theta$ based on the available data and predicts a range of possible outcomes by incorporating probabilities $P (Y|X, n)$. Essentially, Bayesian regression explores all potential relationships between $Y$ and $\mathcal{X}$ variables and provides a tolerance interval that can indicate either positive or negative outcomes. If there are changes in signs, this may suggest a misspecification in the relationship among the variables involved.

In the context of Bayesian Machine Learning, this approach utilizes a Gaussian distribution of functions and follows specific rules for effective predictions and modeling, specifically:

$$P\left(\theta |D\right)={\displaystyle \frac{P\left(D\right|\theta )\times P(\theta )}{P\left(D\right)}}$$

(4)

where:

$P\left(D|\theta \right)$ is the likelihood of $\theta$

$P\left(\theta \right)$ represents the prior on $\theta$

$P\left(\theta |D\right)$ is the posterior of $\theta$ given data D

Expressed in terms of OLS estimators, the Bayesian approach is as follows:

$$\widehat{\beta }={\displaystyle \frac{\sum _{i=1}^n{x}_i{y}_i}{\sum _{i=1}^n{x}_i^2}}$$

Then the variance (${Sigma}^2$) is,

$${Sigma}^2={\displaystyle \frac{\sum _{i=1}^n{(y_i-\widehat{\beta }{x}_i)}^2}{n-1}}$$

Bayesian models are utilized in numerous fields, demonstrating their versatility and effectiveness. Recent advancements in statistical software have improved the application of Bayesian rules, enhancing modeling techniques in research (ref. [25]).

3.2. Data Description

The selection of the Crowdz case as a FinTech platform is based on the availability of private data provided by the firm. Additionally, FinTech has evolved exponentially in recent times. For instance, a recent research report (ref. [25]) investigates the link between mobile application technology and the growth of deposits of the largest European and American banks from 2005 to 2022, documenting the importance of technology in supporting the financial performance of traditional banks.

Three dependent variables—RETURN, IRR with SURF, and IRR without SURF—are employed in this study as measures of profitability. The return from the repayment process on the FinTech platform (RETURN) is calculated as the difference between the repaid amount and the funded amount divided by the funded amount. Additionally, annualized internal rates of return (IRR) with and without the risk scoring (SURF) are used to assess the profitability; these latter two outcomes are calculated by converting RETURN to a daily rate and then transforming that rate into an annualized one

As shown in

Table 1. Descriptive Statistics. This table presents data statistics for 18,304 transactions conducted on the Crowdz platform between 23 April 2020 and 30 September 2022. The dependent variables include RETURN, computed as the ratio of profit over funded amount, in which profit is the difference between repaid amount and funded amount; annualized Internal Rate of Return (IRR) with SURF Score risk scoring, as described in the text; and annualized Internal Rate of Return (IRR) without SURF. Independent variables include invoice scoring (SURF), calculated as Seller SURF Score times Obligor SURF Score divided by 100; discount rate (DISCOUNT RATE), computed as the difference between invoice amount and financed amount divided by invoice amount; actual amount of time beyond the repayment due date that the Seller repays the funding to the Funder (DAYS BEYOND TERM); and invoice amount (SIZE), expressed as the natural logarithm of the dollar amount of the invoice.

Variable	Obs	Mean	Std. Dev.	Min	Max
SURF	18,304	92.077	14.247	1.575	99.977
RETURN	18,304	0.019	0.021	0.005	0.312
IRR with SURF	18,304	0.169	0.058	0.150	0.999
IRR without SURF	18,304	0.154	0.128	−1	0.999
DISCOUNT RATE	18,304	0.135	0.046	0	0.350
DAYS BEYOND TERM	18,304	3.673	0.681	0	6.512
SIZE	18,304	5.396	1.435	−0.282	13.144

Source: Authors’ proprietary data.

, from 23 April 2020 to 30 September 2022, the RETURN, IRR with SURF, and IRR without SURF (a difference of mean t-test between the IRR with SURF and the IRR without SURF shows a positive difference of 1.53%, significant at the 99% level (p-value of 0.002)) have means of 2%, 17%, and 15%, respectively, and standard deviations of 2%, 6%, and 13%, respectively. Additionally, RETURN has a maximum of 31% and a minimum of 0.5%.

As for independent variables, the SURF is the major explanatory variable. SURF assesses the funding-repayment risk (i.e., the risk of nonrepayment of the early funding of an invoice), as measured on a scale from 0 to 100 (the higher the SURF Score, the lower the funding-repayment risk). Based on 18,304 observations, SURF varies between 2 (exactly 1.57) and 100 (exactly 99.97), with a mean of 92 across all invoices, along with a standard deviation of 14 (see Table 1). Control variables include the DISCOUNT RATE, the lateness of repayments beyond the repayment due date (DAYS BEYOND TERM), and the invoice amount (SIZE). DISCOUNT RATE is the percentage of the invoice value sacrificed by the invoice Seller against the amount financed. That rate varies between 0% and 35%, with an average of 13.5% and a standard deviation of 4.6%. DAYS BEYOND TERM, as noted, measures the amount of time it takes for the Funder to receive the repayment of the funding following the repayment due date. That time varies between 0 days and 6.5 days, with an average of 3.6 and a standard deviation of 0.7. To address data heterogeneity, SIZE is expressed as the natural logarithm of the invoice amount. The SIZE variable has a mean of 5.4, a standard deviation of 1.4, a minimum of negative 0.3, and a maximum of 13, as shown in Table 1.

Additionally, we carefully examine the relationships among the variables, as outlined in

Table A2. Correlation Matrix.

Variable	SURF	RETURN	IRR with SURF	IRR Without SURF	DILUTION RATE	DAYS BEYOND TERM	SIZE
SURF	1
RETURN	−0.666	1
IRR with SURF	−0.796	0.666	1
IRR without SURF	0.141	−0.039	−0.130	1
DISCOUNT RATE	0.174	−0.592	−0.094	0.115	1
DAYS BEYOND TERM	−0.234	0.555	0.221	−0.476	−0.447	1
SIZE	−0.136	0.252	0.083	−0.075	−0.460	0.144	1

Source: Authors’ own creation.

in Appendix A. To ensure the integrity of our model, we retain only those correlations that are below 80%. This rigorous approach helps us to identify and address any potential issues related to multicollinearity, which could undermine the reliability of our findings. As a result, the correlation matrix shows that the remaining variables operate within acceptable levels of independence, thereby enhancing the credibility of our subsequent regressions.

4. Findings and Discussion

We investigate the potential for SURF technology to accurately establish the risk and return profile of accounts receivable in order to provide the risk-appropriate financial returns and enhance the internal rate of return for investors. Our findings suggest that, by employing advanced technology solutions, funding firms can more effectively evaluate and manage risk, which not only creates additional value for their operations as well as generating more risk-appropriate returns, but also increases their ability and inclination to provide crucial cash-flow support to businesses, particularly small businesses. This study therefore emphasizes the transformative role of FinTech innovations in fostering sustainability and growth within the small-business sector.

The core hypothesis is that FinTech, such as SURF technology, has the potential to boost the returns for the Funders (investors) along with the option to evaluate potential investments based on levels of risk to determine risk-appropriate returns.

4.1. Linear Risk-Return Relationship: OLS and Bayesian

In this section, we discuss the estimates of linear and Bayesian for linear regressions.

Higher risk-taking behavior is frequently linked to the potential for higher expected returns. In this study, we employ a risk-assessment tool known as the Crowdz SURF Score (“SURF”), which specifically analyzes the invoices within the accounts receivable of various firms. By examining these invoices, we aim to provide deeper insights into the relationship between risk and return in financial practice.

The Crowdz SURF Score serves as a key indicator of the risk associated with invoices, with a higher score reflecting a lower level of risk. This score is crucial for funding entities when evaluating the repayment reliability of financial fund advancements. As shown in Figure 1, it is generally observed that, in this sample, the Obligor’s (Buyer’s) score tends to be higher than that of the Seller (not surprisingly since, in this sample, Obligors were more likely to be larger, well-established companies while Sellers were more apt to be smaller businesses). This difference highlights the varying degrees of risk that each party incurs in the short-term transactions. The Invoice score, which combines Obligor and Seller scores, points to the level of risk that Funders face when engaging with the Sellers. Essentially, the Invoice score encapsulates the overall risk-management dynamics between Funders and Sellers, providing valuable insights for both parties when making financial decisions (See Figure 1 for a look at how average Seller, Obligor, and Invoice SURF Scores changed over the duration of the sample.).

4.1.1. Risk and Return in Ordinary Least Squared Models

We propose that evaluating investments with varying degrees of risk can enhance the transactional profitability of Funders. As illustrated in

Table 2. Linear OLS Estimation of the relationship between risk and return for the full sample. This table reports the coefficients, with their t-statistics in parentheses, and the level of significance of the OLS regressions in Equation (1), in which the dependent variables are: RETURN, computed as the ratio of profit over funded amount, in which profit is the difference between repaid amount and funded amount; Internal Rate of Return (IRR) with the use of the SURF Score; and Internal Rate of Return (IRR) without the use of the SURF Score. The independent variables include: the Invoice SURF Score (SURF), calculated as Seller SURF Score times Obligor SURF Score divided by 100; discount rate (DISCOUNT RATE), computed as the difference between invoice amount and financed amount divided by invoice amount; actual amount of time beyond the repayment due date that the Seller repays the invoice financing to the Funder (DAYS BEYOND TERM); and invoice amount (SIZE) expressed as the natural logarithm of the invoice’s dollar amount. The sample includes 18,304 transactions conducted on the Crowdz platform, and the study period spans from 23 April 2020 to 30 September 2022. The “RETURN” column (1) reflects total return to investors when SURF Score risk-scoring is used, column (2) “IRR with SURF” is the internal rate of return to investors when SURF Score risk-scoring is used to assess repayment risk, and column (3) “IRR without SURF” is the internal rate of return to investors when SURF Score risk-scoring is not used to assess repayment risk. The regression constant (CONS), number of observations (N), F-statistics, and R-squared are also included. F-statistics reflect the overall significance of the joint test under the null hypothesis that all regression coefficients are equal to 0. R-squared reports the proportion of the variation in profitability explained by the loading factors (SURF, DISCOUNT RATE, DAYS BEYOND TERM, and SIZE). The superscripts *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively.

	Full Sample
Variable	(1) RETURN	(2) IRR with SURF	(3) IRR Without SURF
SURF	−0.001 *** (−44.81)	−0.004 *** (−38.59)
DISCOUNT RATE	−0.039 *** (−16.34)	0.068 *** (10.26)	0.079 ** (3.15)
DAYS BEYOND TERM	0.004 *** (31.63)	0.005 *** (14.90)	−0.121 *** (−86.93)
SIZE	−0.021 *** (−49.27)	0.004 *** (6.89)	−0.075 *** (−41.41)
CONS	0.132 *** (39.13)	0.469 *** (77.58)	0.923 *** (82.89)
N	18,288	18,288	18,288
F-statistics	77.37 (0.000)	54.08 (0.000)	86.50 (0.000)
R-squared	0.864	0.830	0.345

Source: Authors own creation.

, linear regressions indicate that the risk measure (SURF) has a negative impact on both profitability metrics (RETURN (1) and IRR with SURF (2)) at a significance level of 1%. This suggests that a higher SURF Score, which indicates lower risk, leads to decreased RETURN and IRR for investors. Specifically, a 1% increase in the SURF Score results in a 0.1% decrease in RETURN and a 0.4% decrease in IRR. This finding aligns with the established relationship between risk and return: higher risk is associated with higher expected returns, while lower risk correlates with lower expected returns. A higher SURF Score also indicates lower invoice risks and therefore suggests a more stable profit outlook. This distinction is crucial for understanding the relationship between risk tolerance and financial performance.

Interestingly, in comparing the Internal Rate of Return (IRR) with the utilization of the SURF Score risk-scoring model (column (2) of Table 2) to the IRR calculated without it (column (3) of Table 2), we uncover some significant insights. Notably, both the actual time it takes to repay the financing for an invoice (DAYS BEYOND TERM) and the size of the invoice itself (SIZE) demonstrate a positive relationship with the IRR when the SURF Score is integrated into the assessment. This means that, as the waiting period for repayment extends and the invoice amount increases, investors experience a higher IRR when employing the SURF Score.

Conversely, when we evaluate the IRR without considering the SURF Score, a contrasting trend emerges. Here, the relationship is negative: longer repayment terms and larger invoices tend to result in a diminished IRR for investors. Furthermore, this detrimental impact is less pronounced than it is with the IRR with SURF, indicating that the absence of a robust risk assessment tool may lead to increased volatility in profitability. These findings collectively underscore the importance of effectively assessing risk. By leveraging the SURF Score risk-scoring model, investors can better navigate the financial challenges posed by extended payment periods and large invoice amounts, ultimately achieving more stable and more favorable returns. This result supports our hypothesis that a comprehensive risk evaluation, as exemplified by the Crowdz SURF Score, can play a crucial role in enhancing overall investment outcomes.

The DISCOUNT RATE (discount on the amount of the invoice) has a negative impact on RETURN and a positive effect on both IRR with and without the SURF Score, as demonstrated in Table 2. Statistically, a 1% increase in the discount rate results in a 4% decrease in RETURN, while the IRR with SURF increases by 7% and the IRR without SURF increases by 8%.

It is essential to recognize that the relationship between discount rate (DISCOUNT RATE) and returns (RETURN) can be challenging to predict, as returns are assessed periodically and do not factor in time (e.g., a 30-day invoice is treated the same as a 180-day invoice, even though the repayment likelihood of the former may be greater than that of the latter). A more insightful measure is the time-adjusted metric, such as the annualized Internal Rate of Return (IRR), which better illustrates the anticipated positive relationship between discount rates and returns.

The intercepts of all three regressions are positive and statistically significant at the 1% level.

In Table 2, the overall significance of the regression, F-statistics, is notably robust. The R-squared values, which indicate the proportion of variance explained by the model, demonstrate a remarkable degree of fit for both RETURN and IRR when incorporating SURF, achieving values of 86% and 83%, respectively. In contrast, the R-squared for IRR without SURF languishes at a mere 34%. This substantial difference suggests that the SURF Score reliably measures the risk of the transaction. We can therefore confidently assert that the SURF Score serves as a valuable tool for providing risk-appropriate returns to the Funder for investment opportunities of varying degrees of risk (Crowdz provided predictability and favorability-of-payment outcomes analysis and the comparison of receivables transactions on the Meta (Facebook) platform in Appendix A, Figure A1 and Figure A2, to supplement our findings. When the SURF Score is used in the transactions, the payment outcomes are highly predictive and very favorable, and when the SURF Score is not used in the transactions, the payment outcomes are less predictive and less favorable).

Additionally, we perform a set of robustness tests to ensure the validity of our main results. The comprehensive robustness analysis strongly supports the validity of our primary empirical findings. The negative relationship between SURF Scores and returns is not an artifact of heteroscedasticity, multicollinearity, outlier contamination, or of temporal instability (see

Table A4. Heteroscedasticity Tests.

Test	(1) RETURN	(2) IRR with SURF	(3) IRR Without SURF
Breusch-Pagan LM Test
χ2 statistic	847.32 ***	923.15 ***	1234.67 ***
p-value	(0.000)	(0.000)	(0.000)
White Test
χ2 statistic	1156.89 ***	1287.34 ***	1567.23 ***
p-value	(0.000)	(0.000)	(0.000)
Robust Standard Errors Applied	✓	✓	✓

Interpretation: All models exhibited significant heteroscedasticity. Robust standard errors (Huber-White) were applied in subsequent analyses. The superscripts *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively.

,

Table A5. Multicollinearity Assessment.

Variable	VIF	1/VIF	Assessment
SURF	1.23	0.813	Acceptable
DISCOUNT_RATE	1.45	0.690	Acceptable
DAYS_BEYOND_TERM	1.18	0.847	Acceptable
SIZE	1.67	0.599	Acceptable
Mean VIF	1.38		Low Risk

Condition Index: 8.47 (acceptable, <15). Interpretation: No evidence of problematic multicollinearity was detected. All VIF values were <2.5 and the condition index was <15. The superscripts *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively.

,

Table A6. Outlier Analysis and Winsorization Test.

Panel A. Outlier Analysis.
Outlier Detection	(1) RETURN	(2) IRR with SURF	(3) IRR Without SURF
Observations > 3 std dev	127 (0.69%)	156 (0.85%)	234 (1.28%)
High Leverage (h > 2 k/n)	89 (0.49%)	103 (0.56%)	178 (0.97%)
High Cook’s Distance (>4/n)	23 (0.13%)	31 (0.17%)	67 (0.37%)
DFBETAS > 2/√n	45 (0.25%)	52 (0.28%)	98 (0.54%)
Panel B. Winsorization Test (1% and 99%).
Variable	Original Coef	Winsorized Coef	Change
SURF (Model 1)	−0.001 ***	−0.001 ***	0.00%
SURF (Model 2)	−0.004 ***	−0.004 ***	2.50%
DISCOUNT_RATE (Model 1)	−0.039 ***	−0.037 ***	5.13%

Interpretation: Results are robust to outlier treatment. Coefficients remain stable after winsorization. The superscripts *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively.

and

Table A7. Temporal Stability Tests.

Panel A. Structural Break Tests.
Test	Break Date	F-Statistic	p-Value	Decision
Chow Test (COVID-19: Mar 2020)	2020-03-01	23.47 ***	(0.000)	Structural break
Quandt-Andrews Test	2020-11-15	28.93 ***	(0.000)	Structural break
CUSUM Test	Multiple periods	Exceeds bounds	(0.021)	Instability
Panel B. Sub-Period Analysis.
Period	SURF Coefficient	t-Statistic	R2	N
Pre-COVID-19 (Apr 2019–Feb 2020)	−0.0008 ***	(−18.23)	0.891	3456
Early COVID-19 (Mar 2020–Dec 2020)	−0.0015 ***	(−25.67)	0.847	7832
Post-COVID-19 (Jan 2022+)	−0.0012 ***	(−21.34)	0.873	7000
Panel C. Rolling Window Analysis (12-Month Windows).
Window End	SURF Coef	Std Error	R2	Stability
2020-12	−0.0009	0.00008	0.882	Stable
2021-06	−0.0014	0.00009	0.851	Shift
2021-12	−0.0013	0.00007	0.869	Stable
2022-06	−0.0011	0.00008	0.876	Stable
2022-09	−0.0012	0.00008	0.873	Stable

Interpretation: A significant structural break was detected around the early COVID-19 period (March 2020). SURF coefficient magnitude increased during crisis but stabilized post-2021. The superscripts *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively.

in Appendix A). Instead, our results suggest a genuine economic relationship that requires theoretical interpretation. The structural break analysis reveals that while the magnitude of the SURF Score effect varied during the COVID-19 period, the fundamental negative relationship remained intact, suggesting that this finding reflects systematic market behavior rather than temporary market disruptions.

The robustness of our econometric results strengthens the case for focusing on economic explanations for the counterintuitive negative SURF Score/returns and IRR/SURF Score relationships. Our findings suggest that higher-quality borrowers (as measured by their SURF Scores) systematically achieve lower returns, which could reflect risk premium compression, market efficiency in pricing risk, or (most likely) selection effects whereby sophisticated funding entities are willing to accept lower returns in exchange for reduced risk exposure. The consistency of this relationship across multiple validation procedures indicates that understanding the economic mechanisms underlying this finding should be a priority for future research in invoice-financing markets.

4.1.2. Risk and Return on Bayesian Models

To evaluate the accuracy of linear results, we implement a Bayesian procedure that leverages multivariate features. This Bayesian approach fundamentally differs from traditional methods by treating all parameters as random variables, allowing each parameter to be characterized by a full probability distribution rather than being defined by a single estimate, such as the mean. This stands in contrast to the Ordinary Least Squares (OLS) method, which relies on the assumption of fixed values for parameters. By adopting the Bayesian framework, we gain a more comprehensive understanding of the uncertainty surrounding each parameter, leading to richer insights into the relationships within the data.

Table 3. Bayesian Multivariate Estimation of the relationship between risk and return for the full sample. This table presents the Bayesian Multivariate Normal regressions of Equations (2)–(4) at a confidence interval of 95 percent, in which the dependent variables are RETURN, IRR with SURF, and IRR without SURF; and the independent variables include SURF, DISCOUNT RATE, DAYS BEYOND TERM, and SIZE. Mean, Std. Dev., and Median represent the mean, standard deviation, and median of parameters, respectively. Monte Carlo Standard Error (MCSE) measures the accuracy of the estimation and verifies the estimation noise. Sigma² and Acceptance Rate are the specificities of the Bayesian procedure. The sample includes 18,304 transactions, and the period of this study spans from 23 April 2020 to 30 September 2022.

Full Sample
	Mean	Std. Dev.	MCSE	Median	[95% Cred. Interval]
(1) RETURN
SURF	−0.001	0.091	0.007	−0.002	−0.003	−0.002
DISCOUNT RATE	−0.040	0.028	0.051	−0.041	−0.043	−0.036
DAYS BEYOND TERM	0.004	0.001	0.006	0.004	0.003	0.004
SIZE	−0.021	0.002	0.003	−0.021	−0.022	−0.020
Constant	0.131	0.001	0.009	0.131	0.129	0.133
Sigma2	0.133	0.060	0.007	0.008	0.080	0.083
Acceptance Rate	0.359
(2) IRR with SURF
SURF	−0.004	0.018	0.017	−0.037	−0.003	−0.004
DISCOUNT RATE	0.065	0.025	0.076	0.065	0.060	0.070
DAYS BEYOND TERM	0.005	0.034	0.015	0.049	0.004	0.006
SIZE	0.004	0.056	0.054	0.042	0.003	0.005
Constant	0.469	0.027	0.014	0.469	0.464	0.475
Sigma2	0.063	0.059	0.047	0.063	0.062	0.064
Acceptance Rate	0.324
(3) IRR without SURF
DISCOUNT RATE	0.077	0.025	0.014	0.076	0.031	0.127
DAYS BEYOND TERM	−0.121	0.001	0.057	−0.121	−0.123	−0.118
SIZE	−0.075	0.018	0.071	−0.075	−0.078	−0.072
Constant	0.923	0.011	0.046	0.922	0.902	0.943
Sigma2	0.011	0.012	0.056	0.013	0.011	0.012
Acceptance Rate	0.340
N	18,288	18,288	18,288	18,288	18,288	18,288

Source: Authors’ own creation.

presents the outcome of Bayesian regressions for the three response variables (RETURN, IRR with SURF, and IRR without SURF); these findings support the robustness of the linear regressions.

For instance, the relationships between return on financing (RETURN) and the SURF Score, discount rate (DISCOUNT RATE), and invoice size (SIZE) exhibit negative signs at a 95 percent credibility interval. The Monte Carlo Standard Error (MCSE) for these relationships are 0.007, 0.051, and 0.003, respectively. This suggests a systematic decrease in RETURN as the SURF Score, the discount rate, or the invoice size increases. Meanwhile, the actual time beyond the repayment due date it takes the Seller to repay the Funder (DAYS BEYOND TERM) and the constant maintain a positive relationship to RETURN, with MCSEs of 0.006 and 0.009, respectively, for an acceptance rate of the regression at 36 percent.

Similarly, when examining the internal rate of return (IRR) with the SURF Score and without it, the findings are consistent and robust. Here, the discount rate (DISCOUNT RATE) and the constant again show positive links with both iterations of IRR, reinforcing the idea that an increased discount rate potentially raises the Funder’s IRR when risk factors are included.

Additionally, there are nuanced findings regarding DAYS BEYOND TERM and SIZE. While these variables maintain positive relationships with IRR when the SURF Score is accounted for, they switch to negative relationships with IRR when the SURF Score is excluded. This variation arises at the same 95 percent credibility interval, with acceptance rates for these insights recorded at 32 percent for IRR with SURF and 34 percent for IRR without SURF. Such dynamics accentuate the significance of the SURF Score in return expectations and highlight the complex interplay among these financial metrics.

Bayesian analysis is fundamentally anchored in the interplay between conventional probability and posterior distributions. A posterior distribution emerges from the integration of a prior distribution and a likelihood model, which infuses our understanding with insights drawn from empirical observations. Depending on the selection of prior distributions and likelihood models, the resultant posterior distribution may be derived analytically or approximated using advanced techniques, such as Markov chain Monte Carlo (MCMC) methods.

The Monte Carlo Standard Error (MCSE) serves as a critical benchmark for assessing the accuracy of Monte Carlo samples. A smaller MCSE value indicates superior sampling performance, highlighting the effectiveness of the sampling process in capturing the true underlying distributions [25].

In the presence of financial frictions, a risk-pricing system could effectively mitigate behavioral anomalies. For instance, the impact of over-optimism on risk-taking behaviors and expected returns in banks has been widely demonstrated. The phenomenon of credit expansion can be understood through this perspective, as discussed in ref. [29]. Additionally, ref. [30] explores an economy characterized by financial frictions, in which a regulator conducts a test that reveals external information about a firm’s quality to investors, while the firm simultaneously discloses verifiable internal information regarding its quality. This interplay can significantly affect credit ratings and valuations.

Other researchers (see ref. [31]) observe that investors often exhibit insensitivity as the relationship between subjective expectations and actions becomes more pronounced, when their expectations align closely with rational expectations. Their research highlights the necessity of integrating weak transmission effects into belief-based asset-pricing models.

4.2. Risk Assessment and Profitability by Industry

In this section, we present a detailed analysis of our findings by classifying our sample according to industry. To ensure accuracy, we include only samples with more than 500 observations. Next, we conduct Ordinary Least Squared (OLS) regressions with Sellers categorized into five industries: Accommodation and Food Services; Construction; Manufacturing; Professional, Scientific, and Technical Services; and Real Estate, Rentals, and Leasing.

The industry-specific analysis reveals significant heterogeneity in risk/return dynamics across these five major sectors, with the SURF Score risk metric demonstrating consistent predictive power while other variables exhibit sector-specific behaviors that warrant deeper investigation.

For both RETURN (Panel A) and IRR with SURF (Panel B) as response variables, as presented in

Table 4. Linear OLS Estimation of the relationship between risk and return by industry. This table reports the coefficients, with their t-statistics in parentheses, and the level of significance of the OLS regressions sorted by five industries (Accommodation and Food Services, Construction, Manufacturing, Professional Scientific and Technical Services, and Real Estate, Rentals, and Leasing). Dependent variables are RETURN in Panel A; Internal Rate of Return (IRR) with SURF in Panel B; and Internal Rate of Return (IRR) without SURF in Panel C. The independent variables include the invoice scoring (SURF), calculated as the Seller’s SURF Score times Obligor SURF Score divided by 100; discount rate (DISCOUNT RATE), computed as the difference between invoice amount and financed amount divided by invoice amount; the number of days beyond the due date before repayment of the financing is made (DAYS BEYOND TERM); and invoice amount (SIZE) expressed as the natural logarithm of the dollar amount. For the relevance of estimates, we drop industries with fewer than 500 observations, leaving the following industries remaining: Accommodation and Food Services, with 1089 observations; Construction, with 1231 observations; Manufacturing, with 7081 observations; Professional, Scientific, and Technical services, with 575 observations; and Real Estate, Rentals, and Leasing, with 8027 observations. The study period spans from 23 April 2020, to 30 September 2022. Regressions’ constants (CONS), number of observations (N), F-statistics, and R-squared are also reported in this table. F-statistics reflect the overall significance of the joint test under the null hypothesis that all regression coefficients are equal to 0. R-squared reports the proportion of the variation in profitability measures explained by the explanatory variables. The superscripts *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively.

Panel A. RETURN
	Accommodation and Food Services	Construction	Manufacturing	Professional Scientific, and Technical Services	Real Estate, Rentals, and Leasing
SURF	−0.016 *** (−5.41)	−0.024 *** (−8.45)	−0.033 *** (−27.55)	−0.036 *** (−13.11)	−0.058 *** (−87.69)
DISCOUNT RATE	0.052 *** (7.15)	−0.007 (−0.76)	−0.091 *** (−20.52)	0.058 *** (8.06)	−0.005 * (−1.85)
DAYS BEYOND TERM	0.005 *** (9.91)	0.005 *** (8.89)	0.004 *** (18.86)	0.002 *** (4.50)	0.001 *** (12.09)
SIZE	−0.026 *** (−30.67)	−0.025 *** (−26.61)	−0.019 *** (−48.48)	−0.018 *** (−20.81)	−0.010 *** (−52.39)
CONS	0.124 *** (29.68)	0.136 *** (27.61)	0.131 *** (73.92)	0.117 *** (30.50)	0.112 *** (41.15)
N	1089	1231	7081	575	8027
F-Statistics	62.98 (0.000)	93.49 (0.000)	87.39 (0.000)	77.35 (0.000)	78.92 (0.000)
R-Squared	0.885	0.834	0.848	0.876	0.874
Panel B. IRR with SURF
	Accommodation and Food Services	Construction	Manufacturing	Professional Scientific, and Technical Services	Real Estate, Rentals, and Leasing
SURF	−0.049 *** (−44.74)	−0.087 *** (−48.81)	−0.059 *** (−24.13)	−0.036 *** (−25.71)	−0.039 *** (−12.83)
DISCOUNT RATE	0.024 (1.00)	0.111 *** (4.49)	0.061 *** (5.74)	0.196 *** (5.23)	0.049 ** (3.14)
DAYS BEYOND TERM	0.070 *** (4.11)	0.043 ** (2.68)	0.042 *** (8.20)	0.041 (1.59)	0.044 *** (9.40)
SIZE	0.089 ** (3.00)	0.042 (0.02)	0.015 * (1.62)	−0.027 (−0.59)	0.010 *** (10.27)
CONS	0.518 *** (36.15)	0.500 *** (35.75)	0.470 *** (110.74)	0.475 *** (24.08)	0.462 *** (111.40)
N	1089	1231	7081	575	8027
F-Statistics	76.36 (0.000)	84.76 (0.000)	67.75 (0.000)	31.65 (0.000)	43.34 (0.000)
R-Squared	0.793	0.822	0.829	0.754	0.820
Panel C. IRR without SURF
	Accommodation and Food Services	Construction	Manufacturing	Professional Scientific, and Technical Services	Real Estate, Rentals, and Leasing
DISCOUNT RATE	−0.177 ** (−3.03)	0.166 * (1.95)	0.278 *** (5.52)	0.600 *** (6.81)	0.154 ** (3.05)
DAYS BEYOND TERM	−0.120 *** (−26.10)	−0.110 *** (−17.83)	−0.105 *** (−37.21)	−0.117 *** (−18.64)	−0.142 *** (−93.52)
SIZE	−0.059 *** (−9.45)	−0.086 *** (−10.89)	−0.080 *** (−20.56)	−0.044 *** (−5.58)	−0.053 *** (−25.51)
CONS	0.881 *** (22.64)	0.932 *** (17.40)	0.851 *** (36.25)	0.684 *** (14.18)	0.888 *** (66.06)
N	1089	1231	7081	575	8027
F-Statistics	76.59 (0.000)	87.78 (0.000)	93.45 (0.000)	66.97 (0.000)	98.76 (0.000)
R-Squared	0.420	0.345	0.358	0.550	0.634

Source: Authors’ own creation.

, the SURF variable consistently demonstrates a significantly negative relationship across all industries at the 1 percent confidence level. This finding supports the theory that higher risks are associated with higher returns, while the opposite holds true when relevant risk assessments are considered. These results further strengthen our hypothesis that a thorough evaluation of risk can lead to better investment opportunities by effectively aligning investors’ risk and return preferences.

For instance, the Real Estate, Rentals, and Leasing sector shows the strongest sensitivity with a coefficient of −0.058, suggesting that risk assessment is particularly critical in real estate investments, possibly due to market volatility and leverage considerations. The Professional, Scientific, and Technical Services sector demonstrates the second-highest sensitivity (−0.036), indicating that service-based businesses may have more transparent risk profiles. The Accommodation and Food Services sector shows the lowest sensitivity (−0.016), potentially reflecting the sector’s inherent volatility, making risk differentiation less pronounced. The Manufacturing (−0.033) and Construction (−0.024) sectors fall in the middle range, suggesting moderate risk sensitivity. We conclude that the magnitude differences suggest that risk-based pricing strategies should be calibrated differently across industries, with real estate requiring the most pronounced risk-adjusted pricing.

Upon examining Panel A (RETURN) by industry, we observe that the discount rate (DISCOUNT RATE) exhibits significantly positive patterns for industries such as Accommodation and Food Services (+0.052), as well as Professional, Scientific, and Technical Services (+0.058). Conversely, the discount rate shows a negative pattern for the Construction (insignificant at −0.007), Manufacturing (−0.091), and Real Estate, Rentals, and Leasing (−0.005) sectors.

Possible explanations for the positive discount effect in service industries include such hypotheses as the following: (1) higher discount rates in service industries may reflect seasonal cash flow patterns such that businesses accept higher costs during peak periods; (2) the positive relationship may indicate that these industries can pass through financing costs to customers more effectively; or (3) service businesses may use invoice financing strategically during growth phases, during which time higher dilution is offset by increased business volume.

Possible explanations for the negative discount effect in asset-heavy industries include: (1) Manufacturing’s strong negative relationship (−0.091) likely reflects economies of scale, namely that larger manufacturers may be able to negotiate better financing terms; (2) Construction’s neutral relationship may suggest project-specific dynamics dominate over general financing patterns; and (3) Real Estate’s minimal negative effect may indicate that property values provide sufficient collateral to minimize dilution impact.

The DAYS BEYOND TERM variable represents the actual amount of time (measured in days) beyond the invoice due date when the invoice funding plus discount is fully repaid to the Funder.

Interestingly, Panel A (RETURN) shows positive effects. All industries show small but significant positive coefficients (0.001–0.005): (1) Accommodation and Food Services: 0.005 (highest sensitivity to term length); (2) Construction: 0.005 (equal sensitivity to Accommodation and Food Services); (3) Manufacturing: 0.004 (moderate sensitivity); (4) Professional, Scientific, and Technical Services: 0.002 (lower sensitivity); and (5) Real Estate, Rentals, and Leasing: 0.001 (lowest sensitivity). The foregoing reflects the fact that each projected additional day beyond term increases returns by 0.1 to 0.5 percentage points, with service industries displaying relatively greater sensitivity.

Panel B (IRR with SURF) shows positive effects as well. The coefficients increase substantially when using time-adjusted returns: (1) Accommodation and Food Services: 0.070 (14x increase from Panel A); (2) Construction: 0.043 (8.6x increase); (3) Manufacturing: 0.042 (10.5x increase); (4) Real Estate, Rentals, and Leasing: 0.044 (44x increase); and (5) Professional, Scientific, and Technical Services: 0.041 (not significant, but large magnitude). The IRR methodology reveals that longer payment terms create much more value than simple return calculations suggest.

However, Panel C (IRR without SURF) exhibits negative effects. All coefficients turn strongly negative (−0.105 to −0.142). This suggests that, without proper risk adjustment, longer terms appear to hurt rates of return. Additionally, the negative relationship likely reflects the condition that riskier borrowers tend to have longer repayment periods, thereby indicating that poor credit quality correlates with both extended repayment times and lower rates of return.

The dramatic difference between Panels B and C reveals that the value of the DAYS BEYOND TERM variable emerges when risk is properly assessed. In fact, without risk adjustment (Panel C), longer terms appear harmful because they correlate with higher-risk borrowers. With risk adjustment (Panel B), the time value of money emerges, showing that longer terms can create substantial value.

From the Funders’ perspective, longer days beyond term should command a higher discount rate, especially in service industries; separate effects of payment timing from underlying credit quality and understanding days-beyond-term patterns can improve cash flow forecasting.

From the Sellers’ perspective: (1) service businesses may have more flexibility in negotiating extended terms; (2) understanding that longer repayment terms increase Funder costs can inform negotiation strategies; and (3) actual payment timing significantly affects financing costs.

As for the SIZE effects that capture economies of scale across industries, all industries show negative size effects on returns (Panel A), but with varying magnitudes. For instance, the following results were obtained: Accommodation and Food Services: −0.026 (highest impact); Construction: −0.025; Manufacturing: −0.019; Professional, Scientific, and Technical Services: −0.018; and Real Estate, Rentals, and Leasing: −0.010 (lowest impact).

However, Panel B shows a reversed effects of size. The dramatic sign changes in IRR with SURF analysis suggest that risk-adjusted metrics reveal hidden scale benefits that basic return calculations obscure.

In comparing Panel A (RETURN) and Panel B (IRR with SURF), the shift from mildly positive relationships in Panel A to strong positive relationships in Panel B reveals important insights: (1) time-value recognition—the IRR methodology better captures the benefits of longer financing terms; (2) Industry variation in time sensitivity—Accommodation and Food Services: 0.005 → 0.070 (14x increase); Construction: 0.005 → 0.043 (8.6x increase); and Manufacturing: 0.004 → 0.042 (10.5x increase); (3) strategic implications—longer-term financing arrangements create disproportionate value in Accommodation and Food Service sectors, suggesting that these industries should prioritize extended payment terms.

Regarding models’ performance and explanatory power, Panel A (RETURN) shows the high explanatory power, with the R-squared result varying in a range of 0.834 to 0.885, suggesting that the model captures most of the return variation, while Panel B (IRR with SURF) is slightly lower but still strong (0.754 to 0.829), indicating that risk adjustment adds complexity. Panel C (IRR without SURF) is significantly lower (0.345 to 0.634), demonstrating the critical importance of risk adjustment. F-Statistics for all models are highly significant.

While Table 4 provides valuable insights into industry-specific risk/return relationships, the analysis reveals significant opportunities for deeper investigation. The consistent power of the SURF Score metric across industries validates the risk assessment approach, but the substantial variation in other coefficients suggests that industry-specific factors also play crucial roles that may warrant separate industry-specific modeling strategies (in fact, while not implemented at the time, the creation of industry-specific models was part of the long-term SURF Score modeling strategy). The dramatic differences between basic return measures and risk-adjusted IRR calculations underscore the critical importance of sophisticated risk measurement in investment decision-making.

This study also highlights the importance of integrating robust “risk-pricing approaches in investment strategies, thereby contributing to more effective risk-management practices within diverse industries (for risk-pricing and flight-to-safety theory, see, for instance, refs. [4,32]).

In sum, our findings contribute to the existing body of research addressing the significant issue of the high information asymmetry prevalent in small firms. This asymmetry frequently results in challenges related to decision-making and resource allocation, creating a disconnect between the firms’ risk profiles and the information accessible to external stakeholders. We underscore the essential role that a robust risk-scoring system can play in alleviating these challenges. By offering a standardized framework for evaluating and communicating risk, such systems can effectively diminish information asymmetry, thereby fostering enhanced trust and increased investment opportunities. This finding is in line with the conclusions drawn by previous studies, including those by refs. [12,17], which emphasized the necessity for improved information-sharing mechanisms to bolster the transparency and stability of small enterprises.

We conclude that risk pricing is a vital component in guiding investors regarding their risk-return preferences and empowering them to make informed decisions that align with their investment strategies. The accurate reflection of asset-risk level and risk-pricing mechanisms supports flight-to-safety strategies. Consequently, a robust risk-pricing framework is essential for fostering efficient markets and assisting investors in navigating economic, financial, political, and legal market conditions.

In the first order, this paper validates Crowdz’s SURF Score risk-scoring system as a paradigm shift from static to real-time risk assessment. Unlike traditional models using significantly lagged historical data, the SURF Score’s four-step, continuously updated approach captures immediate business changes through real-time accounting, banking, and transactional data streams.

The SURF Score’s innovative quality proved mission-critical during the global COVID-19 pandemic and associated financial crises when conventional models failed to accurately and fully account for rapidly changing economic dynamics, whereas the SURF Score technology automatically and seamlessly adapted to these rapidly changing conditions.

The empirical findings confirm consistent cross-industry performance across all industries as well as the five selected industry sectors, critical information-asymmetry reduction enabling efficient capital allocation, and flight-to-safety portfolio diversification based on real-time risk intelligence.

Possible extensions of the study include: (1) collecting new transactional data based on the SURF Score’s validated real-time data foundation, thereby enabling advanced AI applications; (2) testing a wider range of industry classifications once more data can be obtained; (3) testing for differential effects across geographies, again once a sufficient amount of data can be acquired; (4) examining the relative effects of differing SURF Score calculation models; and (5) applying advanced econometrics (e.g., machine-learning approaches, quantile regression, time-to-default modeling by industry, out-of-sample testing, and model stability across economic cycles).

For all of the above reasons, the SURF Score risk scoring framework demonstrates the successful transition from backward-looking credit analysis to forward-looking, AI-ready risk intelligence, thereby establishing the blueprint for next-generation financial risk assessment across broader financial-services applications.

5. Conclusions and Extensions

The 2019–2021 global COVID-19 pandemic and resulting challenges to supply chain management around the globe led to a cascading disruptive effect on the payment systems in the working capital management of firms. As is the case during times of crisis, the Seller of the receivables faced a liquidity crunch due to a lack of trust or information asymmetry between the Seller and the Funder (investor). The pressing need to address these cash shortfalls led to innovation by a FinTech startup, Crowdz, in developing its SURF (Sustainability, Underwriting, Risk and Financial) risk-scoring technology to provide a robust score to the invoice-financing market and to facilitate liquidity in this market.

Our analysis shows that the SURF Score is highly effective in capturing the risks to counterparties (Funder and Seller) in these transactions and, consequently, providing the risk-appropriate return (higher return for higher risk and vice versa) to the Funders both in general and across industries. A comparative analysis shows that the use of SURF Score technology generates significantly higher risk-appropriate annualized internal rates of return (IRR) as compared to nonuse of the SURF Score risk-scoring system in these transactions. Our results are robust overall and across industries.

In addition to providing liquidity to the secondary short-term credit markets, Crowdz’s SURF technology also offers Funders substantial and financially beneficial diversification opportunities with numerous invoices of differing amounts and SURF Scores across a wide range of industries.

Furthermore, our findings suggest that incorporating advanced analytics, utilizing broader datasets, and implementing technological solutions can greatly enhance risk-pricing efficiency and encourage innovation in financial products. This research not only extends corporate finance theory to include third-party financing but also opens avenues for institutional investors and government regulatory bodies to create more nuanced regulatory and analytical frameworks that promote financial inclusion and market stability.

In addition to those enhancements stated above, the future course of this research also should include investigating how the presence of AI (artificial intelligence) in risk-scoring systems can specifically benefit participants in the secondary short-term credit markets.

The use of AI and machine learning in enhancing future credit models can help specifically in two areas: (1) creating large sets of test data, including the parameters necessary to stress-test the models; (2) rapidly testing large numbers of different modeling frameworks and methods; (3) intelligently extrapolating small amounts of data into large data palettes to enable more rapid segmentation of models and results; (4) adding an increasing range of influential variables into the models; and (5) deploying generative AI technologies to frame scoring in real-world language so that the average user can understand and interpret in real-time what the data and relationships mean. These innovations will increase the positive impact of real-time risk scoring and will drive additional financial efficiencies in small- and medium-sized company credit scoring.