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Abstract

This study presents a teaching case that analyzes the applicability of the Z-Score bankruptcy prediction model to manufacturing firms listed in Hong Kong. Although the Z-Score model has been studied extensively, there are very few studies in the context of the Hong Kong stock market. Given that the Hong Kong stock market has high retail investor participation and low liquidity, whether the Z-Score model is relevant to Hong Kong investors is an important but unanswered question. The Z-Score model predicts the bankruptcy of firms by considering financial ratios involving firm liquidity, solvency, profitability, leverage, and activity. Financial and stock return data on the manufacturing firms listed in the Hong Kong Stock Exchange from 1981 to 2020 are collected from Thomson Reuters Datastream to examine the applicability of the Z-Score model in Hong Kong. Firms are then classified into bankrupt or non-bankrupt groups based on their Z-Scores. The annual stock returns in the subsequent year are analyzed for the two groups after classification. When the Z-Score threshold is set at 0, investing in the non-bankrupt group and short-selling the bankrupt group earns an annual return of 11.99% in the subsequent year. The results are robust to alternative periods and lagged values of the Z-Score. This suggests that stock prices do not reflect all the accounting data and that investors can increase their returns using the Z-Score model. As retail investors have limited resources, it may be difficult for them to fully implement the Z-Score model for a portfolio that consists of thousands of stocks. However, they can still avoid substantial losses by not investing in firms with low Z-Scores.

Keywords

Z-Score model data analytics financial distress investment return teaching case

Introduction

This paper presents a teaching case that provides students, teachers, and researchers with an overview of the Z-Score bankruptcy prediction model and its application in identifying poorly performing firms listed on the Hong Kong Stock Exchange. It also shows investors how to increase their investment returns by analyzing listed firms’ accounting ratios involving liquidity, solvency, profitability, leverage, and activity.

Various corporate default prediction techniques have been extensively studied. In general, they can be broadly classified into three generations of statistical models: discriminant analyses, binary response models, and hazard models.¹ The first generation of corporate default studies focuses on discriminant analyses, which generate credit score for rankings of default risk based on reduced-form models with explanatory variables related to corporate default. A firm is predicted to be in financial distress if the credit score is above a certain threshold. The works by Beaver,² Altman,³ and Mare et al.⁴ are some well-known studies that generate credit scores based on various financial ratios. The second generation of corporate default studies focuses on binary response models, which predict a firm’s state as either normal or in default by logistic or probit function. Since the representative work by Ohlson,⁵ many variations of the binary response models have been proposed by scholars over the last four decades, such as Zmijewski,⁶ Foreman,⁷ Campbell et al.,⁸ Kukuk and Ronnberg,⁹ and Aretz et al.¹⁰ The third generation of corporate default studies focuses on hazard models, which calculate the probability of default based on survival analysis with an explicit hazard function. Shumway ¹¹ is among the first cohort of scholars to predict corporate default with the Cox’s hazard regression model. Since then, Chava and Jarrow,¹² Nam et al.,¹³ Bonfim,¹⁴ Dakovic et al.,¹⁵ Duan et al.,¹⁶ Figlewski et al.,¹⁷ Machek and Hnilica,¹⁸ Tian et al.,¹⁹ and Traczynski ²⁰ extend the hazard models to incorporate, inter alia, industry effects, market variables, macroeconomic factors, credit ratings, and multiple time periods. Although each statistical model merits further studies and examination, this teaching case focuses on the Z-Score model because it is a relatively simple and straightforward discriminant analytical model which enables students without advanced statistical background to comprehend the corporate default prediction process. When compared to the binary response models and hazard models, it is easier for students to learn and apply the discriminant analytical model (i.e., the Z-Score model) to real-world data in class.

Altman³ first proposed the Z-Score bankruptcy prediction model using accounting ratios to predict financial distress. Over the years, different variations of the Z-Score bankruptcy prediction model have been developed.^21–27 The basic principle in all of these models is that accounting ratios are informative and value-relevant to investors and hence can be used to predict financial distress.

The efficacy of the accounting-based prediction model has been tested by many empirical studies.^22,28–30 Generally, the findings conclude that accounting-based prediction models have high predictive accuracy for firm financial distress. Hence, the Z-Score model is used by many researchers and practitioners worldwide as an important tool to predict firm bankruptcy.

Although the performance of the Z-Score model in predicting financial distress is widely recognized, the relevant association between the Z-Score and the subsequent stock returns of listed firms is unclear. On the one hand, Markowitz’s classic portfolio theory asserts that there is a tradeoff between investment returns and risk.³¹ Investors should be compensated for bearing risk such that the risk-compensated returns of all of the alternative investments are identical in equilibrium. Based on this argument, investing in firms with a low Z-Score carries a high bankruptcy risk and therefore should be compensated by higher stock returns than investing in firms with a high Z-Score. In other words, there should be a negative relationship between the Z-Score and the subsequent stock returns. This argument is ingrained in the concept of the default risk premium as documented by Aretz et al.¹⁰ On the other hand, one may argue that the stock markets are inefficient and investors price stocks irrationally. For example, the Hong Kong stock market has a high retail investor participation rate and low liquidity, making it vulnerable to bias caused by investor sentiment. According to an international survey by Finder,³² 57% of adults in Hong Kong have invested in shares, which is much higher than the world average of 34% (see Figure 1). The World Bank’s DataBank also reveals that Hong Kong Exchanges and Clearing Limited has a market turnover of just 59%, which is much lower than that of other major stock markets (e.g., the United States, 109%; China, 207%; Japan, 119%) (see Figure 2). With a high retail investor participation rate and low liquidity, the prices of stocks listed in Hong Kong may not be rational and may not incorporate all of the information revealed by accounting figures. Therefore, the risk of financial distress reflected by accounting ratios may not be fully priced, and investors may get poor returns by investing in firms with low Z-Scores. In other words, there could be a positive association between the Z-Score and the subsequent stock returns.

Figure 1.

Retail investor participation by country. This figure presents retail investor participation rates by country from a survey of 23,659 people in 16 countries. Source: Finder (2021).

Figure 2.

Stock market turnover ratio by jurisdiction. This figure presents the stock market turnover ratio by jurisdiction. Source: DataBank by the World Bank.

Given that the positive or negative effect of the Z-Score on the subsequent stock returns is primarily an empirical issue, this teaching case analyzes stocks listed in Hong Kong from 1981 to 2020 to find empirical evidence for the relationship between the Z-Score and stock returns, and it examines whether the five accounting ratios (i.e., liquidity, solvency, profitability, leverage, and activity) in the Z-Score formula are informative and value-relevant to investors. The findings contribute to the literature in at least two ways. First, this teaching case sheds light on the inconclusive relationship between the Z-Score and stock returns. While studies focus on the performance of the Z-Score model in predicting firm bankruptcy, there is limited evidence regarding whether the Z-Score improves investor returns. This teaching case fills this gap by examining this topic using listed firms in the last four decades. Second, very few studies investigate the application of the Z-Score model to firms in Hong Kong. Most of the Z-Score studies focus on firms in the United States, the United Kingdom, and European countries. As the Hong Kong Stock Exchange is the fourth-largest stock market in the world by market capitalization and has a high retail investor participation rate and low liquidity, a teaching case of the Z-Score model focused on the Hong Kong market is timely and relevant to investors.

This teaching case also contributes to the teaching of investment, accounting, and financial analysis by enhancing students’ understanding of corporate default prediction technique and by letting students have hands-on experiences in dealing with real-world data. Students will have the opportunity to apply the Z-Score model to identify poorly performing manufacturing firms listed in the Hong Kong Stock Exchange. In addition, they will also learn how to enhance the returns of their stock investment portfolios by avoiding the investment in firms with low Z-Score. Upon completion of this teaching case, students are expected to achieve the following learning outcomes:

1. Identify the accounting ratios that are relevant to the prediction of corporate default.

2. Apply the Z-Score model to a firm’s accounting data and analyze the model results.

3. Interpret the implications of Z-Score model on stock selection and portfolio return.

This teaching case is designed for accounting and finance senior undergraduate students who have some basic knowledge about financial statements, investment, and statistics. Students should have taken introductory undergraduate courses on the above subjects before completing this teaching case. They should be able to understand the fundamentals of financial statements, evaluate portfolio performance, and comprehend the statistical analysis of financial models. When teachers discuss this teaching case with students, four teaching scenarios are proposed as follows.

Scenario 1: Teachers introduce the concept of discriminant analyses and the Z-Score model. Students are then asked to download accounting data following the instructions in this teaching case and to mimic the results. This scenario enables students to have hands-on experience in handling real-world data.

Scenario 2: Teachers follow the instructions in this teaching case and demonstrate the application of Z-Score model to analyze manufacturing firms listed in Hong Kong. Students are then asked to apply the Z-Score model to other industries, such as financials, utilities, health care, real estate, etc., and determine the appropriate Z-Score threshold for each industry. This scenario enables students to extend the application of the Z-Score model to industries other than manufacturing.

Scenario 3: Following the steps in this teaching case, teachers can demonstrate the application of Z-Score model to analyze manufacturing firms listed in Hong Kong. Students are then asked to apply the Z-Score model to the manufacturing firms listed in other countries, such as China, the United States, the United Kingdom, etc., and determine the appropriate Z-Score threshold for each country. They will analyze the applicability of the Z-Score model across jurisdictions and appreciate the effect of market characteristics on the Z-Score threshold.

Scenario 4: After demonstrating the application of the Z-Score model to manufacturing firms listed in the Hong Kong Stock Exchange from 1981 to 2020, teachers can ask students to apply the Z-Score model to specific periods, such as the recent year, the financial crisis in 2008, and the bursting of dot-com bubble in 2001, to analyze whether the applicability of the Z-Score model is time-specific.

The remainder of this paper is organized as follows. Section Key concepts provides the context for this study and discusses the Z-Score bankruptcy prediction model together with its corresponding accounting ratios. It also explains the insights into the Z-Score model that are relevant to students, teachers, researchers, and practitioners. Section Key lessons presents the findings of applying the Z-Score model to Hong Kong-listed firms and explains the key lessons using evidence-based heuristics. Section Discussion describes the teaching plan and potential re-use of accounting data to develop more teaching cases in the future. Section Implications concludes the paper by describing the implications of the study for investment professionals and the challenges of implementing the Z-Score model in real-world scenarios.

Key concepts

This section presents an overview of the Z-Score bankruptcy prediction model. I describe each component of the model and then download the required data to fit the Z-Score model and classify listed firms into different groups based on the Z-Score threshold.

Z-Score Model

When Altman first proposed the Z-Score model to predict firm bankruptcy,²¹ he considered 22 financial ratios to be potentially important for evaluation. These variables were further classified into five categories: liquidity, solvency, profitability, leverage, and activity. Altman studied 33 firms from the manufacturing industry that filed bankruptcy petitions between 1946 and 1965, and their paired sample was chosen on a stratified random basis to identify the most representative ratio in each category together with its corresponding weight. Based on this analysis, he proposed the following Z-Score model:

Z = 1.2 X_{1} + 1.4 X_{2} + 3.3 X_{3} + 0.6 X_{4} + 0.999 X_{5}

(1)

Where X₁ = Working Capital/Total Assets is a liquidity ratio, calculated as total working capital scaled by the firm’s total assets. A high value implies that the current assets exceed current liabilities and hence the firm has high liquidity.

X₂ = Retained Earnings/Total Assets is a solvency ratio that represents the cumulative earnings retained by the firm over the years scaled by the firm’s total assets. A high value implies that the firm has more retained earnings, which translates into greater flexibility during adversity (e.g., financial crises and economic downturns). Hence, a high value of X₂ denotes high solvency.

X₃ = Earnings before Interest and Taxes/Total Assets is a profitability ratio that measures the earnings generated per unit of asset. A high value implies that the firm can generate earnings and hence has high profitability.

X₄ = Market Value of Equity/Book Value of Total Liabilities is a leverage ratio that reflects the capital structure by comparing the value of equity to liabilities. A high value signifies that the firm has a higher value of equity or lower value of liabilities and hence has low leverage.

X₅ = Sales/Total Assets is an activity ratio that measures the efficiency of the firm in generating sales by scaling the total sales to total assets. A high value represents efficient operations because more sales are generated per unit of asset.

The Z-Score incorporates different dimensions of the firm’s operations and predicts bankruptcy because a low Z-Score implies that a firm has low liquidity, poor solvency, low profitability, high leverage, and low efficiency. Altman proposed Z-Score thresholds of 1.8 and 3 (i.e., firms with a Z-Score below 1.8 are very likely to go bankrupt, while those with a Z-Score above 3 are not likely to go bankrupt).²¹ After several decades of development, Altman revised the Z-Score threshold to 0 (i.e., a firm is vulnerable if its Z-Score is below 0).³³

Data collection

All of the stock return data and accounting figures are collected from Thomson Reuters Datastream (Datastream). As this study focuses on firms listed in Hong Kong, the sample is confined to stocks listed on the Hong Kong Stock Exchange between 1981 and 2020, spanning 40 years of data. Furthermore, only manufacturing firms¹ are included in the sample because the financial ratios for non-manufacturing firms are very different from those of manufacturing firms. Altman’s Z-Score model was also applied to only manufacturing firms. Next, I extract the accounting information required as the input for the Z-Score model from Datastream. The accounting data and Datastream codes are total assets (WC02999), current assets (WC02201), current liabilities (WC03101), retained earnings (WC03495), earnings before interest and tax (WC18191), the market value of equity (MV), the book value of total liabilities (WC03351), and sales (WC01001). The total return index (RI) for each listed firm is also downloaded to analyze stock returns. I use total returns instead of stock prices because the former considers dividend distributions and assumes that dividends are re-invested to purchase additional units of the firm stock on the ex-dividend date, which is a more realistic measurement for investor returns. Last, I remove firms with missing data on any of the above accounting information or the total return index. I winsorize the values of the total return index at the 5th and 95th percentiles to minimize the influence of outliers. The final sample consists of 6,823 observations from manufacturing firms listed in Hong Kong between 1981 and 2020.

As this teaching case is designed for students without any prior experience in using DataStream, this paragraph serves as a step-by-step guide to help them download the firm data required for corporate default prediction. First, open an Excel file with the add-ins “Refinitiv Eikon – Microsoft Office” installed and enabled. Second, choose “Time Series Request” under the tab “Refinitiv Eikon Datastream.” A window that looks like Figure 3 will pop up. Third, click “Find Series” and select manufacturing firms listed in the Hong Kong Stock Exchange. Fourth, click “Datatypes” and select the DataStream codes described in the previous paragraph. Fifth, input the start date as 31/12/1981 and end date as 31/12/2020. Finally, click the “Submit” button. The requested accounting data and stock return data for the whole sample will then be downloaded from DataStream. See Figure 3 for a screenshot of the data-collection toolkit “Refinitiv Eikon Datastream Excel Formulas.” For students’ easy reference, the whole sample is also available for download at the public data repository “Open Science Framework (OSF),” with web link https://osf.io/hctv6/?view_only=728bfa3165564839bb67e090218224ca.

Figure 3.

Screenshot of the data-collection toolkit “refinitiv eikon datastream excel formulas.”

Bankrupt group versus non-bankrupt group

The Z-Score threshold used to classify firms into the bankrupt and non-bankrupt groups is subtle. Altman proposed that firms with a Z-Score below 1.8 are likely to go bankrupt, while firms with a Z-Score above 3 are financially sound.²¹ However, Altman later revised the Z-Score threshold to 0.³³ As the Hong Kong stock market has low liquidity and a high retail investor participation rate, it is unclear whether the above thresholds are applicable to Hong Kong-listed firms. Furthermore, even if firms are accurately classified into the bankrupt and non-bankrupt groups, whether the subsequent stock returns are associated with the Z-Score threshold is questionable. In Section Key lessons, I will present empirical evidence of the association among stock returns and different Z-Score thresholds in the context of Hong Kong listed manufacturing firms.

Key lessons

This section documents the results of applying the Z-Score model to Hong Kong-listed firms. The subsequent stock returns of the bankrupt and non-bankrupt groups with different Z-Score thresholds are also discussed. I then explore how the Z-Score model helps investors increase their returns.

Z-Score and stock returns

Panel A of Table 1 shows the descriptive statistics of the annual stock returns for the entire sample. Before classifying the firms into the bankrupt and non-bankrupt groups, the average annual stock returns for the entire sample is 4.69%, with a standard deviation of 49.19%. The median annual return is −4.77%, which means that more than half of the listed firms have negative returns during the sample period.

Table 1.

Descriptive statistics of annual stock returns.

Mean	Std. Dev.	Q1	Median	Q3	N
Panel A: Whole Sample
0.0469	0.4919	−0.3028	−0.0477	0.2853	6,823
Panel B: Bankrupt Group with a Z-Score Threshold of 3
0.0518	0.4960	−0.2959	−0.0500	0.2853	3,715
Panel C: Non-Bankrupt Group with a Z-Score Threshold of 3
0.0410	0.4870	−0.3129	−0.0458	0.2853	3,108
Panel D: Bankrupt Group with a Z-Score Threshold of 1.8
0.0337	0.5046	−0.3186	−0.0803	0.2761	1,968
Panel E: Non-Bankrupt Group with a Z-Score Threshold of 1.8
0.0522	0.4867	−0.2927	−0.0349	0.2864	4,855
Panel F: Bankrupt Group with a Z-Score Threshold of 0
−0.0646	0.5177	−0.4283	−0.2105	0.1440	481
Panel G: Non-Bankrupt Group with a Z-Score Threshold of 0
0.0553	0.4889	−0.2918	−0.0377	0.2913	6,342

Panel A documents the descriptive statistics of annual stock returns for the whole sample. Panels B and C present the descriptive statistics of the subsequent annual stock returns after the firms are classified into the bankrupt and non-bankrupt groups, respectively, with a Z-Score threshold of 3. Panels D and E present the descriptive statistics of the subsequent annual stock returns after the firms are classified into the bankrupt and non-bankrupt groups, respectively, with a Z-Score threshold of 1.8. Panels F and G present the descriptive statistics of the subsequent annual stock returns after the firms are classified into the bankrupt and non-bankrupt groups, respectively, with a Z-Score threshold of 0.

Panels B and C of Table 1 present the descriptive statistics of the annual stock returns in the year after the firms are classified into the bankrupt and non-bankrupt groups using the Z-Score threshold of 3. The bankrupt group has a lower median and higher mean annual stock returns than the non-bankrupt group. Moreover, the differences in the mean and median values of the stock returns between the two groups are not economically significant. It is difficult to draw any conclusion, as there is no evidence that there is a difference between the stock returns of the bankrupt and non-bankrupt groups. Hence, the Z-Score threshold of 3 does not seem relevant for Hong Kong investors.

Next, I divide the firms in my sample into the bankrupt and non-bankrupt groups based on the Z-Score threshold of 1.8. Panels D and E of Table 1 show their stock returns in the subsequent year. The mean and median annual returns of the bankrupt group are lower than those of the non-bankrupt group by 1.85% and 4.54%, respectively. However, the difference between the means of the bankrupt and the non-bankrupt groups is not statistically significant. The t-test for difference in means yields a value of 1.38 with a p-value of 0.167. I find no evidence to support that the Z-Score threshold of 1.8 helps investors increase their returns.

Altman suggests that the Z-Score threshold of 0 is more applicable to recent data;³³ hence, I use this revised threshold to classify firms into bankrupt and non-bankrupt groups. Panels F and G of Table 1 show the results. The mean and median annual returns of the bankrupt group are lower than those of the non-bankrupt group by 11.99% and 17.28%, respectively, and are highly economically significant. The t-test to compare the means of annual returns between bankrupt and non-bankrupt groups yields a t-statistic of 4.92 with a p-value of less than 0.0001, suggesting that the difference between the annual return of the bankrupt and non-bankrupt groups is highly statistically significant. By purchasing the non-bankrupt group and short-selling the bankrupt group, investors can earn an annual return of 11.99%. These results suggest that stock prices do not reflect all of the accounting information and that investors price firms irrationally. This is not surprising, as the Hong Kong stock market has low liquidity and a high retail investor participation rate. In short, of all the alternative Z-Score thresholds proposed by Altman, the Z-Score threshold of 0 is most applicable to Hong Kong-listed firms and investors.

Figure 4 presents the distributions of the annual stock returns of the whole sample, bankrupt group, and non-bankrupt group. When the Z-Score threshold is set at 0, 65% of the firms in the bankrupt group have negative stock returns in the subsequent year, suggesting that the Z-Score threshold of 0 is highly relevant to Hong Kong investors.

Figure 4.

Distributions of stock returns.

Performance in different time periods

Although the results in Section Z-Score and stock returns suggest that the Z-Score threshold of 0 increases the return of Hong Kong investors, one may be skeptical as to whether such an observation is time-specific. In other words, does the conclusion change when the Z-Score threshold of 0 is used for different periods? To address this question, the whole sample is divided into two subsamples. The post-millennium subsample consists of data from 2001 to 2020, and the pre-millennium subsample consists of data from 1981 to 2000. The two subsamples are analyzed using the Z-Score model with a threshold of 0 separately, and the results are presented in Table 2.

Table 2.

Descriptive statistics of subsamples.

Mean	Std. Dev.	Q1	Median	Q3	N
Panel A: Bankrupt Group with a Z-Score Threshold of 0 for the Post-Millennium Subsample
−0.0621	0.5153	−0.4207	−0.2084	0.1440	461
Panel B: Non-Bankrupt Group with a Z-Score Threshold of 0 for the Post-Millennium Subsample
0.0543	0.4886	−0.2921	−0.0389	0.2885	5822
Panel C: Bankrupt Group with a Z-Score Threshold of 0 for the Pre-Millennium Subsample
−0.1226	0.5808	−0.5540	−0.2415	0.1278	20
Panel D: Non-Bankrupt Group with a Z-Score Threshold of 0 for the Pre-Millennium Subsample
0.0664	0.4931	−0.2816	−0.0248	0.3246	520

Panels A and B present the descriptive statistics of subsequent annual stock returns after the firms are classified into bankrupt and non-bankrupt groups, respectively, with a Z-Score threshold of 0 for the post-millennium subsample. Panels C and D present the descriptive statistics of subsequent annual stock returns for the firms classified into bankrupt and non-bankrupt groups, respectively, with a Z-Score threshold of 0 for the pre-millennium subsample

For the post-millennium subsample, the mean and median stock returns for the bankrupt group are lower than those of the non-bankrupt group by 11.61% and 16.95%, respectively. The difference in the mean of stock returns for these two groups is also statistically significant, with a t-statistic of 4.90 and a p-value of less than 0.0001. For the pre-millennium subsample, the mean and median stock returns for the bankrupt group are lower than those of the non-bankrupt group by 18.90% and 21.67%, respectively. The difference in the means of stock returns for the two groups is marginally statistically significant, with a t-statistic of 1.67 and a p-value of 0.0953. The substantial decrease in the t-statistic for the pre-millennium subsample is probably due to the limited number of observations. As noted in Panel C of Table 2, only 20 observations are available for the bankrupt group in the pre-millennium subsample. In short, I find no evidence that the Z-Score threshold of 0 is only applicable to a particular period and not to others.

Lagging Z-score by 1 Year

In Section Z-Score and stock returns, the Z-Score at the end of the current year is used to classify firms into bankrupt and non-bankrupt groups. The annual stock returns in the subsequent year for these two groups are then analyzed. However, one may argue that the accounting figures at the end of the current year are not immediately available because it takes time for firms to audit and publish their financial statements. The accounting ratios used to construct the Z-Score are usually available to the public several months after the financial year-end. Hence, the analysis in Section Z-Score and stock returns may not be realistic for industry practitioners. To address this, I repeat the analysis by lagging the Z-Score by 1 year. The Z-Score at the end of year t-1 is used to classify firms into the bankrupt and non-bankrupt groups to analyze the annual stock returns in year t + 1. The results are presented in Table 3.

Table 3.

Descriptive statistics of annual stock returns when Z-score is lagged.

Mean	Std. Dev.	Q1	Median	Q3	N
Panel A: Whole Sample
0.0526	0.4906	−0.2943	−0.0430	0.2875	6,107
Panel B: Bankrupt Group with a Z-Score Threshold of 3
0.0492	0.4907	−0.2967	−0.0521	0.2845	3,259
Panel C: Non-Bankrupt Group with a Z-Score Threshold of 3
0.0564	0.4906	−0.2902	−0.0254	0.2905	2,848
Panel D: Bankrupt Group with a Z-Score Threshold of 1.8
0.0161	0.4969	−0.3305	−0.09787	0.2399	1,715
Panel E: Non-Bankrupt Group with a Z-Score Threshold of 1.8
0.0668	0.4875	−0.2793	−0.0202	0.3000	4,392
Panel F: Bankrupt Group with a Z-Score Threshold of 0
−0.0609	0.5241	−0.4384	−0.2153	0.1767	401
Panel G: Non-Bankrupt Group with a Z-Score Threshold of 0
0.0606	0.4872	−0.2831	−0.0325	0.2925	5,706

Panel A documents the descriptive statistics of annual stock returns for the whole sample. Panels B and C present the descriptive statistics of the annual stock returns at year t + 1 when the firms were classified into bankrupt and non-bankrupt groups, respectively, with a Z-Score threshold of 3 at year t-1. Panels D and E present the descriptive statistics of the annual stock returns at year t + 1 when the firms were classified into bankrupt and non-bankrupt groups, respectively, with a Z-Score threshold of 1.8 at year t-1. Panels F and G present the descriptive statistics of the annual stock returns at year t + 1 when the firms were classified into bankrupt and non-bankrupt groups, respectively, with a Z-Score threshold of 0 at year t-1

Table 3 shows that the empirical results are similar to those in Table 2. With a Z-Score threshold of 0, investing in the non-bankrupt group and short selling the bankrupt group earns an annual return of 12.15%. The difference between the mean returns of the two groups is statistically significant, with a t-statistic of 4.51 and a p-value of less than 0.0001. When the Z-Score threshold is set at 1.8 and 3, the empirical results remain similar regardless of whether the Z-Score is lagged.

Discussion

This section discusses the teaching plan and re-use of accounting data to develop more teaching cases in the future.

Teaching plan

This teaching case is designed for a three-hour class. The teaching plan varies according to the teaching scenario preferred by the teacher. Table 4 presents the suggested teaching plans for each of the teaching scenario mentioned in Section Introduction.

Table 4.

Teaching plans for various teaching scenarios.

Time	Stages	Activities/Procedures
Scenario 1
60 min	Introduction	Teachers introduce the concept of discriminant analyses and explain the details of the Z-Score model
60 min	Consolidation via hands-on experience	Students are asked to follow the instructions in this teaching case and to mimic the results with the accounting data of the sample. Teachers shall provide assistance to students during the process
60 min	Discussion and conclusion	Teachers discuss the implications of the Z-Score model and explain the practical limitations of model implementation
Scenario 2
60 min	Demonstration	Teachers demonstrate the application of Z-Score model to analyze manufacturing firms listed in Hong Kong
60 min	Consolidation via hands-on experience	Students are asked to apply the Z-Score model to other industries, such as financials, utilities, health care, real estate, etc., and determine the appropriate Z-Score threshold for each industry. Teachers shall provide assistance to students during the process
60 min	Discussion and conclusion	Teachers discuss the impact of industry-specific characteristics on the applicability of the Z-Score model and the limitations of the model
Scenario 3
60 min	Demonstration	Teachers demonstrate the application of Z-Score model to analyze manufacturing firms listed in Hong Kong
60 min	Consolidation via hands-on experience	Students are asked to apply the Z-Score model to the manufacturing firms listed in other countries, such as China, the United States, the United Kingdom, etc., and determine the appropriate Z-Score threshold for each country. Teachers shall provide assistance to students during the process
60 min	Discussion and conclusion	Teachers discuss the impact of country-specific characteristics on the applicability of the Z-Score model and the limitations of the model
Scenario 4
60 min	Demonstration	Teachers demonstrate the application of Z-Score model to analyze manufacturing firms listed in Hong Kong from 1981 to 2020
60 min	Consolidation via hands-on experience	Students are asked to apply the Z-Score model to specific periods, such as the recent year, the financial crisis in 2008, and the bursting of dot-com bubble in 2001, to analyze whether the applicability of the Z-Score model is time-specific. Teachers shall provide assistance to students during the process
60 min	Discussion and conclusion	Teachers discuss the impact of time-specific factors on the applicability of the Z-Score model and the limitations of the model

This table presents the suggested teaching plans for each of the teaching scenario mentioned in Section Introduction.

Re-use of accounting data to develop more teaching cases in the future

As explained in Section Introduction, the Z-Score model in this teaching case belongs to the discriminant analytical model for corporate default prediction. Although the Z-Score model is relatively simple and straightforward, it requires some stringent assumptions to hold, such as multivariate normal distributions for the explanatory variables and identical defaults for each firm.³⁴ Students with more advanced statistical background may be interested in teaching cases related to other corporate default prediction models. The accounting data from this teaching case can be re-used for the development of teaching cases related to binary response models and hazard models in the future. Interested readers can download the sample data from the public data repository “Open Science Framework (OSF),” with web link https://osf.io/hctv6/?view_only=728bfa3165564839bb67e090218224ca.

Implications

This section describes the broader implications of the teaching case to the students, teachers, researchers, and industry practitioners. In particular, the challenges of applying the Z-Score model to investing Hong Kong listed firms are discussed. Then, the limitations of the Z-Score model are explained before concluding the study with suggested application of the Z-Score model.

Challenges of applying the Z-Score model

Although Section Z-Score and stock returns shows that investing in the non-bankrupt group and short-selling the bankrupt group earns a return of 11.99% in the subsequent year, it would be extremely difficult for retail investors to implement such an investment strategy. First, as Panels F and G of Table 1 show, there are 481 and 6,341 observations in the bankrupt and non-bankrupt groups, respectively. Retail investors do not have the expertise or capital resources to invest in and manage a portfolio containing thousands of stocks. Second, not all of the stocks listed in Hong Kong are available for short-selling. Investors can only short-sell stocks designated by Hong Kong Exchanges and Clearing Limited. Retail investors are also subject to numerous restrictions on short selling. Third, the mean returns presented in Table 1 are calculated by taking the simple average of all of the stocks in the bankrupt/non-bankrupt groups. If the investors want to mimic those returns, they would have to invest an equal amount in each stock. Given that each stock is traded at different values and trading odd lots is very costly, it is extremely difficult for retail investors to invest the same amount in each stock. Fourth, stock trading of investors is subject to transaction costs, such as commission and bid-ask spread, which erode their investment returns. As the trading strategy in Section Z-Score and stock returns requires regular re-balancing of positions involving thousands of stocks, the transaction costs involved are not trivial and should be taken into consideration during implementation.

Limitations of the Z-Score model

As the Z-Score model described in Section Z-Score model is designed to analyze manufacturing firms, it is questionable whether it applies to other industries, such as banking, insurance, and securities firms. Every industry has its unique features and caution must be exercised when applying the Z-Score model across industries. For example, firms in the financial industry are usually more leveraged than firms in the manufacturing industry. A low equity-to-liability ratio might be alarming for a manufacturing firm but is normal among financial firms. Blindly following the Z-Score model without considering the unique characteristics of each industry and making appropriate adjustments accordingly may affect the performance of the model. To help students appreciate the limitations of the Z-Score model across industries, teachers may follow teaching scenario 2 in Section Discussion and ask students to apply the Z-Score model to other industries and determine the appropriate Z-Score threshold for each industry.

Suggested applications of the Z-Score model

Given the challenges and limitations of the Z-Score model described in Sections Challenges of applying the Z-Score model and Limitations of the Z-Score model, it may be difficult for retail investors to make substantial profits by investing in all of the stocks in the non-bankrupt group and short-selling all of the stocks in the bankrupt group. However, they can avoid substantial losses by not investing in any of the stocks in the bankrupt group. As Panel F of Table 1 shows, investors lose 6.46% per annum on average by investing in the bankrupt group. The median annual loss is as high as 21.05%. Investors can use the Z-Score model to invest in listed manufacturing firms and drop all firms with a Z-Score below 0 from their investment portfolios. A negative Z-Score is an indication that the firm is likely to be in default with poor subsequent stock returns. Doing so may improve the overall performance of their investment portfolios and avoid substantial investment losses due to corporate default. In addition, investors are advised not to only rely on the Z-Score model for making investment decisions. Other techniques documented in the literature, such as technical analysis ³⁵ and bibliometric analysis,³⁶ should also be taken into consideration.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was fully supported by the University Grants Committee of the HKSAR, China [RMGS Project Acc. No.: 700043].

ORCID iD

Derrick WH Fung

Note

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Identifying poorly performing listed firms using data analytics

Abstract

Keywords

Introduction

Key concepts

Z-Score Model

Data collection

Bankrupt group versus non-bankrupt group

Key lessons

Z-Score and stock returns

Performance in different time periods

Lagging Z-score by 1 Year

Discussion

Teaching plan

Re-use of accounting data to develop more teaching cases in the future

Implications

Challenges of applying the Z-Score model

Limitations of the Z-Score model

Suggested applications of the Z-Score model

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

Note

References