1 Introduction

According to Ministry of Finance ePortal, by the end of 2017, FDI registered capital into Vietnam was 35,88 billion USD, increased 44,4% compared to 2016, reached its highest since 2008. Real estate is reported to be one of the country’s top 3 most FDI-attractive industries, with 8.5% total registered capital, equal to approximately 3 billion USD in value, higher than the figures of the past 5-year period [39]. The growing trend also applies for stock price of listed real estate companies with remarkable surge in stock price that continues in 2018 as a result of positive business outcome of 2017 [40]. Thus, it would be necessary to forecast whether this trend will continue to grow for the next years to come.

Real estate is believed to grow even stronger in the next year because of many cultural and economic advantages. This remarkable growth in property sector has gained the attention from investors in both Vietnam and foreign countries. Such attractiveness results in market’s high demand for portfolio of properties and of real estate securities. However, there are doubts whether this growing trend would last.

Hence, it is crucial to evaluate the overall operations of property enterprises to develop appropriate investment strategies. Furthermore, assessing the industry's top firms is also needed to visualize the potential of the real estate market in the future, which eventually helps policymakers develop appropriate law amendments that can foster the Vietnam economy's growth in general.

Given the circumstances, this study is conducted to closely monitor market changes and provide updated findings about the real estate field. DEA model is applied with relevant metrics to connote the overall competitiveness and performances of real estate core corporates. The grey system theory has proved to be a rational and reliable concept, as it has been backed up with scientific research and applied in studies conducted by well-known scholars (e.g. [21,22,23, 30]. The research looks into empirical data of firm’s operation and forecasts future outcome, which can be used as a resource for investors to make decisions. The study provides useful parameters to decide whether to invest in the real estate fields and what companies to invest in, both for direct and indirect investments. Forecast results can also be useful for policy makers to foster market growth and facilitate a more efficiency environment for all industry players with the primary objectives to answers these research questions.

  • Research question 1: What is the performance of Vietnamese real estate corporations?

  • Research question 2: What is the future trend of Vietnamese real estate corporations?

2 Literature review

2.1 Evaluating real estate companies’ performance

The purpose of this part is to look into the previous studies relating to the field. Anderson et al. [2] applied DEA and the data from 1992 to 1996 to measure efficiency of technical and scales for the economies of Real Estate Investment Trusts (REITs). From the result of the study, the paper came up with conclusion that REITs are inefficient. In addition, the research also indicated that the performance could be increased by many REITs through expansion. Other significant studies that can be named are work of Bers and Springer [4], Miller and Springer [19], Miller et al. [20], Zheng et al. [38] and Wang and Wang [31].

2.2 DEA and Malmquist index

Initially, Farrell [10] proposed a concept of evaluating performance by using multiple inputs–one output model. Charnes et al. [5] later developed Farrell’s further and adopt a model of many inputs and many outputs. In this concept, by using linear combination, the collected data is transformed into single virtual input and output. From this, efficiency frontier and the relative efficiency index of each DMU are calculated, running between 0.00 and 1.00. This metrics show whether a DMU is in constant, increasing or decreasing returns to scale. Evaluating operation efficiency is of high importance, both to economic scholars as well as policy makers [10].

2.3 Selection of inputs and outputs

This study looks into previous research for direction of inputs and outputs choice. Table 1 summarizes inputs and outputs chosen to assess real estate-related companies using DEA method.

Table 1 Previous studies of DEA inputs and outputs for real estate
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2.4 Grey system theory

The grey system theory has proved to be a rational and reliable concept, as it has been backed up with scientific research and applied in studies conducted by well-known scholars. Many academic papers from specialists have provided in-depth analysis of the theory, such as Wen [34] about the model’s prediction capability. Other remarkable researches about the concept’s relational studies are: Tsai et al. [28], Lin and Wu [15], Wei [32]. In addition, the grey system theory has lots of application in various fields. Its relational analysis was utilized by Kuo et al. [12] to support the decision-making process in many industries. Overall, the grey system theory demonstrates major advantages with its multifunctionality in different industries and few limitations with regard to data input and output [8, 9, 17, 29].

2.5 GM (1,1) model

The GM (1,1) model has been utilized in a variety of practices of many industries. Different methods of the model are exploited to adapt the distinct requirements and characteristics of each application. Some authors with significant works that are relevant to the subject; for example, YuChun et al. [37], Lin and Yang [14], Lin et al. [16], Wu et al. [35], The research of Mao and Chirwa [18], Chen and Chen [7].

Overall, the GM (1,1) model proves its strength of pinpointing accuracy forecast in many fields. Different methods were practised in the above studies when employing this model, which varies between contexts. Such diversity will be taken into consideration in this research when the model is utilized to provide a complete, in-depth analysis.

3 Methodology

DEA is a nonparametric method used to assess operational efficiency from estimation of production frontiers and efficiencies of selected decision-making units, in this case are listed real estate companies.

Three main advantages of data envelopment analysis are that it can process multiple inputs and outputs. Furthermore, it can be processed without the need to assign weights for any factors or proposing hypothesis.

The proposed research process for this study is shown as follows (Fig. 1).

Fig. 1
figure 1

Flow chart of proposed method

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The proposed method is comprised of four main parts: data collection, data manipulation, followed by integration and evaluation. The last part is analysis and conclusion.

The process:

  • Step 1. Choosing the decision-making unit

  • Step 2. Choosing the input and output variables

  • Step 3: Grey prediction

  • Step 4: Measuring error

  • Step 5: DEA model integration

  • Step 6: Pearson correlation

  • Step 7: Analysing the performance of the companies

3.1 Data collection

Data is collected on Vietstock.vn. Process illustration is shown as follows.

  • Step 1: Go to Vietstock.vn website

  • Step 2: Enter Company’s Stock Code in Search Box

  • Step 3: Arrive at Company’s Page on Vietstock website

  • Step 4: Open “Financial” Tab on the Company’s Page

  • Step 5: Collect data and store in Excel tables

4 Data analysis and discussion

4.1 Collecting the DMU

Initially in this study, 20 domestic listed real estate companies with highest market capitalization were selected as DMUs for empirical study in the period from 2013 to 2017. However, 4 were eliminated because they went listed during the 5-year period, which leads to lack of information within the research time. This leaves the study with 16 remaining companies in the DMUs list, with details as following (Table 2).

Table 2 Top 20 listed real estate companies with highest market capitalization (1 April 2018)
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4.2 Establish input/output variables

Due to the limitation by the access to data in this study, the final inputs and outputs indicators are shown in tables of this studies. The data are collected from Vietstock Website. Template of data collected is as follows (Table 3).

Table 3 Collected data of all DMUs (2013)
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4.3 Grey forecasting model

GM (1,1) model is used to forecast input and output values from 2018 to 2022. Below is example of DMU16 empirical data being processed using GM (1,1) model (Table 4).

Table 4 DMU16 (TDH)—collected data (2013–2017)
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The detailed calculation process is as follows:

Step 1. Primitive series

$$X^{\left( 0 \right)} = \left( {16.587.130,43; 16.587.130,43; 18.245.521,74; 30.864.521,74; 35.493.043,48} \right)$$

Step 2. Accumulated generating operation (AGO):

$$\begin{aligned} & X^{\left( 1 \right)} = \left( {16.587.130,43; 33.174.260,87; 51.419.782,61; 82.284.304,35; 117.777.347,83} \right) \\ & x^{\left( 1 \right)} \left( 1 \right) = x^{\left( 0 \right)} \left( 1 \right) = 16.587.130,43 \\ & x^{\left( 1 \right)} \left( 2 \right) = x^{\left( 0 \right)} \left( 1 \right) + x^{\left( 0 \right)} \left( 2 \right) = 33.174.260,87 \\ & x^{\left( 1 \right)} \left( 3 \right) = x^{\left( 0 \right)} \left( 1 \right) + x^{\left( 0 \right)} \left( 2 \right) + x^{\left( 0 \right)} \left( 3 \right) = 51.419.782,61 \\ & x^{\left( 1 \right)} \left( 4 \right) = x^{\left( 0 \right)} \left( 1 \right) + x^{\left( 0 \right)} \left( 2 \right) + x^{\left( 0 \right)} \left( 3 \right) + x^{\left( 0 \right)} \left( 4 \right) = 82.284.304,35 \\ & x^{\left( 1 \right)} \left( 5 \right) = x^{\left( 0 \right)} \left( 1 \right) + x^{\left( 0 \right)} \left( 2 \right) + x^{\left( 0 \right)} \left( 3 \right) + x^{\left( 0 \right)} \left( 4 \right) + x^{\left( 0 \right)} \left( 5 \right) = 117.777.347,83 \\ \end{aligned}$$

Step 3. GM (1, 1) different equations. Use mean equation to obtain the following mean

$$\begin{aligned} & z^{\left( 1 \right)} \left( 2 \right) = \frac{1}{2}\left( {16.587.130,43 + 33.174.260,87} \right) = 24880695,65 \\ & z^{\left( 1 \right)} \left( 3 \right) = \frac{1}{2}\left( {33.174.260,87 + 51.419.782,61} \right) = 42297021,74 \\ & z^{\left( 1 \right)} \left( 4 \right) = \frac{1}{2}\left( {51.419.782,61 + 82.284.304,35} \right) = 66852043,48 \\ & z^{\left( 1 \right)} \left( 5 \right) = \frac{1}{2}\left( {82.284.304,35 + 117.777.347,83} \right) = 100030826,1 \\ \end{aligned}$$

Step 4. a and b calculation. Substitute the primitive series values to grey differential equation:

$$\left\{ {\begin{array}{*{20}l} {16.587.130,43 + a \times 24880695,65 = b} \hfill \\ {18.245.521,74 + a \times 42297021,74 = b} \hfill \\ {30.864.521,74 + a \times 66852043,48 = b} \hfill \\ {35.493.043,48 + a \times 100030826,1 = b} \hfill \\ \end{array} } \right.$$

Then,

Let \(B = \left[ {\begin{array}{*{20}c} {\begin{array}{*{20}c} { - 24880695,65} & 1 \\ { - 42297021,74} & 1 \\ \end{array} } \\ {\begin{array}{*{20}c} { - 66852043,48} & 1 \\ { - 100030826,1} & 1 \\ \end{array} } \\ \end{array} } \right]\), \(\hat{\theta } = \left[ {\begin{array}{*{20}c} a \\ b \\ \end{array} } \right]\), \(y_{N} = \left[ {\begin{array}{*{20}c} {16.587.130,43} \\ {18.245.521,74} \\ {30.864.521,74} \\ {35.493.043,48} \\ \end{array} } \right]\)

$$\left[ {\begin{array}{*{20}c} a \\ b \\ \end{array} } \right] = \hat{\theta } = \left( {B^{T} B} \right)^{ - 1} B^{T} y_{N} = \left[ {\begin{array}{*{20}c} { - 0,2751572273} \\ {9196688,815} \\ \end{array} } \right]$$

Apply a and b calculated value to the differential equation to generate the whitening equation

$$\frac{{{\text{d}}x^{(1)} }}{{{\text{d}}t}} - 0,2751572273 \times x^{(1)} = 9196688,815$$

The final forecasting formula:

$$X^{\left( 1 \right)} \left( {k + 1} \right) = \left( {X^{\left( 0 \right)} \left( 1 \right) - \frac{b}{a}} \right)e^{ - ak} + \frac{b}{a}$$

With the values of “k” above, we get the results as shown in Table 5.

Table 5 Forecast results of chartered capital—TDH (DMU16)
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For 1 ≤ i ≤ 10, suggested by 26,27, Animasaun et al. [3], Wakif et al. [33], Koriko et al. [13], it is worthy to remark that the rate of change in X1(i) with k is 56832468.35 while the rate of change in X0(i) with k is 13422320.02.

All DMUs inputs and outputs data in the period 2018–2022 can be forecasted using above calculation process. An example of forecast template can be viewed in below table of data for 2018 (Table 6).

Table 6 Forecast results of all DMUs (2018)
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4.4 Forecasting accuracy

In many cases, forecasting goes with errors. In this paper, mean absolute per cent error (MAPE) is used to evaluate the accuracy of a forecasting error. Small value of MAPE indicates that the forecasting value is close to the actual value.

MAPE results of the DMUs are as follows (Table 7).

Table 7 MAPE Results of all companies
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Out of 16 selected, MAPE of all companies used is about 11%, within feasible range and thus proves the accuracy of forecasting results. Moreover, these high accuracy reflect the Vietnamese real estate market, which is developed recently. Therefore, the GM(1,1) model accepted as an accuracy tool used for the projection of the future data.

4.5 DEA model analysis

In this study, Pearson correlation is applied to evaluate the relationship between two variables. High correlation coefficient figures indicate close relationship between each set of inputs and outputs and vice versa, low correlation coefficient points out that the variables are not closely related.

Absolute value of correlation coefficient is 1, at which point set perfect linear relationship. Details on correlation efficient are interpreted in Table 8.

Table 8 Correlation range
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The results show strong correlation between the inputs and outputs set throughout the years 2013–2017. Such findings reaffirm appropriate choice of inputs and outputs. Correlation of forecast data in 2018 also falls within acceptance range (Table 9 and “Appendices”). Hence, no factor removal is needed.

Table 9 Correlation of inputs and outputs—2013
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4.6 Results

4.6.1 Empirical results

Using DEA software, Malmquist productivity index is calculated to analyse operation of the selected real estate companies from 2013 to 2017. The results are presented as follows (Table 10).

Table 10 Efficiency change (2013–2017)
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All 16 companies have average catch-up efficiency index approximately equal to 1. There are no great differences between DMUs’ efficiency change given the max value 1,8 (KBC, 2014–2015) and the min value nearly 0.8 (PDR-2016–2017).

The “efficiency changes” are showing consistency among most of the selected companies over the period 2013–2017. Some companies with more fluctuated pattern are KBC, SCR and NLG, with slight increase during the period. PDR alone experiences slight drop with catch-up efficiency being 0.7 in last year frame (Table 11).

Table 11 Frontier Shift (2013–2017)
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The above table reflects more noticeable though not significant margins between firms’ innovation effect. HDG, ITA, FLC, NBB with their lowest being around 0.4–0.6. Maximum frontier shift value 2.5 is 2 unit higher than the minimum value of 0.4. Overall, average index of all DMUs stays around 1.

As illustrated in the chart, companies that experience strong fluctuation in frontier shift throughout the 5 years are QCG and FLC. SJS shows most remarkable drop: started the period with highest figures then ended the period at around 0.8. TDH trend alone surges significantly at the end of 2017. Notably, besides some abrupt changes, most companies’ level of technical changes fluctuates around 0.5 to 1.5 (Table 12).

Table 12 Malmquist Productivity Index (MPI) (2013–2017)
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The above table illustrates the Malmquist Productivity Index (MPI) scores during the research period. The MPI score of TDH shows strongest growth within the time frame. Others’ scores fluctuate around 0.5 to 1.5, with exceptions of KBC, QCG and SJS with their peaks reach up to around 2.5 before falling back to the common zone.

4.6.2 Forecasting results

The tables below show the DEA results of forecast data for 16 decision-making units (“Appendices”).

From 2018 to 2022, indexes for catch-up efficiency of firms remain stable around 1. Some exceptions are KBC, QCG and DXG with these values fall below average, while SCR and IJC are somewhat above average though with some fluctuations throughout 5 years (“Appendices”).

Forecast results indicate that most companies’ technical efficiency has slight improvement in the next few years, with barely any value falls below 1. Average score of most KDH, SCR and KBC figures run between 1 and 2, somewhat above average. DXG, TDH and NLG have most remarkable growth. TDH index in 2018 is 4 while the figures for NLG and DXG are around 2. The trend shows more positive sign in late period as TDH reaches 9 in 2022 (“Appendices”).

Compared to historical analysis, forecast data MPI results reflect more differences between the DMUs. The highest MPI score is 9.04 (TDH, 2021–2022) while minimum value for some is 0.9. Standard deviation for firms’ Malmquist index in this period ranges from 0.8 to 2.3 with average value being 1.5, threefold the figure of the last 5-year timeframe.

Based on Malmquist results for forecast data, it is clearly seen that three are 3 main trends for MPI in 2018–2022. The first group with MPI growth margins more than 2. This group includes 3 DMUs: TDH, NLG and DXG. The second group includes KBC, KDH, SCR, with MPI running between 1 and 2. The remaining DMUs have their Malmquist productivity index stabilize at 1.

4.7 Results summary

Overall, based on the results generated, ranking of listed real estate companies can be divided in descending order as follows:

These Group 1 and Group 2 can respond to the first research question:

  • Group 1: Robust growth

The group includes TDH-DMU16, NLG-DMU7 and DXG-DMU3.

  • Group 2: Steady growth

In this group, there are KBH-DMU5, KDH-DMU2 and SCR-DMU11.For the second research question, the Group 3 below from the research results can respond to:

  • Group 3: Slight Improvement

Overall, future forecast data of the remaining firms show increase in operational efficiency with improved Malmquist index compared to the past few years. This indicates continuous growth for the real estate industry in the next years to come.

5 Conclusion

From empirical data from 2013 to 2017, the research applied GM (1,1) model to forecast future operational data of 16 listed real estate companies. Performance evaluation is assessed using DEA’s multiple input–multiple output model.

As there was remarkable growth in the real estate industry last year, forecasting these values is necessary for investors, real estate companies and policymakers to analyse the market prospect and make the right decision. Accuracy is difficult to reach in this case, given the significant surge in some companies' business trends in 2016 and 2017. However, it did not make any changes to the data retrieved to not interfere with the direction (if any). The average MAPE for 11 out of 16 DMUs is 11 per cent within the acceptance area. This result confirms the accuracy of forecast data for most of the studied companies.

After forecasting, DEA model is applied to evaluate these companies individually based on their operational performance. Findings from this analysis indicate that the industry will continue to grow in the next few years, just like the expectation of many investors. The study could also provide insights for managers to improve their portfolios by investigating the patterns of top-performing real estate firms. Companies with high operational efficiency like TDH and NLG all show strong development in the housing market for middle-income clients; therefore, it is recommended that investment should put consideration for this sector to yield high ROIs for upcoming years.

This study with appropriate model application and analysis factors adoption has provided more in-depth insight about the potential of the real estate field and formed a firm foundation for further research. Further development if carried out in an appropriate direction shall provide more benefits to the industry’s top companies as well as policy makers, which eventually will foster the country’s economy in general.

Given yielded results, the research findings can be used as a guiding material for investors who are building their investment portfolio. To be more specific, beside choosing the companies’ securities, ranking results can be used to analyse the potential segments of real estate market (high-end or low-end, tourism real estate or industrial real estate…) to take further investing move. Similarly, policy makers can have directions to make law amendments that create incentives driving the market forwards.

With that given, the research still has some limitations. Firstly, some top players in the real estate market are not chosen as target of this study due to their absence on the stock market and hence the lack of published historical data. Also, abrupt change in 2017 affects accuracy of the forecasting model. Hence, further market observations should be taken in order to utilize this study’s ranking results.

Future studies should be continued in 2 directions:

  1. 1.

    Include more detailed inputs and outputs (such as number of employees, land area owned…) to not leave out important factors when evaluating the industry.

  2. 2.

    Take consideration of market segmentation and demand as it requires more in-depth research in demography, finance, assets understanding and macroeconomics in order to make the best decision when investigating in real estate field.