An Empirical Study Applying Log Periodic Structures for Prediction of Realty Market Crashes in India

Abstract

The real estate market comprise of one of the most basic requirements of a human being that is shelter. A lot of money of the owners of the properties is invested in this market across the globe. The volatility in the real estate or realty market affects each and every human being. The crashes in the market lead to erosion of a large amount of value in terms of money, so if a technique is developed that can predict the upcoming crash, then this can help avoid losses of the investors. The present study tries to analyse downward movements in the Indian realty market by applying log-periodic structures. The period of the study is 1997–2011. The crashes were not predicted by using log-periodic structures as per the findings of the study. Thus the study concludes that it may not be appropriate to apply log-periodic structures to predict crashes of realty market in India.

Keywords

Log-periodic Structures Log Periodicity Realty Market Crashes

Introduction

Indian Economy and Real Estate Market

The GDP of India was ₹3561.93 billion in the first quarter of 1996–1997 and ₹8347.80 billion in the second quarter of 2009–2010 (base 1999–2000) and ₹13244.84 billion in the last quarter of 2010–2011 (Base 2004–2005). As per the estimates of 2011, the economy of India is growing at a rate of 5.5 per cent (Q1 2012) with a GDP of $4.457 trillion with contribution of agriculture standing around 17 per cent, that by industry around 26 per cent and by services around 56 per cent with a total labour force of 487.6 million. The industries contributing majorly include telecommunication, textiles, chemical, food processing, steel, transportation equipment, cement, mining, petroleum, pharmaceuticals and software.

India exports goods and services worth $299.4 billion (2011) and imports for $461 billion (2011). The main export partners of India are UAE around 13 per cent, US around 11 per cent, China around 6 per cent, Singapore around 5 per cent (2011) and import partners include China 12.1 per cent, UAE around 8 per cent, Saudi Arabia around 6 per cent, US around 5 per cent, Switzerland around 5 per cent (2011). The Indian economy has grown with 6.5 per cent for 2011–2012. The above growth has been complemented with growth in BSE Sensex. So it is necessary to look at the Indian capital market scenario. The various sectors of the economy have contributed to this robust growth. The role of financial sector has been significant in this growth. The stock market, the commodities market, the foreign exchange market and the real estate market have evolved along with the Indian economy. The following sections explain the state of the real estate market and the problem of high volatility and crashes in this market.

The free float market capitalization of BSE Realty Index was ₹296,727,900 thousand, the turnover is ₹2,753,363 thousand and number of trades is 192,465 as on 25 January 2013. As shown in Figure 1, the value of BSE Realty Index as on 2 January 2006 was 1317.89 and as on 07 January 2008, it was 13614.17 and as on 19 August 2011, it was 1674.74.

Figure 1.

Source: Author’s own compilation.

The Government of India approved FDI in the real estate sector in 2005 subject to complying with the requirements of minimum development area, minimum investment options and timelines for the project completion. The result of the same was an increase in FDI figures from a minimum 0.1 USD in 2003–2004 to 27.1 billion USD in 2008–2009. The year 2006 saw the emergence of real estate players through initial public offerings and listing of such companies on the stock exchanges. Furthermore, top qualified institutional buyers were tapped by the real estate buyers to raise equity funds in 2009. The good sentiments of all the sectors indicate overall development in the GDP to touch 8.50 per cent in 2010. This could be attributed to the robust results declared by the major sectors such as manufacturing, IT, hospitality, tourism, entertainment, and the like. Though the real estate market has recovered from the dumps of 2008, still the growth was not commensurate with the overall growth of the economy. In the financial year 2006–2008, the property market witnessed thriving business as it was looking good and the corresponding prices rushed forward. The growth in sales in real estate companies was 93 per cent in financial year 2007 and 82 per cent in 2008. However, in the financial year 2008, the financial crisis had strike the property market most horribly and it resulted in a sudden and sharp reduction in the availability of credit from banks and other institutions leading to diminishing demand in real estate sector and there was a downfall of around 38 per cent in sales figure of property market companies in 2009. Nevertheless, after the slump period of around 15 months, the economy of India showed signs of return to a normal state. As an outcome of this, the sales of the property market companies grew by around 4 per cent during the financial year 2010. Housing, infrastructure, industrial construction and commercial real estate are some of the segments that construction business can be divided into. Numerous reasons caused a disproportionate price build up in the form of a speculative bubble. One of the major reasons was inadequate availability of urban land for the development of the projects. The increase in interest rates and the slowdown in housing loan also restrained demand. The sector witnessed a sharp decline with liquidity declining and demand shrinking due to the worldwide economic recession. Customers and developers are witnessing a sluggish comeback with demand picking up in diverse pockets of the country.

Due to crashes in financial markets, huge amount of money is lost by investors within minutes to hours and the participants who are hurt the most are small investors. Financial market crashes are attracted to both the academic researchers and non-academic researchers as these crashes are social phenomenon resulting into an impulsive and spectacular decline in wealth. Crashes can be distinguished from bear markets in the sense that they are witnessed by considerable and quick reduction of prices frequently by fear and unexpected selling. Typical to this situation is the prevalence of underlying economic factors. The situation of fear is further provoked due to the propensity of the participants to behave in a group is referred to as herding. Herding can be defined as a progression in which persons in collection begin behaving collectively with no premeditated course. This is because of two reasons, namely, external economic situations and the psyche that results into the above mentioned herd behaviour. The excessive volatility to which financial markets are often subject to leads to certain real downbeat things and this inadequacy is found to be very much consistent with soaring volatility in the prices of securities and indices. The state of affairs further worsens up when something that emerges in one market adversely affects the other markets linked to it. Thus it is would be very useful and important if the crashes are predicted and preventive measures are taken by the authorities to avoid them or at least lessen their effect.

Objective

The objective of the study is to find out whether signals can be generated prior to beginning of a downward trend in Indian realty market using log-periodic structures. If prediction of crashes becomes possible, then measures may be taken by the regulatory bodies and authorities to avoid an enormous approaching loss of money and mental distress to many investors and lives of some of them.

Literature Review

Pros and Cons of Log-Periodic Structures

Superiority of Log Periodic Structures Over Other Techniques

Haugen and Lakonishok (1988) have found that returns in the month of January are high as compared to returns in any other month in a book entitled The Incredible January Effect. There are other studies which show that there are high returns on particular days of the week like French (1980) has found significantly on Monday in his study. Studies have been done which show particular order in returns near the change of the month like the one by Lakonishok and Smidt (1988) and also near holidays as done by Ariel (1990). The common disadvantage with the above patterns is that they are not reliable from period to period. The phenomena of predicting future returns from initial dividend yields (i.e., dividend–price ratio) do not work every time with individual companies as shown by Fluck, Malkiel, and Quandt (1997). Lo, Mamaysky, and Wang (2000) have employed advanced statistical methods that do not involve any assumptions as to the forms or parameters of a frequency distribution and have found that both the double bottoms pattern and head and shoulders pattern may have some modest predictive power. Head and shoulders pattern is usually considered as reversal pattern and is generally seen in an upward moving market. Double bottoms pattern is also considered as a reversal pattern but generally appears after a prolonged downward moving market. Log-periodic structures may prove to be an improved solution to the above mentioned problems and a superior method than others.

Shortcomings of Log Periodic Structures

Laloux, Potters, Cont, Aguilar, and Bouchaud (1999) have critically evaluated the current declaration that crashes in the securities market can be forecasted by the use of log periodic power law or by additional techniques motivated by the science behind the term known as critical phenomena. Particularly, the correction in the October of 1997 does not emerge to be the build-up end of a geometric progression of local minima. They have asserted that dependability on the present arguments on the ability to predict the crashes are not dependable at current juncture of time.

Some of the findings of Katarzyna and Piotr (2010) support the scepticism regarding the chances of precise forecast of date of occurrence of crash as calculated using log periodicity. Nonetheless, a posteriori analysis of the historical prices is suitable as it can be seen from a very high level of coefficient of determination. They have studied the crash in financial markets that occurred in 2008 using the indices of various financial markets. Merely for Hang Seng index, they obtained the assessment of critical time well-matched to the explanation of critical point as the juncture at which there is an alteration in the vital movement of price determination. While in rest of the occasions, it was the instance when the price of the index plummets penetratingly in small portion time.

Studies on Log-periodic Structures Specifically Relevant for realty market crashes

Zhou and Sornette (2005) have examined the quarterly mean of the prices at which the fresh residences were sold in the USA in totality, in 50 states and District of Columbia of the USA. They found that 22 states exhibit unambiguous signatures of a fast-growing bubble. They have used log-period power law in their analysis of bubble.

Xiao Qin and Tan Gee Kwang, Randolph (2005) have fitted modified log periodic model to property indices of Hong Kong and Korea and have got encouraging results. They consider the power law log periodicity theory successful in their analysis. A very helpful signature of price behaviour is a highly reliable signal of alarming market crash. They have estimated the highly non-linear log-periodic model by using a hybrid approach uniting scatter search, genetic adaptor and Tabu search. They have applied methodologies suggest by Johansen and Sornette et al. to Seoul Housing Price, Hong Kong Office Price and Korea General Construction Stock Price. They have also given the economic rationale behind the model given by Johansen and Sornette et al.

Zhou and Sornette (2007) have studied 27 indexes of price of residences of Las Vegas for a duration of June of 1983 to March of 2005 and their study has confirmed the presence of a real estate bubble. Their analysis exhibits the existence of very momentous variations meaning that the bubble of Las Vegas appears to have come before the universal USA bubble. They have used power law for analysis in their study.

After the analysis of above literature, it is found that log-periodic structures are able to predict financial market crash of more than 25 per cent at a very early stage. This study proposes to apply log-periodic structures in Indian real estate market to predict the crashes. A lot of work has been done on log-periodicity for different financial markets across the globe but for India not much has been done till date. This study will find out whether log-periodic structures can be used to predict price movements in Indian realty markets.

Research Methodology

Identifying ‘Crash’ in Indian Real Estate Markets

As suggested by Bree and Joseph (2007), a crash may be defined as a downfall of 25 per cent or more in the value of the prices during a period of 60 weekdays and also the value of the peak should be the highest in the past one year of 262 weekdays. The same has also been adapted for the present study.

Real Estate Market Crashes in India

The average standard deviation of returns of BSE Realty Index for 60 days is calculated and it came out to be 17.55 per cent. Maximum value of standard deviation was 77.59 per cent and minimum was 3.25 per cent. Since the standard deviation was 17.55 per cent, falls higher than this are taken for the purpose of the study. All of the above three crashes (Table 1) have been selected for study. Out of these three crashes, two have been selected as they are more than 25 per cent as required by the definition of crash, another crash of 19.41 per cent has been selected as it was the only crash closest to the average percentage fall of 32.23 per cent as there was no other crash for comparison after selecting the two crashes as above.

Table 1.

The Crashes in the Indian Real Estate Market which Occurred on BSE Realty Index From 2006 to 2011

From Date (Peak)	Close Value of Index	+60 Working Days from Peak	–262 Working Days from Peak	To Date	Close Value of Index	Percentage Fall
23 July 2007	8379.28	17 October 2007	04 July 06	23 August 2007	6752.71	–9.41
14 January 2008	13647.15	10 April 2008	26 December 06	24 March 2008	6806.18	–0.13
21 October 2009	4741.82	19 January 2010	18 September 2008	03 November 2009	3453.63	–7.17

Source: Author’s own compilation.

The free float market capitalization of BSE Realty Index was ₹296727.9 million, the turnover was ₹2753.363 million and number of trades was 192,465 as on 25 January 2013. The value of BSE realty index as on 2 January 2006 was 1317.89 and as on 7 January 2008, it was 13614.17 and as on 19 August 2011, it was 1674.74. The average standard deviation of returns of BSE Realty Index for 60 days is calculated and it came out to be 17.55 per cent. Maximum value of standard deviation was 77.59 per cent and minimum was 3.25 per cent. Since the standard deviation was 17.55 per cent, falls higher than this are taken for the purpose of the study. There are three such crashes and all the three have been selected for study. Out of these three crashes, two have been selected as they are more than 25 per cent as required by the definition of crash, another crash starting 19.41 per cent has been selected as it was the only crash closest to the average percentage fall of 32.23 per cent as there was no other crash for comparison after selecting the two crashes as above.

The Log-periodic structures (Equation (1))

ŷ_t(1)ABt_ct^βC t_c – t^βt_ct

is rewritten as: ŷ_t(2)ABtCt

where f (t) = (t_c – t) and tt_ctt_ct

From non-linear parameters, the optimal parameter values were obtained by using matrix multiplication: t_it_it_iAt_it_it_it_i²t_it_iBt_it_it_it_it_it_i²C

N is the total number of the days for which data is under observation.

Findings and Discussion

Analysis of warning signs originated before beginning of a descending movement on Indian Real Estate Market using log-periodic structures (Table 2).

Study of first crash starting 23 July 2007 using the parameters of the previous crash on BSE Realty Index

As there is no crash available that is more than 25 per cent before 23 July 2007 for the period of study starting from 2 January 2006, the study of first crash starting 23 July 2007 is not possible since to predict the next crash using the Log-periodic structures, the parameters of the last crash are required.

Study of second crash starting 14 January 2008 using the parameters of first crash starting 23 July 2007

The plotting of the time series is considered as the first step in its analysis. Figure 2 is the plot of the data from 2006 to 2007.

Table 2.

The Date and Serial Number of Crashes Under Study

Crash	Date
First	23 July 2007
Second	14 January 2008
Third	21 October 2009

Source: Author’s own compilation.

Figure 2.

Source: Author’s own compilation.

The values of A, B, and C are calculated using MATLAB programme.

(\begin{matrix} 1936738.70 \\ 1508630.79 \\ - 69087.01 \end{matrix}) = (\begin{matrix} 388 ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ & 333.15 & - 41.97 \\ 333.15 & 308.98 & - 49.23 \\ - 41.96 & - 49.23 & 164.87 \end{matrix}) (\begin{matrix} A \\ B \\ C \end{matrix})

Thus, A = 10640.37, B = –6536.28 and C = 337.59. When a function is required to be fitted on the data, it is essentially the minimization of the residual sum of squares, for which the function to be optimized may be written as min F (θ) = Σ (y (t_i) -ŷ (t_i))², where, θ = (t_c, , ,). This is done by using MATLAB programme. The corresponding values of beta, omega and phi are also found out using Microsoft Excel worksheet and MATLAB.  = 0.40,  = 0.00,  = 3.10.

Table 3 shows parameter values of log-periodic structures for first crash starting 23 July 2007 on BSE Realty Index. Figure 3 is the plot of BSE Realty Index actual data with data projected by using above parameter values. If any of the peaks of BSE Realty Index data is about to touch log-periodic structures (projected BSE Realty Index) plot or crosses it, then a great fall (crash) is in the offing. But the same was not predicted by the log-periodic structures plot in Figure 3. None of the peaks of the BSE Realty Index data prior to crash is near to the Log-periodic structures plot, thus no indication is generated of trend reversal. Thus, no indication of crash was produced by log-periodic structures. This was based on the parameter values that were generated at the time of last crash that is 23 July 2007.

Study of third crash starting 21 October 2009 using the parameters of second crash starting 14 January 2008

Table 3.

Parameter Values of Log Periodic Structures for First Crash Starting 23 July 2007 on BSE Realty Index

Parameters	Values
A	10640.37
B	–6536.28
C	337.59
B	0.40
Ω	0.00
f	3.10

Source: Author’s own compilation.

Figure 3.

Source: Author’s own compilation.

The plotting of the time series is considered as the first step in its analysis. Figure 4 is the plot of the data from 2006 to 2008. Considering Equations (1) and (2), from non-linear parameters, the optimal parameter values were obtained by using matrix multiplication. The assessment of parameters A, B, and C is done using MATLAB programme. Thus, A = 15517.06, B = –9935.36 and C = 98.50. When a function is required to be fitted on the data, then it is essentially the minimization of the residual sum of squares, for which the function to be optimized may be written as min F (θ) = Σ (y (t_i)–ŷ (t_i))², where θ = (t_c, , , ). This is done by using MATLAB programme. The corresponding values of beta, omega and phi are also found out using excel worksheet and MATLAB.  = 0.40,  = 2.00,  = 3.1.

Figure 4.

Source: Author’s own compilation.

Table 4 shows parameter values of log-periodic structures for second crash starting 14 January 2008 on BSE Realty Index. Figure 5 is the plot of BSE Realty Index Actual data with data projected by using above parameter values. If any of the peaks of BSE Realty Index data is about to touch log-periodic structures (projected BSE Realty Index) plot or crosses it, then a great fall (crash) is in the offing. But the same was not predicted by the log-periodic structures plot in Figure 5. None of the peaks of the BSE Realty Index data is near to the log-periodic structures plot, thus no indication is generated of trend reversal using log-periodic structures. This was based on the parameter values which were generated at the time of last crash that is 14 January 2008.

Table 4.

Parameter Values of Log Periodic Structures for Second Crash Starting 14 January 2008 on BSE Realty Index

Parameters	Values
A	15517.06
B	–9935.36
C	98.50
B	0.40
Ω	2.00

Source: Author’s own compilation.

Figure 5.

Source: Author’s own compilation.

Table 5 shows comparison of parameters of log-periodic structures equation for BSE Realty Index. The values of the above non-linear parameters show that for BSE Realty Index, the value of β is 0.4 for all the three crashes. Whereas the value of ω = 0 and value of  = 3.1 in two out of three crashes. Thus, the value of β is within the range  = 0.33 ± 0.18 as suggested by Bree and Joseph (2007) for all the three crashes. But value of  is outside the suggested range of  = 6.36 ± 1.56. And the value of  is within the specified range 0 ≤  ≤ 2 as suggested by them. Table 5 also shows that the values of linear parameters A, B and C change according to the period chosen for analysis of crash.

Table 5.

Comparison of Parameters of Log-periodic Structures Equation for BSE Realty Index

Crash Year	2007	2008	2009
Parameters	Values	Values	Values
A	10640.4	15517.1	2919.97
B	–6536.3	–9935.4	2059.43
C	337.59	98.5	–478.1
B	0.4	0.4	0.4
Ω	0	2	0
f	3.1	3.1	2.7

Source: Author’s own compilation.

Conclusion

The volatility of the financial markets is a cause of profound anxiety and agony to all the participants especially to the small investors. A crash produces chaos in any financial market specifically ruining lives of many investors. A variety of studies have been done about realty market movements but only modest work is available for study of crashes in general and using log-periodic structures in particular for Indian Realty markets. The present study analyses crashes of Indian Real Estate markets from 1997 to 2011 using log-periodic structures. The results of the study showed that log-periodic structures were not able to predict any of the crashes in realty market of India so it may be said that log-periodic structures may not be applied for realty market in India.

Limitations and Scope for Further Research

The period of study and analyses of the data is from July 1997 to August 2011. The research can be advanced for a longer duration. If the data is analysed for an extended duration, it can capture more irregular and rare price movements that may further increase the strength of the predictions made thereafter. This study was done on the time series of daily data. Tick size market data may be used for analysis to increase the sturdiness of the results.

Footnotes

Declaration of Conflicting Interests

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

Funding

The authors received no financial support for the research, authorship and/or publication of this article.

References

Ariel

R. A.

(1990). High stock returns before holidays: Existence and evidence on possible causes. Journal of Finance, 45(5), 1611–1626.

Bree

D. S.

, & Joseph

(2007, November). Log-periodic power law fits to financial crashes: A preliminary replication. Retrieved from https://www.researchgate.net/publication/45899349_Fitting_the_Log_Periodic_Power_Law_to_financial_crashes_a_critical_analysis

BSE Index Reach—Realty, Retrieved on 26 June 2019 from https://www.bseindia.com/indices/IndexArchiveData.html

CREDAI Real Estate Review Issue April, May, June 2010, Cover Story - Path-breaking Innovations in Real Estate, CREDAI Magazine, April 2010

Fluck

, Malkiel

B. G.

, & Quandt

R. E.

(1997). The predictability of stock returns: A cross-sectional simulation. Journal of Financial Economics, 8, 66–69.

French

(1980). Stock returns and the weekend effect. Journal of Financial Economics, 8, 55–69.

Haugen

R. A.

, & Lakonishok

(1988). The incredible January effect. Homewood, IL: Dow Jones-Irwin.

Katarzyna

B-L.

, & Piotr

(2010). Note on log-periodic description of 2008 financial crash. Retrieved from https://arxiv.org/abs/1005.2044

Lakonishok

, & Smidt

(1988). Are seasonal anomalies real? A ninety-year perspective. Review of Financial Studies, 1(4), 403–425.

10.

Laloux

, Potters

, Cont

, Aguilar

J. P.

, & Bouchaud

J. P.

(1999). Are financial crashes predictable? Europhysics Letters, 45(1), 1–5.

11.

A. W.

, Mamaysky

, & Wang

(2000). Foundations of technical analysis: Computational algorithms, statistical inference, and empirical implementation. Journal of Finance, 55(4), 1705–1765.

12.

Xiao

, and Tan

G. K. R.

(2005). Bubbles, can we spot them? Crashes, can we predict them? Retrieved from http://repec.org/sce2005/up.18847.1107074423.pdf

13.

Zhou

W.-X.

, & Sornette

(2005). Is there a real-estate bubble in the US? Retrieved from http://arxiv.org/abs/physics/0506027

14.

Zhou

W.-X.

, & Sornette

(2007). Analysis of the real estate market in Las Vegas: Bubble, seasonal patterns and prediction of the CSW indexes. Retrieved from http://arxiv.org/abs/0704.0589