1 A WORK PROJECT, PRESENTED AS PART OF THE REQUIREMENTS FOR THE AWARD OF A MASTER DEGREE IN FINANCE FROM THE NOVA – SCHOOL OF
BUSINESS AND ECONOMICS.
FINANCIAL CRASHES PREDICTION USING THE BSEYD MODEL: EVIDENCE IN SEVERAL EMERGING MARKET COUNTRIES
LILIANA PATRICIA CAMPOS FRANCO & 39597
A PROJECT CARRIED OUT ON THE MASTER IN FINANCE PROGRAM, UNDER THE SUPERVISION
OF:
ANDRÉS MORA
2
Financial crashes prediction using the BSEYD Model:
Evidence in several emerging market countries
1Author: Liliana Patricia Campos Franco Advisor: Andrés Mora
Abstract
This work aims to predict financial market crashes in several emerging countries. For this purpose, the Bond Stock Earning Yield Differential (BSEYD) model proposed by Ziemba and Schwartz (1991) is applied to the market indexes of Brazil, Mexico, Greece, Czech Republic, Turkey, India, Indonesia, and Taiwan. This model is based on the relationship between the yield on nominal Treasury bonds and the returns on stocks (measured by the Price/Earnings stocks ratio of the Stock Market Index). As a main result, this study finds that, on average, 68.3% of crashes are predicted correctly.
Keywords: Crash prediction, signals, BSEYD Model, Emerging Markets
1. Introduction
Over the past few months, there has been a growing concern about a nearby financial crisis that may have a significant impact on the global economy. Therefore, investors have tried to predict when the next financial crash will occur in developed and emerging markets using different financial prediction tools and models. Developed countries, such as the United States, are concerned about the yield curve’s being inverted because the yield on nominal Treasury bonds of short term is higher than the long term one. Since August 2019, the yield of the 10-year long term bonds has fallen 34.77 basic basis points in comparison to the three-month short-term bonds. The growing demand for long-term bonds has contributed to the decrease on the interest rate. These have resulted in reduced demand and increased yields of short-term bonds. According to the
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Financial Times 2009, the is due to trade war between the United States and China, which has raised concerns about the economic growth of the global economy inverting the “normal” yield curve and increasing the belief of a possible recession economy. The situations mentioned above have led to the development of model proposals that study the market’s signals and crashes, intending to improve the decision-making portfolio allocation.
Financial market crashes might be a consequence of several factors. For instance, the market might have entered in an unstable phase, and any small variation may trigger such instability (Sornette, 2003). Another factor can be the lack of information due to the transaction costs in the security market. This means that a significant change in asset price can happen without substantial news (Lee, 1998). Another example is an unusual movement in the stock prices derived from public news events of important firms (Hong and Stein-Lee, 2003; 1998). Finally, before the market crash takes place, prices increase continuously for a while (Lee, 1998), and soon after, the high prices turn negative, decrease and remain low for a period (Hong and Stein -Read, 2003; 1998).
The leading research on predicting financial market crashes comes from the model of Bond-Stock Earnings Yield Differential (henceforth, BSEYD Model) proposed by Ziemba and Schwartz in 1991. This model employs the yield on nominal Treasury bonds with a maturity of 10 and 30 years and the P/E ratio of the stock market index of the analyzed country. The BSEYD Model allows us to observe the possible signs of near-crashes, the crashes, and the history of the signals and crashes of the economy for a given country. It is essential to highlight that when the BSEYD model was applied in developed countries such the United States, Iceland, and China (Ziemba and Lleo, 2017), the crashes during 2006-2009 were successfully identified. However, this model has not been applied in emerging markets so far. This research aims to assess if the model proposed by Ziemba and Schwartz succeeds in identifying financial crashes in the markets of Mexico, Brazil, Greece, the Czech Republic, Turkey, Indonesia, India, and Taiwan. Additionally, this work extends the period of study proposed by the authors of the BSEYD Model in the United States and China.
This manuscript is organized as follows: Section 2 overviews the relevant literature about crash prediction, Section 3 describes the methodology of the BSEYD model, Section 4 presents the results applied to several emerging market countries, Section 5 extends the results of Lleo and Ziemba (2015) for the US and Chinese cases, and finally, section 6 provides the main conclusions.
4 2. Literature overview
To facilitate the understanding of this document, we would like to provide a clear definition of a market crash. A market crash occurs when a certain economic index drops in an anomalous way, due to exogenous factors, causing a variety of adverse economic situations, such as mass bankruptcies and recession of economies (Sornette, 2003). This type of behavior in markets is a consequence of different factors. As Sornette (2003) described, a crash may occur because the market has entered an unstable phase, in which any minimal alteration can trigger a significant change. Lee indicates that a market crash occurs when a substantial change in the price of any stock happens, without any previous information or news (1998), and similarly, Ziemba describes that a market crash occurs when the drop in the last maximum price of any financial instrument is more than 10% (2017). Hong and Stein Lee point out that a market crash happens due to a long unusual movement in the stock prices because of a significant firm public’s news event (1998, 2003).
Throughout the years, many different models have been proposed to predict this financial phenomenon accurately. These models can be classified into two big groups: probabilistic models and models based on economic variables. In 1996, Sornette began to analyze the behavior of the S&P 500 to find patterns in the oscillations of the prices in the stock market index, suggesting there was a characteristically log-periodic signature in dynamical critical points that had similarities with the behavior of earthquakes. These findings denoted the beginning of the market crashes as a phenomenon to study and strengthened the stock market as dynamic, collaborative systems. By using stock market indices from the United States, Hong Kong, and Russia, Sornette demonstrates the existence of growing financial bubbles that may turn into a market crash. He found that these financial bubbles follow the same power law in the analyzed markets (Sornette, 1999). Later, Ko, Song, and Chang (2018) applied the log-periodic structure of Sornette in the Korean stock market to forecast a market crash to produce a financial crash warning. This study classified the financial market crashes into domestic and global crises. Sornette (2002) found that the behavior of catastrophic events such as materials rupture, earthquakes, turbulence, etc., follows a similar behavior to financial crashes. Therefore, models that predict such events are successfully
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applied to predict market crashes. Additionally, he proposed a model to predict the state of development of a financial bubble, given that a bubble is the result of a non-sustainable growth pace of the market price (Sornette, 2002), which makes the market highly susceptible to any disturbance.
In the same line, Gresnigt, Kole, and Franses in 2015 proposed a model in which financial market crashes are interpreted as earthquakes in mid-term (5 days). Using a sample of the S&P 500 the authors produced an Early Warning System (EWS). As a result, it was discovered that stock returns behavior of a financial crash was very similar to the seismic activity of earthquakes. Besides, the EWS model of Gresnigt et al. (2015) outperforms the EWS based on the volatility models forecasting extreme price movements; nevertheless, the latter is less time-consuming. Lebaron and Samanta (2005) found that financial market crashes occur more frequently in developing markets than in developed markets. Additionally, that the risk of the occurrence of a market crash depends on the deliberate region, they reached such conclusions utilizing the Extreme Value Theory, which analyzes the probability of extreme events and the tails in emerging and developed markets. In the same year, Grech and Mazur (2004) indicated that the crashes in the Dow Jones Industrial Average index (DJIA) index could be predicted using the Hurst exponent, making accurate predictions from the period ranged between 1929 and 2003. In another study, Grech and Pamuta (2008) investigated the time series of the Warsaw Stock Exchange Index (WIG) with local fractal properties employing the Hurst exponent that varies on time. The main finding is a high correlation between the WIG local fractal properties and financial market crashes.
There was a real concern due to finding the best way to improve the accuracy of the prediction of financial market crashes. Hence, Wang, Meric-G, Liu, and Meric-I (2009) focused on main factors that make a market crash occur in the stock market indexes and how the market crashes influence in the behavior of individual stocks applying multivariate regression in US firms. As a result of the study, stocks with “higher betas, larger capitalization, lower levels of illiquidity, more return volatility, higher debt ratios, higher of liquid assets, lower cash flows per share and lower assets profitability” (Wang et al., 2009, p. 1) tends to lose more value when there are crash days.
Additionally, Rivera-Castro, Miranda, Borges, Cajueiro, and Andrade (2012) studied the events that cause abrupt changes in the stock series trend, to improve the decision making of investors’ portfolios, the study was applied on the DJIA index. They found that such events can be diagnosed
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by a highlight difference between extreme prices and Gaussian Kernel function that provides a very accurate description of the events
Most of the prediction of financial market crash literature was applied to developed markets, but Jarrow, Kchia, and Protter (2011) were interested in determining if risky assets prices exhibit a bubble in emerging markets by using Brownian motion, the results confirmed that the price of risky assets does illustrate the bubbles and also the absence of the bubble. Additionally, Wu, Meng, and Velazquez (2015) were concerned about the spread of financial market crashes in the regional stock markets, such as the stock market indices of Europe, the United States, Latin America, and Asia. Through the TVC-GARCH model and the multivariate skew-Student density, they discovered that if the market crash starts in Asia, it can move first to Europe and then to the United States. But if the crash begins in the United States, the effect in Asia can be seen the very next day. Therefore, “the probability of observing Asian crashes conditional on US 1-day lagged crashes is much higher than the probabilities of observing crashes in other regions conditional on the contemporaneous crashes in the Asian market” (Wu et al., 2015, p. 1150).
Recently, a new methodology, namely Hawkess process has been successfully applied to financial risk quantification (Gresnigt, Kole, and Franses, 2016), and Egorova and Klymyuk (2017) applied this type of process to predict currency crashes by the observation of the returns during market failures and past events (exogenous or endogenous), specifically in USD/RUB currency. The authors conclude that such a model is a powerful and accurate tool to predict currency crashes. Despite the investors trying to hedge their portfolios against any event that might cause return loses to them, sometimes effectiveness of information results in panic and irrational investments. Chen and Huang (2018) stated that when investors act irrationally, the stock market index tends to collapse, and this should be considered as a warning signal; they reached such conclusion by employing Fourier spectrum analysis applied to the Dow Jones Index.
Alternatively, there is the possibility to predict financial market crashes employing economic variable models. Klein and Moore (1983) determined two types of indicators to forecast the business cycle in an economy. First, economic indicators like employment, income, and trade could show if a country was prosperous or economically depressed. Second, lagged indicators were useful to provide early warnings of the business cycle because of the reactions of the economic climate. In the same line, Hertzberg and Beckman (1989) revised the essential index
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indicators again to predict business cycle behavior, stating that index of leading indicators involved the average weekly hours of production, new orders of manufacturers (consumer goods and material industries) and index of stock prices (500 common stocks). Important lagged indicators were the average duration of unemployment (weekly ratio), manufacturing and trade inventories to sales, and the average prime rate that the banks charge, among others.
Flood, Hodrick, and Kaplan (1986) tried to predict rational bubbles employing misspecification models and econometric methods. These models showed that the asset price volatility could not predict movements in the markets. Later, Campbell and Vuolteenaho (2004) used the Modigliani and Cohn (1979) hypothesis to evaluate the role of inflation, establishing that almost 80% of the variation in the time-series in the stock-market mispricing was due to inflation, concluding that inflation is practically uncorrelated with the subjective risk premium. On the other hand, Flavin (1983) started to employ the long-term interest rates in bounds with the stock prices to show that the volatility (variance bounds) test in small samples tends to be biased and therefore, there is a violation of market efficiency due to volatility measures. In the same line, Kleidon (1986) by using time series in nonstationary of prices, earnings, and dividends, determined that the stock prices are nonstationary, and these can be account as a gross violation of variance bounds, which demonstrates that the stock prices change when the expectation of future cash flows also changes. Apart from that, Campbell and Shiller (1988) presented an autoregressive approach for the US stock market data to demonstrate that a long historical average of real earnings is a reliable predictor of the present value of future real dividends. Later, Campbell and Shiller (1989, 2001) used Monte Carlo simulation to test and evaluate price-earnings ratios and dividends-price ratios that are forecasting variables for the stock market index. Similarly, Lewellen (2004) studied dividend yields in stock markets by using regressions in small-samples to test the forecasting power in stock returns. As a result, Lewellen showed that from 1946 to 2000, the dividend yield could predict market returns. In a study of crash predictor, Kumar, Moorthy, and Perraudin (2003) successfully established a logit model, based on lagged macroeconomic and financial data, to predict crashes in emerging market currencies. This model was used as a trading strategy where an investor could decide to go long or short in the currency market, depending on whether the crash probabilities were low or high.
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Ziemba and Schwartz (1991) developed a simple model that was the difference between stock and bond rates of return, in which the main idea was the relationship between stocks and bonds when they compete for investment dollar, where stocks were favored when interests are low, and bonds were maintained when the interest rate was high. Hence, the authors determined that a financial crash could be predicted with a 10% fall in the stock market index within one year. An extension of the Ziemba-Schwartz model was proposed by Assness (2002), known as the Fed model, which consists on the comparison between the stock market’s earnings yield (E/P) and long-term government bonds with the aim of forecast stock returns and find crashes. Therefore, when long-term bonds returns are high, the E/P of stocks are low. That is explained by Berge, Consigli and Ziemba (2008) when the bond yield is too high; it occurs a market adjustment that results in a change from stocks into bonds. When the needed adjustment is significant, it can cause an equity market correction. Nevertheless, the Fed model has disadvantages as it does not consider time-varying risk premiums in portfolios; neither consider inflation (Berge et al., 2008). Aditionally, Campbell and Vuolteenaho (2004) suggested that this model “incorrectly extrapolates past nominal growth rates without taking into account the impact of time-varying inflation”. In contrast, the Fed model was tested again by Estrada (2006), proving that this is one of the best models to predict crashes. Following the first model developed by Ziemba and Schwartz (1991) the Bond-Stock Earnings Yield (BSEYD) model is based on the difference between the returns of the long-term treasury bonds and the reciprocal of the Price-Earnings ratio of a specific stock market index. Then, Consigli, MacLean, Zhao, and Ziemba (2009) propose a stochastic model of equity returns based on an extension of the BSEYD model that includes a risk premium in which bond-stock yield difference endogenously produce market correction. Later, it was tested for economies like United States, Germany, Canada, The UK, and Japan between 5 and 10 years by Berge and Ziemba (2003) the authors found that “in all countries except Canada, the final wealth of the strategies exceeds the buy and hold for the stock market, with some months in cash and a higher Sharpe ratio.”
In the same line, Lleo and Ziemba (2015) studied United States, China, and Iceland to identify signals to warn a financial market crash, employing the BSEYD model and Monte Carlo simulation; as a result, the model provides a 72% accuracy. Consigli and Ziemba (2009) defined The Bond-stock yield differential model as a risk factor that influences the risk process. They analyzed this through peaks over the threshold of the US market from 1985 to 2004. In which,
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they presented the effectiveness of the BSEYD model using also maximum likelihood. On top of that, Lleo and Ziemba (2017) presented an extension of the study of financial market crashes identification in the S&P 500 (United States) from 1964 to 2014. But, with the difference of demonstrating the robustness of the model with likelihood statistics and four measures to predict crashes: price-earnings ratio (P/E Ratio), the logarithmic price-earnings ratio (P/E Ratio), the BSEYD model and the logarithmic BSEYD model. As a result, it was displayed that the logarithm measures flatten prices, and therefore, the crashes cannot be observed.
To contribute to the literature of economic variables models to predict financial crashes. This study demonstrates that the BSEYD model (and its posterior refinements) proposed by Ziemba and Schwartz (1991) is successfully applied in emerging countries as Mexico, Brazil, Greece, Czech Republic, Turkey, Indonesia, India, and Taiwan. That is, it was possible to identify the signals and crashes of financial markets according to each stock market index and long-term treasury bonds of each country named. The next section describes the methodology of the model to be employed.
3. Methodology
This section presents the process we used to predict financial markets crashes in emerging markets. First, we focus on the identification of financial crashes through the analysis of the Stock Market Index of each selected country. Then, we move to identify the signals of a financial market crash through the BSEYD model, and finally, we compare the crashes and signals obtained for each country. This comparison is performed to check if the BSEYD model is successful when applied to each emerging country. All of these, employing the Lleo and Ziemba’s (2017) process to identify crashes and signals.
3.1. Definition of a correction
In order to identify financial market crashes accurately, we apply the identification procedure defined in Lleo and Ziemba (2017) where a crash is formally identified on the day when the closing price crosses the 10% threshold. First, we identify all the local troughs in the data set; this is “Today is a local trough if there is no lower closing price within ±d business days” (Lleo and Ziemba,
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2017, p. 66). Second, to identify the crashes, three conditions must hold: (1) the closing level of the market index2 is down at least 10% from its highest level within the past year today, and the
loss was less than 10% yesterday, (2) this highest level reached by the market index before the present crash differs from the highest level corresponding to a previous crash, (3) this highest level occurred after the local trough that followed the last crash.
These rules guarantee that the crashes we identify are distinct, given that two crashes are not distinct if they occur within the same larger market decline. Additionally, the following key assumptions and restrictions are necessary.
a. One year is equivalent to 252 trading days.
b. d is equal to 90 days that are counted forward and backward with the aim of creating a local through for the crash’s identification.
c. A local trough is a time window of 180 days.
d. The highest level and closing level found in the local trough (i) given forward cannot be repeated.
3.2. Signal construction
Regarding the market crashes signals identification close to the near future, we employ the yield on nominal Treasury bonds of 10 years given a reference country. In general, the signal occurs when the returns of the bond adjusted by the reciprocal of the P/E ratio or stock earnings yield (𝑀(𝑡) or BSEYD in this case) exceeds the time-varying threshold we define as 𝐾(𝑡). This is, 𝑀(𝑡) > 𝐾(𝑡) and it is shown in the Equation (1) following notation of Lleo and Ziemba (2017):
𝑆𝑖𝑔𝑛𝑎𝑙(𝑡) = 𝑀(𝑡) − 𝐾(𝑡) > 0 (1)
In other words, the signal occurs when the expression 𝑀(𝑡) − 𝐾(𝑡) is greater than 0. Given the Equation (1) above, it is essential to highlight the next crucial parameters:
The 𝑀(𝑡) measure for the crash prediction comes from the model BSEYD, first developed by Ziemba and Schwartz (1991) and applied in more than eight countries (Berge and Ziemba,2003; Lleo and Ziemba, 2015; 2017), and it is defined as the difference between the yield on nominal
2 Lleo and Ziemba (2017) take the S&P 500 as the market index reference for United States. In this paper we use the following index: MEXBOL, IBOV, ASE, PX, XU100, LQ45, SENSEX, TWSE, SET50 for each country we evaluate.
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Treasury bonds of 10 years (𝑟(𝑡)) and the reciprocal of the P/E ratio or stock earnings yield (see Equation 2). Therefore, M(t) is equal to BSEYD.
𝐵𝑆𝐸𝑌𝐷(𝑡) = 𝑟(𝑡) −𝐸(𝑡)
𝑃(𝑡) (2)
Intuitively, 𝑀(𝑡) assess the relative market valuation.
The 𝐾(𝑡) or time-varying threshold measure is a confidence level based on normal distribution or Cantelli’s inequality. In our case, we employ the normal distribution centered in zero with mean (𝜇𝑡ℎ) and variance 𝜎𝑡ℎ (see Equation 3),3 where h is the time horizon of the trading days in reference
(252 days in this case). The mean and variance expressions can be found below in Equations (4) and (5), respectively.
𝑋𝑛~𝑁(𝜇𝑡ℎ, 𝜎𝑡ℎ) (3)
Following Equation (4), the moving average is determined by the sum of the yields on nominal 10-year Treasury bonds (𝑟(𝑡)) divided by the time horizon h. Also, Equation (5) presents the moving standard deviation, which is equal to the square root of the squared difference between the yield on nominal 10-year Treasury bonds (𝑟(𝑡)).
𝜇𝑡ℎ = 1 ℎ∑ 𝑟𝑡−𝑖 ℎ−1 𝑖=0 (4) 𝜎𝑡ℎ = √ 1 ℎ−1∑ (𝑟𝑡−𝑖− 𝜇𝑡) 2 ℎ−1 𝑖=0 (5)
As performed in Lleo and Ziemba (2017), we compute the 𝐾(𝑡) threshold using a standard one-tail 95% standard confidence interval based on a Normal distribution. “The choice of a 95% confidence level is standard in the literature. Increasing the confidence level eliminates false positives but reduces the number of signals, whereas reducing the confidence level has the opposite effect. Empirical research suggests that a 95% level with an annual horizon strikes a good balance between signal sensitivity and the risk of false positives […] In a Normal distribution, we expect 5% of the observations to lie in the right tail” (Lleo and Ziemba, 2017, p.p. 70- 71). Finally, a time interval between the signals identified is important for the following constraints:
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1. When a signal occurs, it must be at least 30 days after the last signal was identified. 2. The signal must occur between the last 504 trading days (2 years) of the financial market
crash identified.
3. The signal must take place at most 251 days after the peak date.
4. Empirical Results
This section describes the data of the emerging countries that we analyzed and presents the results of the signals and crashes identification for eight emerging markets using the previously described methodology. In this case, the country indices are divided by country groups, Latin American group formed by Mexico and Brazil indices. The second one is Emerging Europe computed by Greece, the Czech Republic, and Turkey indices, and the last one is Emerging Asia confirmed by Indonesia, India and Taiwan indices. See Appendix 1 for details of the data employed, and Appendix 2 for details of crash dates, maximum price dates, minimum price dates, and the prices given on these dates. The daily data employed for the study of each country was obtained from the Bloomberg platform4 and is composed of stock market index close price, stock market index P/E ratio, and the yield on nominal Treasury bonds of 10 years, all analyzed variables in USD. Table 1 shows descriptive statistics of each emerging market studied.
Table 1. Emerging markets descriptive statistics.
Country Mexico Brazil Greece Czech
Republic Turkey Indonesia India Taiwan
Period 2006-2018
2007-2018 1998-2018 2006-2018 2004-2018 2003-2018 2000-2018 2000-2018
Data 3,391 3,127 5,421 3,337 3,912 4,030 4,956 4,753
Yield’s
ticker GMXN10YR GEBR10Y GGGB10YR CZGB10YR GTRU10YR GIDN10YR GIND10YR GVTW10YR Mean 6.99
11.80 7.55 2.75 5.88 9.16 7.75 1.93
Variance 1.146 1.99 29.77 2.33 1.87 5.74 1.58 0.91
4For Mexico, the data for the period January 2 of 2006 to December 31 of 2018, (3,391 observations). Brazil, the data for the
period January 5 of 2007 to December 31 of 2018, (3,127 observations). Greece, the data for the period March 23 of 1998 to December 31 of 2018, (5,421 observations). The Czech Republic, the data for the period March 17 of 2006 to December 31 of 2018, (3,337 observations). Turkey, the data for the period January 2 of 2004 to December 31 of 2018, (3,912 observations). Indonesia, the data for the period July 22 of 2003 to December 31 of 2018, (4,030 observations). India, the data for the period January 3 of 2000 to December 31 of 2018, (4,956 observations). Taiwan, the data for the period October 12 of 2000 to December 31 of 2018 (4,753 observations).
13 Stock
Market index’s ticker
MEXBOL IBOV ASE PX XU100 LQ45 SENSEX TWSE
Mean,
P/E Ratio 20.62 42.43 18.35 80.46 10.79 16.82 18.22 21.75
Variance,
P/E Ratio 30.48 12533.9 285.10 112482.7 10.73 12.61 12.66 326.35
As observed in Table 1, long-term bond’s yield of Taiwan presents the lowest average and volatility, while Brazil has the highest average yield, but Greece exhibits the lowest volatility. For P/E ratio, Turkey (Czech Republic) presents the lowest (highest) average and volatility.
4.1. Latin America
Table 2 illustrates the total number of crashes, the total number of signals, and the correct and incorrect percentage of predictions found for Latin America countries. According to this table, Mexico has a higher percentage of correct predictions than Brazil. As we see Mexico’s signals are 8 and its crashes 7, while Brazil’s signals are 13 and 9 crashes. In consequence, Mexico has 87.5% correct predictions and only 12.5% incorrect predictions, and Brazil has 69.2% correct predictions and 30.8% incorrect predictions.
Table 2. Latin America total crashes and signals identified.
Country Number of crashes identified Number of signals identified Number of incorrect predictions Correct prediction percentage Incorrect prediction percentage Mexico 7 8 1 87.5% 12.5% Brazil 9 13 4 69.2% 30.8%
Figure 1 and 2 shows the signal time series related to the BSEYD model measured using the yield on nominal Treasury bonds of 10 years from Mexico and Brazil. In this case, it is important to highlight, that Mexico presents signals of a possible financial crash in 2018, meanwhile in Brazil not.
14 Figure 1. Signal for BSEYD model computed using the yield on Treasury Notes Mexico,
2006-2018.
Figure 2. Signal for BSEYD model computed using the yield on Treasury Notes Brazil,
2007-2018.
Signal crash identification
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4.2. Emerging Europe
The analysis concerning Greece was carried out for a period of 20 years from 1998 to 2018, in which 18 crashes and 13 signals were identified. Thus, the proportion of correct predictions was 54.54%; while, the proportion of incorrect prediction was 45.45% (Table 3). Figure 3 shows the signal time series related to the BSEYD model measured using the yield on nominal Treasury bonds of 10 years from Greece. Similarly, Table 3 illustrates the total number of crashes, the total number of signals, and the correct and incorrect percentages of predictions, but now for countries from the Emerging Europe group. As we can see, the Emerging European group obtained more than 55% correct and predictions and less than 45% incorrect predictions.
Table 3. European total crashes and signals identified.
Country Number of crashes identified Number of signals identified Number of incorrect predictions Correct prediction percentage Incorrect prediction percentage Greece 18 33 15 54.5% 45.5% Czech Republic 8 14 6 57.1% 42.9% Turkey 13 21 8 61.9% 38.1%
Figure 3. Signal for BSEYD model computed using the yield on Treasury Notes Greece,
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For the Czech Republic’s country index, the total number of correct predictions was 8, and the total number of incorrect predictions 14. It means that there are more than 55% correct predictions and less than 45% incorrect predictions of this stock index. Figure 4 illustrates the signal time series related to the BSEYD model measured using the yield on nominal Treasury bonds of 10 years from the Czech Republic.
Figure 4. Signal for the BSEYD model computed using the yield on Treasury Notes Czech
Republic, 2006-2018.
The available data for Turkey starts in 2004; thus, the period analyzed was 14 years. For this period, 13 crashes and 21 signals were identified for the Turkish index. Out of this, 61.90% of the predictions were correct, and 38.1% were incorrect. Figure 5 (in the next page) displays the crashes and signals identified by the BSEYD model with the yield on nominal Treasury bonds of 10 years from Turkey.
4.3. Emerging Asia
In Emerging Asia, Indonesia, with 75% has a higher percentage of correct predictions than India, with 69.2% and Taiwan with 61.9%. On the one hand, for Indonesia, the model identified 16 signals for 16 crashes for the Indian stock market index and the Indian yield on treasury bonds. On the other hand, the model identified many more signals for the crashes in India and Taiwan, which in consequence predicts correctly the crashes between 60% and 70% in these two countries. Table
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4 shows crashes and signals identified for emerging Asia countries, and it also illustrates the percentage of correct and incorrect predictions similar to previous tables.
Figure 5. Signal for BSEYD model computed using the yield on Treasury Notes Turkey,
2004-2018.
Table 4. Total crashes and signals identified in Asia.
Country Number of crashes identified Number of signals identified Number of incorrect predictions Correct prediction percentage Incorrect prediction percentage Indonesia 12 16 4 75.0% 25.0% India 18 26 8 69.2% 30.8% Taiwan 13 21 8 61.9% 38.1%
The first emerging Asia country analyzed is Indonesia. We examine the LQ45 index (Indonesian stock market index) data for a reference period of 15 years, from 2003 to 2018. The model provides only 25% incorrect predictions, 12 crashes, and 16 signals identified. Figure 6 shows the crashes and signals identified by the BSEYD model with the yield on nominal Treasury bonds of 10 years for the Indonesia case.
Signal crash identification
18 Figure 6. Signal for BSEYD model computed using the yield on Treasury Notes Indonesia,
2003-2018.
For India 18 crashes and 26 signals were identified for the Indian Stock Index. This means that 69.23% of the predictions were correct, and 30.76% were incorrect from 2000 to 2018, i.e. 18 years of analysis. The results mentioned above are observed in Figure 7, for the BSEYD model with the yield on nominal Treasury bonds of 10 years from India.
Figure 7. Signal for BSEYD model computed using the yield on Treasury Notes India, 2000-2018.
Signal crash identification
Signal crash identification
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For Taiwan like India, the data were obtained starting in the year 2000. In 18 years, 13 crashes and 21 signals were identified for this stock index. That is, 61.90% of predictions were correct, and 38.1% were incorrect. Figure 8 shows the BSEYD model with the yield on nominal Treasury bonds of 10 years from Taiwan.
Figure 8. Signal for BSEYD model computed using the yield on Treasury Notes Taiwan,
2000-2018.
In summary, for the analyzed emerging stock indices, the BSEYD model (Ziemba and Lleo, 2017) could be successfully applied. On average, it was possible to obtain correct predictions more than 70% of the time for the Latin American group, more than 50% of the time for the Emerging Europe Group, and more than 60% of the time for the Asian group (See Table 5 for a summary of the results for emerging markets evidence in our work). Therefore, we can conclude that this model can be used for emerging markets to get signals and possible future market crashes. According to the last results, it is essential to highlight that in the Latin American group, it is a signal for a close financial crash in Mexico in 2018; as we can see in Figure 1, price is falling, and it has already passed the threshold. In the European group, we can see in Figure 6 that the signal for Turkey, there is also a signal. Eventually, in Asian emerging group happened the same for Indonesia and India, where the prices fall until passing the threshold.
20 Table 5. Summary of total crashes and signals identified for the analyzed emerging market
countries Country Number of crashes identified Number of signals identified Number of incorrect predictions Correct prediction percentage Incorrect prediction percentage Mexico 7 8 1 87.5% 12.5% Brazil 9 13 4 69.2% 30.8% Greece 18 33 15 54.5% 45.5% Czech Republic 8 14 6 57.1% 42.9% Turkey 13 21 8 61.9% 38.1% Indonesia 12 16 4 75.0% 25.0% India 18 26 8 69.2% 30.8% Taiwan 13 21 8 61.9% 38.1% 5. Further Results
In this section, we keep monitoring and developing an early warning system for financial market crashes employing the BSEYD model (performed by Lleo and Ziemba in 2015) for China and the United States. We aim to identify signals for a possible financial market crash soon (in 2020 or 2021).
5.1. The United States
Lleo and Ziemba (2015) performed the analysis from January 31, 1964, to December 31, 2014, for the United States employing the S&P 500 stock market index. Then, this section is an extension of Lleo and Ziemba (2015) with S&P 500 daily data from January 31, 1964, to July 31, 2019, for a total of 14,479 observations. Since the purpose is to find accurate signals, and the S&P 500’s daily data is pervasive (55 years), it is necessary to change the assumption of local through. In other words, when a Signal occurs, it must be at least 94 days after the last signal was identified and not 30 days, as it was done before by Lleo and Ziemba (2015).
21
As a result of this change, the percentage of correct predictions for the United States increased by 2.09% compared to that of Lleo and Ziemba (2015) with the extension of S&P 500’s daily data. Besides, the number of incorrect predictions remained constant for both year-ranges owing to the signals, and crashes identified grew up the same. From Table 6, we can observe the difference between crashes and signals identified between both year-ranges.
Table 6. Total crashes and signals identified for the United States.
Year ranges Number of crashes identified Number of signals identified Number of incorrect predictions Correct prediction percentage Incorrect prediction percentage Lleo and Ziemba (2015) 1964 - 2014 28 40 12 70.00% 30.00% Our work 1964 - 2019 31 43 12 72.09% 27.91%
Remarkably, the reciprocal of P/E ratio of the S&P 500 are significantly lower than interest rates of US 10-year government bond yield for the period of 2015 and 2019 (see las column of Table 6). Besides, in January 2018, the S&P 500 enter in danger of a close financial market crash, due to the interest rate of 10-year government bond yield increased but not enough to be greater than the P/E reciprocal ratio of the S&P 500. Figure 9 illustrates the signals identified using the BSEYD model with nominal Treasury bonds of 10-years maturity. As can be observed in Signal behavior of last months from the BSEYD model, it is not foreseen a financial crash in the US, however, this indicator must be continuously monitored.
22 Figure 9. Signal for BSEYD model computed using the yield on Treasury Notes United States,
1964-2019.
Table 6. S&P 500 index, P/E ratios, government bond yields, and the yield premium over stocks,
January 2015 – October 2019.
Year Month S&P 500 Index (a) 10 Yr Gbd PER (b) 1/pe (%) (a) -(b) 2015 Jan 2029,18 1,88 18,10 5,53 -3,65 Feb 2082,94 1,98 18,54 5,39 -3,42 Mar 2079,99 2,04 18,48 5,41 -3,37 Apr 2093,59 1,92 18,69 5,35 -3,43 May 2112,62 2,20 18,88 5,30 -3,10 Jun 2099,28 2,36 18,76 5,33 -2,97 Jul 2093,39 2,32 18,74 5,34 -3,02 Aug 2039,87 2,16 18,25 5,48 -3,32 Sep 1943,35 2,16 17,38 5,75 -3,59 Oct 2024,81 2,06 18,34 5,45 -3,40 Nov 2081,01 2,26 18,77 5,33 -3,07 Dec 2054,38 2,23 18,56 5,39 -3,15 2016 Jan 1922,74 2,08 17,66 5,66 -3,58 Feb 1902,53 1,77 17,48 5,72 -3,95 Mar 2022,56 1,88 18,68 5,35 -3,47 Apr 2075,54 1,80 19,56 5,11 -3,32 May 2067,07 1,80 19,45 5,14 -3,34 Jun 2083,89 1,64 19,61 5,10 -3,46
23 Jul 2146,71 1,49 20,32 4,92 -3,43 Aug 2177,48 1,56 20,59 4,86 -3,30 Sep 2158,70 1,62 20,39 4,90 -3,28 Oct 2143,02 1,75 20,18 4,96 -3,20 Nov 2166,79 2,15 20,39 4,90 -2,76 Dec 2247,41 2,49 21,15 4,73 -2,24 2017 Jan 2273,45 2,43 20,88 4,79 -2,36 Feb 2330,97 2,42 21,34 4,69 -2,27 Mar 2366,82 2,48 21,63 4,62 -2,15 Apr 2357,79 2,29 20,89 4,79 -2,50 May 2396,24 2,30 21,20 4,72 -2,42 Jun 2433,99 2,18 21,44 4,66 -2,48 Jul 2452,91 2,31 21,00 4,76 -2,45 Aug 2456,22 2,20 20,99 4,76 -2,56 Sep 2492,07 2,20 21,26 4,70 -2,51 Oct 2557,00 2,36 21,66 4,62 -2,26 Nov 2593,76 2,35 21,92 4,56 -2,21 Dec 2665,25 2,41 22,46 4,45 -2,05 2018 Jan 2784,60 2,57 22,74 4,40 -1,82 Feb 2706,51 2,86 21,97 4,55 -1,69 Mar 2699,96 2,84 21,86 4,57 -1,74 Apr 2653,63 2,87 20,42 4,90 -2,03 May 2702,36 2,98 20,62 4,85 -1,87 Jun 2754,35 2,91 20,99 4,76 -1,85 Jul 2789,99 2,88 20,28 4,93 -2,05 Aug 2857,82 2,89 20,69 4,83 -1,95 Sep 2901,50 2,99 20,95 4,77 -1,78 Oct 2785,46 3,16 18,62 5,37 -2,22 Nov 2719,90 3,11 18,60 5,38 -2,26 Dec 2563,33 2,83 17,46 5,73 -2,90 2019 Jan 2605,77 2,71 17,20 5,81 -3,11 Feb 2755,90 2,67 18,19 5,50 -2,83 Mar 2803,98 2,57 18,53 5,40 -2,83 Apr 2903,86 2,53 19,07 5,24 -2,72 May 2853,46 2,39 18,79 5,32 -2,93 Jun 2890,17 2,07 19,04 5,25 -3,18 Jul 2996,10 2,05 19,65 5,09 -3,04 Aug 2897,50 1,62 19,04 5,25 -3,63 Sep 2979,50 1,69 19,63 5,09 -3,41 Oct 2977,68 1,70 19,74 5,06 -3,36
24
5.2. China
For China, the analyzed period taken by Lleo and Ziemba (2015) was from June 6, 2005, to December 31, 2014. Now in our work, the period covers from June 6, 2005, to July 31, 2019 (3,693 observations). The stock market index daily data of the SSE Composite Index is taken from the Bloomberg platform. Table 7 shows the total crashes and signals in the year-ranges.
Table 7. Total crashes and signals identified for the Chinese Index.
Year ranges Number of crashes identified Number of signals identified Number of incorrect predictions Correct prediction percentage Incorrect prediction percentage Lleo and Ziemba (2015) 1964 - 2014 7 12 5 58.33% 41.67% Our work 1964 - 2019 10 13 3 77.00% 23.00%
As a result for China, the number of incorrect predictions decreases by 20% because of the increase in the number of identified crashes (3 units) and the non-significant increase in the number of signals (1 unit). Therefore, the correct prediction in the SSE Composite Index grew up by more than 10% and this leads to a considerable decrease in incorrect predictions (18%).
Given the previous results, with the extension of 5 years to the BSEYD Model by Ziemba and Lleo (2015) for the United States and China, the results provide evidence for an increase in the percentage of correct predictions of 17% and a decrease in the percentage of incorrect predictions of 26%. See Appendix 3 and 4 for more details about the crashes identified for the United States and China, respectively.
25 Figure 10. Signal for BSEYD model computed using the yield on Treasury Notes China,
2005-2019.
As observed in Figure 10, the Signal is negative but is increasing to zero level, and this could raise warning for the Chinese financial market.
6. Conclusions
This paper aims to test the BSEYD model in several countries of emerging markets. This model has also been applied to the US and China (Lleo and Ziemba, 2015). But, to the best of our knowledge, this is the first time for emerging markets. According to the results obtained in this work, there is an average of 78.4% correct predictions and an average of 21.6% incorrect predictions for the Latin American group. In the case of the Emerging Europe group, an average of 57.9% correct predictions, and 42.1% incorrect predictions on average. Finally, for the Asian group, an average percentage of correct predictions of 68.7% and an average of 31.3% of incorrect predictions are found. Through the BSEYD model using the difference between the stock market index data and the yield of treasury bonds for each country, signals and financial market crashes
26
were predicted for the country. It is important to consider that the analyzed period taken to study depends on the availability of information for each country.
Given the obtained results, the BSEYD model has satisfactory performance, not only for countries with developed economies but also for countries in emerging economies. Now, considering the obtained results for the eight emerging countries of the study, it was possible to identify the signals and crashes for each of them. Therefore, this model proves to be a useful tool for predicting financial crashes in emerging markets. On average, the BSEYD model predicts crashes successfully more than 65% of the time for the emerging countries analyzed here.
From this analysis, it is possible to contribute to the literature related to the prediction of financial crises in emerging countries. It is important to emphasize that stemming from the BSEYD model of Lleo and Ziemba (2017), it is possible to predict a financial market crash through the signals observed during the period analyzed because it allows anticipating the highly probable event of a financial market crash. For instance, to predict a financial market crash in a country, signals and crashes from previous periods are observed, together with the last date of the observed signal. These could be seen in the graphs of the signal’s prediction showed above.
According to our results, the BSEYD model does not foresee a next financial market crash in the US market. Concerns have recently raised since the US yield curve has inverted in 2019. The Signal indicator from BSEYD model for China is still negative, but approaching to zero level, and this indicator must be monitored in the following months for an early warning in the Chinese market.
Finally, as future research, other methodologies proposed by Lleo and Ziemba (2017) can be employed for the prediction of financial crashes. Moreover, the results obtained here could be improved using different approaches, such as the natural log of the P/E ratio and the natural logarithm of BSEYD. Besides, the comparison may be performed when Cantelli’s inequality is employed for 𝐾(𝑡) the threshold in the BSEYD model.
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30 Appendix Section
Appendix 1. Bloomberg tickers for data
Country Country Generic Govt 10 Year Yield Stock Market Index
Mexico GMXN10YR MEXBOL
Brazil GEBR10Y IBOV
Greece GGGB10YR ASE
Czech
Republic CZGB10YR PX
Turkish GTRU10YR XU100
India GIND10YR SENSEX
Indonesia GIDN10YR LQ45
Taiwan GVTW10YR TWSE
Appendix 2
Country Position Crash date Maximum Price date Maximum Price Minimum Price date Minimum Price Yesterday Price, based on Minimum Price Mexico 2 8/11/2007 18/10/2007 32836.12 21/01/2008 25284.88 26713.83 3 2/07/2008 21/04/2008 32095.04 27/10/2008 16868.66 16978.84 7 17/05/2011 5/01/2011 38696.24 8/08/2011 31715.78 33697.87 10 20/05/2013 28/01/2013 45912.51 20/06/2013 37517.23 39044.95 12 10/12/2014 8/09/2014 46357.24 16/12/2014 40225.08 40334.59 14 7/01/2016 24/04/2015 45773.31 8/01/2016 40265.37 40661.57 17 28/03/2018 24/07/2017 51665.66 29/05/2018 44647.37 44851.05 Brasil 2 8/11/2007 18/10/2007 32836.12 21/01/2008 25284.88 26713.83 3 2/07/2008 21/04/2008 32095.04 27/10/2008 16868.66 16978.84 7 17/05/2011 5/01/2011 38696.24 8/08/2011 31715.78 33697.87 10 20/05/2013 28/01/2013 45912.51 20/06/2013 37517.23 39044.95 12 10/12/2014 8/09/2014 46357.24 16/12/2014 40225.08 40334.59 14 7/01/2016 24/04/2015 45773.31 8/01/2016 40265.37 40661.57 17 28/03/2018 24/07/2017 51665.66 29/05/2018 44647.37 44851.05 Greece 1 31/03/1999 19/03/1999 3774.29 1/04/1999 3121.39 3376.37
31 Country Position Crash
date Maximum Price date Maximum Price Minimum Price date Minimum Price Yesterday Price, based on Minimum Price 2 24/09/1999 17/09/1999 6355.04 7/07/2000 3914.03 3968.83 3 13/06/2000 19/05/2000 4802.61 3/04/2001 2966.65 3032.08 4 8/11/2000 6/10/2000 4027.09 21/09/2001 2105.56 2133.46 5 12/09/2001 28/08/2001 2805.88 24/07/2002 2027.43 2085.89 6 3/07/2002 21/05/2002 2405.57 31/03/2003 1467.30 1517.94 8 4/08/2004 28/04/2004 2553.76 20/08/2004 2227.33 2257.54 11 19/05/2006 8/05/2006 4316.98 14/06/2006 3379.28 3394.78 13 15/01/2008 31/10/2007 5334.50 23/01/2008 4098.75 4253.25 Cezch Republic 2 21/11/2007 29/10/2007 1936.10 16/07/2008 1398.60 1400.30 3 24/06/2008 19/05/2008 1710.80 18/02/2009 628.50 651.50 5 5/02/2010 20/01/2010 1220.30 8/02/2010 1092.80 1094.30 7 3/08/2011 18/01/2011 1276.30 25/11/2011 843.00 852.40 9 27/03/2013 9/01/2013 1066.14 18/04/2013 931.44 950.38 11 8/07/2014 21/02/2014 1046.06 8/07/2014 933.64 951.92 13 24/08/2015 13/04/2015 1058.44 12/02/2016 845.92 847.23 14 8/12/2015 3/08/2015 1040.97 27/06/2016 790.09 819.58 Turkey 1 16/03/2005 28/02/2005 28396.17 18/04/2005 23285.94 23853.34 3 8/03/2006 27/02/2006 47728.50 26/06/2006 31950.56 33132.30 5 22/11/2007 15/10/2007 58231.90 31/03/2008 39015.44 39501.17 7 29/05/2008 28/04/2008 43613.96 5/03/2009 23035.95 23940.66 8 19/11/2009 23/10/2009 51380.65 20/11/2009 45230.95 46114.59 10 29/11/2010 9/11/2010 71543.26 10/08/2011 50307.63 52961.21 11 27/05/2011 3/05/2011 70072.02 24/11/2011 49621.67 51091.51 13 3/06/2013 22/05/2013 93178.87 28/08/2013 65452.40 65519.87 15 24/09/2014 25/07/2014 84218.02 8/10/2014 72943.50 74384.37 16 4/03/2015 26/01/2015 91412.94 14/12/2015 69308.74 70280.34 17 8/06/2015 18/05/2015 88651.88 21/01/2016 68567.89 69603.95 18 16/05/2016 18/04/2016 86343.65 1/12/2016 72519.85 73995.20 20 17/04/2018 29/01/2018 120845.30 16/08/2018 87143.21 90262.95 India 1 21/07/2000 12/07/2000 4964.28 12/04/2001 3183.77 3183.77 2 9/03/2001 15/02/2001 4437.99 21/09/2001 2600.12 2761.66 3 29/04/2002 26/02/2002 3712.74 28/10/2002 2834.41 2875.53
32 Country Position Crash
date Maximum Price date Maximum Price Minimum Price date Minimum Price Yesterday Price, based on Minimum Price 6 26/02/2004 14/01/2004 6194.11 23/06/2004 4644.00 4735.86 7 18/04/2005 8/03/2005 6915.09 19/04/2005 6134.86 6156.78 8 27/10/2005 4/10/2005 8799.96 28/10/2005 7685.64 7798.49 9 19/05/2006 10/05/2006 12612.38 19/07/2006 10007.34 10226.78 10 28/02/2007 8/02/2007 14652.09 16/03/2007 12430.40 12543.85 11 21/01/2008 8/01/2008 20873.33 16/07/2008 12575.80 12676.19 12 4/06/2008 2/05/2008 17600.12 9/03/2009 8160.40 8160.40 14 5/02/2010 6/01/2010 17701.13 5/02/2010 15790.93 16224.95 15 14/01/2011 5/11/2010 21004.96 10/02/2011 17463.04 17592.77 17 20/06/2011 4/04/2011 19701.73 9/01/2012 15814.72 15867.73 19 20/08/2013 23/07/2013 20302.13 21/08/2013 17905.91 18246.04 22 7/05/2015 3/03/2015 29593.73 11/02/2016 22951.83 23758.90 23 24/08/2015 13/04/2015 29044.44 25/02/2016 22976.00 23088.93 24 21/11/2016 8/09/2016 29045.28 21/11/2016 25765.14 26150.24 26 23/03/2018 29/01/2018 36283.25 23/03/2018 32596.54 33006.27 Indonesia 1 7/05/2004 28/04/2004 179.488 25/08/2004 158.362 160272 2 22/08/2005 3/08/2005 263.248 29/08/2005 216.681 229578 4 18/05/2006 11/05/2006 346.943 3/08/2006 306.313 310027 5 7/08/2007 24/07/2007 499.880 16/08/2007 393.974 393974 6 16/01/2008 11/12/2007 621.126 19/08/2008 419.159 428173 8 15/07/2008 29/05/2008 519.111 15/05/2009 340.977 345358 10 10/01/2011 9/11/2010 690.261 24/01/2011 585.220 590236 11 9/08/2011 1/08/2011 742.502 4/10/2011 569.457 584218 13 10/06/2013 20/05/2013 884.134 25/06/2013 719.575 724247 16 8/06/2015 7/04/2015 962.027 9/07/2015 824.732 831643 19 15/11/2016 4/10/2016 946.525 23/12/2016 828.746 828746 20 23/03/2018 23/01/2018 1.132.188 26/04/2018 943.291 978263 Taiwan 1 3/04/2001 15/02/2001 6104.24 3/10/2001 3446.26 3492.12 2 6/05/2002 22/04/2002 6462.30 11/10/2002 3850.04 3947.61 4 23/03/2004 4/03/2004 7034.10 17/05/2004 5482.96 5777.32 6 19/10/2005 3/08/2005 6455.57 28/10/2005 5632.97 5661.18 8 5/06/2006 8/05/2006 7474.05 7/08/2006 6416.61 6442.61
33 Country Position Crash
date Maximum Price date Maximum Price Minimum Price date Minimum Price Yesterday Price, based on Minimum Price 9 12/11/2007 29/10/2007 9809.88 17/12/2007 7830.85 8118.08 11 11/06/2008 19/05/2008 9295.20 20/11/2008 4089.93 4284.09 13 2/02/2010 15/01/2010 8356.89 9/06/2010 7071.67 7151.99 15 5/08/2011 28/01/2011 9145.35 19/12/2011 6633.33 6785.09 Appendix 3.
The S&P 500 Index experienced 33 corrections between January 31, 1964 and July 31,2019
Position Crash date Maximum Price date Maximum Price Minimum Price date Minimum Price Yesterday Price, based on Minimum Price 2 16/05/1966 9/02/1966 94.06 17/05/1966 83.63 84.41 5 5/03/1968 25/09/1967 97.59 5/03/1968 87.72 87.92 7 19/06/1969 29/11/1968 108.37 29/07/1969 89.48 90.21 9 26/01/1970 10/11/1969 98.33 13/08/1970 74.76 75.42 10 4/08/1971 28/04/1971 104.77 23/11/1971 90.16 90.79 13 27/04/1973 11/01/1973 120.24 5/12/1973 92.16 93.59 14 20/11/1973 12/10/1973 111.44 13/09/1974 65.20 66.71 16 8/08/1975 15/07/1975 95.61 16/09/1975 82.09 82.88 18 25/05/1977 21/09/1976 107.83 31/05/1977 96.12 96.27 19 24/10/1977 16/03/1977 102.17 28/02/1978 87.04 87.72 21 26/10/1978 12/09/1978 106.99 14/11/1978 92.49 93.13 22 10/03/1980 13/02/1980 118.44 25/03/1980 99.19 99.28 25 31/08/1981 25/03/1981 137.11 8/03/1982 107.34 109.34 26 9/02/1982 30/11/1981 126.35 12/08/1982 102.42 102.60 28 13/02/1984 10/10/1983 172.65 23/02/1984 154.29 154.31 29 23/05/1984 7/10/1983 170.80 24/07/1984 147.82 148.95 37 30/01/1990 9/10/1989 359.80 30/01/1990 322.98 325.20 38 17/08/1990 16/07/1990 368.95 11/10/1990 295.46 300.39 48 27/10/1997 7/10/1997 983.12 27/10/1997 876.99 941.64 49 14/08/1998 17/07/1998 1186.75 31/08/1998 957.28 1027.14
34 Position Crash date Maximum Price date Maximum Price Minimum Price date Minimum Price Yesterday Price, based on Minimum Price 51 29/09/1999 16/07/1999 1418.78 15/10/1999 1247.41 1283.42 52 14/04/2000 24/03/2000 1527.46 30/11/2000 1314.95 1341.91 53 11/10/2000 1/09/2000 1520.77 4/04/2001 1103.25 1106.46 55 6/05/2002 4/01/2002 1172.51 9/10/2002 776.76 798.55 63 26/11/2007 9/10/2007 1565.15 7/07/2008 1252.31 1262.90 64 26/06/2008 19/05/2008 1426.63 9/03/2009 676.53 683.38 66 20/05/2010 23/04/2010 1217.28 2/07/2010 1022.58 1022.58 68 4/08/2011 29/04/2011 1363.61 3/10/2011 1099.23 1131.42 74 24/08/2015 21/05/2015 2130.82 9/02/2016 1852.21 1853.44 78 8/02/2018 26/01/2018 2872.87 2/04/2018 2581.88 2640.87 79 23/11/2018 20/09/2018 2930.75 24/12/2018 2351.10 2351.10 Appendix 4
The SHCOMP Index experienced 10 corrections between June 06, 2005 and July 31,2019
Position Crash date Maximum Price date Maximum Price Minimum Price date Minimum Price Yesterday Price, based on Minimum Price 2 2/02/2007 24/01/2007 2.975.129 5/02/2007 2.612.537 2.673.212 3 8/11/2007 16/10/2007 6.092.057 17/06/2008 2.794.751 2.874.103 6 12/08/2009 4/08/2009 3.471.442 5/07/2010 2.363.947 2.382.901 8 17/11/2010 8/11/2010 3.159.512 21/10/2011 2.317.275 2.331.366 9 30/09/2011 15/08/2011 2.626.770 31/07/2012 2.103.635 2.109.914 10 28/06/2012 2/03/2012 2.460.693 3/12/2012 1.959.767 1.980.117 11 15/04/2013 6/02/2013 2.434.477 27/06/2013 1.950.012 1.951.495 14 19/06/2015 12/06/2015 5.166.350 15/01/2016 2.900.970 3.007.649 16 7/01/2016 22/12/2015 3.651.767 28/09/2016 2.987.858 2.998.172 18 9/02/2018 24/01/2018 3.559.465 18/10/2018 2.486.419 2.561.614
