Quantitative analysis of large stock market crashes

Elaboration, 2011

33 Pages, Grade: A





Stock Market Prediction Methods
Bollinger Bands
Moving Averages
3-Months Moving Average of Monthly S&P index Data for the past 30 years
Regression Lines

Model Explanation

Financial Crisis – Events Analysis


Data Collection

Research Methodology

Application of Regression Model


Validity of model under different market conditions
S&P 500 value at different sell off scenarios:
At 5% sell off
At 10% sell off
At 15% sell off
At 20% sell off

Interpretation of results
Impact of various Macroeconomic factors on S&P Value




Money Aggregates

Validity of the predictions with the real world data


Matlab Code & GUI

Works Cited


The objective of this study is to structure a dependable model to forecast the timing of entry and exit from the stock markets by using multivariate linear regression analysis. The study uses major macroeconomic indicators such CPI, PPI, GDP, MEI as independent variables and the S&P 500 index value as the dependent variable. The sample consists of 30 years of monthly data. This study includes four different loss scenarios in the S&P 500 index value and analyzesthe data to see if the losses can be absorbed or if furtherlosses will occur. This report discusses the practical implications of using regression analysis and how it is used to predict the market movements. This paper concludes thatour regression model canhelp an investor to anticipate market movements and thus make appropriate buy and sell decisions.


It is a common fact that in today’s world, large amounts of capital is being traded through stock markets via numerous instruments namely bonds, shares, options, futures, swaps,and many more in currencies, commodities and shares of listed companies. Since there are numerous instruments available for trading, portfolio construction usually becomes a confusing task. Generally it is considered that investing in stocks/stock futures/stock options involves a higher degree of risk as it involves the elements of unsystematic risks, whereas index futures and options is relatively less risky as it involves elements of systematic risks. Because of this lesser risky aspect of options and futures, we are only concentrating on index values. Returns offered by these instruments are also so very attractive, even better than the stocks/shares of companies, that predicting the entry and exit in the markets becomes very crucial for most of the investors.

There are numerous tools available to predict the market movements. But for an average investor most of the prevailing models/tools are often too specific and/or yield output which is too complicated to comprehend. Thus, the average investor tends to take on the simplified approach of just buying at the troughs and selling at the peaks. Generally speaking when the investor is making a decision to determine if the market is approaching a peak (hence sell) or a trough (hence buy) they tend to look at the bigger picture of the economy. For example, several months of positive indicators such as steady job growth and profits, which are then followed by a few months of slowing in the numbers would indicate that the market was approaching a peak. Earlier these logical explanations were used by investors to predict market movements and they proved to be quite effective. Today however, logical explanation does not seem to give all the explanations for the market’s movements. The marketat times seems to react in the opposite way. This can also be explained by the advent of electronic trading where large sell/buy orders can be executed in a fraction of a time by large firms through basket trading. Basket trading has the potential to cause high volatility in the index values. As a consequence of having such large numbers of trading firms, volatility is expected to be ever present in the market. For an average investor with high margin facilities, this volatility in the market becomes a problem. The decision to keep the market position open or close the market position becomes crucial in this case because huge volatility can easily erase all the margins and the investors would face losses.

Stock Market Prediction Methods

According to efficient market hypothesis, all the market moving news are incorporated into the stock price as and when the news is out. Therefore investors who believe in efficient markets argue that it is not possible to predict the future stock prices. But technical analysts argue that it is possible to predict patterns from historical data.

Stock Market prediction methods broadly fall into 3 methods namely Time Series Models, Cause and Effect Models and Judgmental Models.

Most of the Time Series models are either univariate or transfer functions. A transfer function model involves several time series data, whereas univariate models involve only one time series. Moving Averages, Exponential smoothing, classical decomposition and Box-Jenkin’s ARMA Models are some of the tools that fall under this category.

Cause and Effect Models are used where there exists a strong cause and effect relationship between the variables, and their relationship is quantifiable. Regression models and Econometric models fall under this category. The regression analyses can be broadly classified into univariate regression analysis and multivariate regression analysis.

Judgmental Models are used when the data are not available or when the data are hypothetical. The most important judgmental models are PERT, Delphi, Analog and Bayesian Models.

Using one or all the above models a stock market prediction tool can be developed. Most of the stock market prediction software tools use technical analysis to predict the share price and index movements. But investors, instead of depending on any one of the above mentioned methods would rather go for a combination of methods to predict future values. Thus the advent of artificial neural networks (ANN). Many of these ANN models use a combination of statistical tools to predict the future prices/index values from the historical data.

Some of the important charts, which are used to predict future values in technical analysis, are:

Bollinger Bands

Another great facet in technical analysis is the concept of trading bands, also referred to as Bollinger Bands. The principal idea behind using Bands is to develop a technique by using moving averages, with two trading bands representing a relative definition of high and low. These high and low points are the determinants for volatility and standard deviation is applied to these price channels. Because trading is generally of erratic nature, analysts make use of these price lines to anticipate price action of a stock. Depending on the risk factor, volatility can be desired but most of the time is dreaded. These price channels are formed through extrapolation within which the price is expected to be contained. At the upper band, the stock is said to be overbought and inversely the stock is said to be oversold when the lower bands are reached. Bollinger Bands include the use of mean, standard deviation and an adjusted multiplier. Whereas Bollinger bands are used to signal the entry/exit points in the market, previous study on the historic analysis of the returns from market show that the returns do not follow any specific distribution pattern and do not always fall within the 95% significance level. Therefore using Bollinger bands for investing does involve some degree of risk.

Moving Averages

To provide a quick overview of the various averages, its significance in finance and its meaning, we find that all these methods aim to scale the direction of a price. Generally, these methods are basic number averaging of past data points, which, depending on the method chosen, can have an applied weight to it, but does not necessarily have to.

The simple moving average calculates the arithmetic mean of a value set. In finance, moving average charts uses price plotted against time to smooth over a predetermined time-period. These are the most commonly used charts and they are generally effective for short-term profits.When a weight multiple is applied to the moving average, it is done so, in an attempt to emphasize the most recent information and allow for a more precise trend estimate by increasing the responsiveness to the current market fluctuations. One such method is the exponential weighted moving average.

In this study, we have found a semi-annual discretization of the moving averages a more appropriate approach as it eliminates any market noise produced by the raw data since the study period is indeed of extensive length. Generally, investors will tend to sell the stock when the S&P course crosses below the moving average line or vice versa. As a statistical method, the moving average forms a very simple tool and is only then formidable when too much volatility is involved. Nevertheless, when volatility is low this statistical tool has rendered to be very useful.

3-Months Moving Average of Monthly S&P index Data for the past 30 years

illustration not visible in this excerpt

Figure 1: Quarterly Moving Average representing data from 1984 to 2012.

Regression Lines

Linear Regression analysis found its way in the finance sector as a method in modeling a single relationship by analyzing two different variables. The most common variables used for creating this relationship are price and time. The correlation between these two factors forming this relationship allows the modeling of capital asset pricing and additionally applies to the concept of quantifying the risk of investment. Regression models come in all shapes and sizes. Some of the important models that are used in today’s trading environment are:

- Simple and multiple regression models
- Linear and non-linear regression models
- Time Series and Cross-sectional models
- Artificial neural network models

One way to gauge how well the model fits is to use the coefficient of determination, also known as . measures how well a regression model approximates the actual data and can further indicate the strength of the relationship between the said variables. This usually happens on a scale from zero to one, where approaching a value of one is said to be of close or best fit and a value close to zero a poor fit.

Model Explanation

The fundamental assumptions underlying most of the stock prediction models involve some sort of continuity argument (i.e. the trend line will continue in a smooth fashion) and that the volatility will remain within certain ranges. In a preceding work, it was hypothesized that when a market mover makes a certain move, be it a large purchase or sell off, in a specific class of stocks, say mortgaged backed securities, that this move will dominate the overall stock market index for a short period of time and hence cause all of the predictive models to become not applicable. We will address the issue of how large of a move may be absorbed into the “bigger market” as opposed to sending the market into a spiral. For example, it is well known that in 2008 the S&P 500 was down 45.5% for the year and the volatility was high to the tune of 100-point moves in both directions within weeks. While these numbers did not quite match the more than fifty percent loss which occurred during the great depression of 1931 the situation was the closest to such behavior that has been observed in time since; however, much discussion was on whether this volatility was truly caused by true “market fundamentals” or if it was caused by other factors, such as computerized trading followed by market movers.

Financial Crisis – Events Analysis

During the second half of 2006, the S&P had fallen roughly around 10%, from the peaks of 1325 in May 2006 to 1220 in June 2006. In the proceeding weeks the macroeconomic and microeconomic news were mostly negative and the general market expectation was that there would be further declines. However, the markets appeared to be contradicting this view and looked to be absorbing this initial shock with the market heading back positive, jumping back over 1300 by the end of August 2007. On the other hand, near the end of 2007, the S&P 500 had again dropped roughly over 10%, falling from1550 in October down to 1440 in November. This event was then followed by negative news both on the macroeconomic front and on investor sentiment front. Hence again one would expect further declines. Again the market appeared to be contradicting this and looked to be absorbing this initial shock with the market heading back positive, jumping back over 1500 by December. But In this case instead of the news being absorbed, there was severe sell offs in the market as the full magnitude of the housing bubble hit the market and the liquidity was absolutely nil. Consequently the market fell over 50% from the market highs of 2007, reaching a bottom below 700 in early 2009.

In this study we try to develop a scheme to determine if after one of these “initial shocks” caused by sudden sell offs in the market, would the market continue to correct and further selling happens or would the market absorb the initial shock and tip back to its equilibrium position. The goal of this study is to predetermine if the initial shock will get absorbed or if the initial shock will cause further selling.


Comparing the two scenarios, wherein one, smaller sell offs in the markets are considered just market noises and wherein the other, sell offs are followed by further severe sell offs, one can easily make the argument that the market is forever in some sort of cycles such as short term, say 4 year, cyclical cycles and longer term, say 30 year secular cycles, with the cyclical cycles embedded into the secular cycles which are perhaps embedded into some longer term cycle. This phenomenon can be observed in the various plots included in the last section; moreover, using this logic one can make an argument that it is natural for the market to reach peaks within secular bear cycles which will always be followed by step declines. Conversely one can make an argument that it is natural for the market to reach troughs within secular bull cycles which will always be followed by step gains. Moreover, while this is a very solid argument and can be very useful in conservative long term investing it is not exactly the question we are attempting to resolve in this study. We rather accept the fact that these kinds of events happen and what we are attempting to determine is if the selloff will trigger much severe sell offs in the market or if it is just normal market noise; perhaps one can best understand this by considering the difference between a correction and a crash.In addition, we attempt to look at what factors are stimulating such an event; namely is it truly correlated to real market data, say perhaps gross domestic product or consumer spending, or if it is being caused by a sudden speculative move from a major firm called “market mover.”


Excerpt out of 33 pages


Quantitative analysis of large stock market crashes
California State University, East Bay
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ISBN (Book)
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Quote paper
Victor Odour (Author), 2011, Quantitative analysis of large stock market crashes, Munich, GRIN Verlag, https://www.grin.com/document/267038


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