## Optimal Investing Timing

To earn money in the stock market, it is important for investors to study the overall stock market because the market exerts a significant influence on the behavior of individual stocks. Since the market risk is a major contributing factor in a stock performance, the ability to understand the market reduces the number of surprises for investors. Generally, the stock market depends on many components, and often it is hard to predict its next move. However, it is not a chaotic thing but rather a complicated system with a certain degree of volatility and uncertainly.

Neither bear nor bull market is bad for knowledgeable investors because both can be used to their benefits - the most important thing is stock market predictability. Basically, the stock market prediction can be built on the following approaches: Efficient Market Hypothesis (it states that the prices captures all known information), Fundamental analysis (it considers companies performance), or Technical analysis (it uses historical prices and volumes statistics to detect trend). Using the combination of these methods may improve the accuracy of prediction. However, even a prediction based on many techniques can fail. Fortunately, there are some principles that work in worst-case scenarios, like these: "everything is subject to change", "it is always darkest before sunrise", or "the good times come back when you least expect them".

While prices are low and the stock market is down, there is a good argument to buy the solid stocks that are likely to make a good recovery. When the market failed and started bottoming the question is if there is only way up left or still some room to go lower. How to identify correctly the current situation? To solve a complicated problem, such science as mathematics uses different kinds of transformation. If a problem exists in time domain, one can transform data into another space (for example, frequency domain), relatively easy get a solution there, and then make an inverse transformation. Since frequencies and periods are just inversely proportional quantities, either of them can be used in a transformed space.

S&P 500 Index (^GSPC) can be considered as a model of the overall market. By looking at the historical stock price chart of ^GSPC, one can notice that the market does not follow just a linear trend - it has some deviations from a linear function. Some cycles are well-known, such as, four-year presidential cycle or annual and quarterly fiscal reporting cycles. In addition, some cycles are defined by intrinsic characteristic properties of the system. The stock market performance curve can be considered as a sum of the cyclical functions with different periods and amplitudes. It would be easy to analyze the repetition of typical patterns in stock market performance if they did not mask themselves. In other words, sometimes cycles overlap to form an abnormal extremum or offset to form a flat period. It is clear that a simple chart analysis has a certain limit in identifying and predicting the trend.

Fortunately, mathematics is able to extract basic cycles so that historical quote curve can be decomposed into a set of sinus (or cosines) functions with different periods, amplitudes, and phases - that is something similar to a spectral analysis or a time series analysis. By selecting data with different historical periods, such spectral analysis can identify the major cycles, which have a dominant effect in a particular time frame.

The recent research by Addaptron Software using SMAP-2 tool helped to detect for 40, 20, 10, and 5-year periods of ^GSPC the following major cycles (lines): 10, 8, 5, and 1.6 year. Since each line has own amplitude it is easy to estimate the significance of timing analysis for overall investment performance. For example, an average annual return for the last 5 years approximated by linear function equals around 13% and the amplitude of cycle with 1.6-year period is equal 4.8%. Therefore, in case of 1.6-year cycle only, the return can be diminished to 13-4.8*2= 3.4% with the worst timing or it can be maximized to 13+4.8*2=22.6% with the best timing.

One of the techniques to build an extrapolation (forecasted curve) is to use the following two steps: (1) applying spectral (or time series) analysis to decompose the curve into basic functions, (2) composing these functions beyond the historical data. As a practical example by Addaptron software, the stock market prediction for the next five years on the basis of spectrum analysis: the stock market will suffer some volatility within the next several months but eventually it will go up until 2010-2011. Then it will crash in 2012-2013. Note, these years are approximate because the phase of cycles is fluctuating and, of course, something extraordinary can change the prediction picture. This prediction can be strengthened or weakened by comparing with other forecasting techniques.

To summarize, the direction of the overall market influences significantly an individual stock. There is no method that has been successfully enough to consistently beat the market. The same is applied to a simple combination of different methods. If all predictions fail, everybody scared, and nothing seems to work, one of the approaches to try is a time series prediction because it analyzes historical data and then builds prediction on the basis of changing performance "as is", objectively, without any pressure of emotion or external information.

* March 2008 Copyright © - Alex Shmatov*