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Standard Deviation Standard deviation is the measure of tightness of a probability distribution. It is a statistical measure of volatility that can be used for a number of different purposes in investment decision making. Standard deviation can be used to make important extrapolations from past data. As a measure of volatility, standard deviation measures the tendency of data to be spread out. When looking at the historic returns of a mutual fund, standard deviation can be used to measure the variation of expected return that has taken place in the past giving a sense of range of performance that can be expected given different probabilities of return for the future. It is also used to measure the risk of a security. The smaller the standard deviation, the tighter the probability distribution, and the lower the risk associated with the security. Standard deviation is calculated by first calculating the mean of a group of data points. There is a minimum number of data points that are necessary to calculate the standard deviation properly. The mean is then subtracted from each element of the data group. Each of the differences is then squared and then summed together. The sum of all the squared differences is then divided by the number of data points minus one. The square root of that end figure is then determined and is called the standard deviation. The advantage of standard deviation is that it uses every value in the population or group of data being used. Standard deviation can be used to measure the variability or volatility of any data set. An example is monthly or quarterly Price/Earnings (P/E) values for a particular security, or average sales over a specified period. If the data points are normally distributed then standard deviation gives you the probability of future data points falling within a certain range of the current mean. This is a basis for risk assessment and allows comparison between the data sets of various securities. Another use of standard deviation is in technical analysis. As a measure of volatility, standard deviation have been used in the construction of Bollinger bands as an upper and lower band that are a certain standard deviation level away from a central moving average. In this way, during times of lower volatility, Bollinger bands contract as the range of prices during the period being used for data points gets smaller, reflecting the lower volatility. When volatility increases for a security, the standard deviation lines widen. John Bollinger developed this technique for looking at expected future price projections and potential reversal points. Mr. Bollinger recommends using a 20 period simple moving average and lines that are 2 standard deviations away from the moving average.
The graph above of PG&E Corp Holdings Co uses a 23 day moving average with Bollinger bands 2 standard deviations away from the central moving average. Notice that there are a number of reversal points where price hits the upper or lower band, followed by a reversal of the price trend. There are also a number of breakouts where price penetrates either the upper or lower bands. When price breaks outside the bands a continuation of the trend is implied. Notice as well there are a number of penetrations like late February 2000 where price penetration does not precede a continuation of the trend. It is very important when using Bollinger bands in analysis to have other confirming evidence of price trend. Investors often wait for penetration by a certain percentage movement of price before considering a breakout signal valid. In addition, using On Balance Volume to provide supporting evidence of demand or supply is often used. Another feature of Bollinger bands is the observation that after periods of lower volatility when bands tighten up, there is a tendency for sharp price changes to follow. This can be partly a product of market mechanics for an active stock with excess stop loss and on stop orders building up outside of a trading range. A trading range is a period of indecision during a time of maturing events and perceptions about the valuation for the security or the market in general. A breakout can be equated to an interim resolution of indecision and often produces sharper response in the market. To the right technical studies are examined in more detail to provide a sense of conformational evidence for traders of the critical day. Click on any of the terms to take a closer look at a technical discussion on that topic. All formations, patterns, indicators and technical tools fail at various times and so should only be used to build a body of evidence in forming a trading decision rather than being solely relied upon. There are a number of valuable studies that lead to intuitive understandings about price and volume but a strong compliment to technical analysis is an understanding of the trends and changes in the fundamentals and economic activity that ultimately lead valuation levels in the markets. Walk through a critical day
A closer view of the most recent signals. You can see the short trend immediately prior to a successful critical day, reverses coming away from the critical day. Often a failed critical day will indicate a stronger bias in the market for continuation of the trend that was in place prior to the critical day. A failed signal can therefore provide as much information and opportunity as a successful one. Take a look at tech studies to develop a sense of trend reversals and use. |
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