Exponential Moving Average vs. Simple Moving Average: An Overview
Exponential Moving Average (EMA) and Simple Moving Average (SMA) are similar in that they each measure trends. The two averages are also similar because they are interpreted in the same manner and are both commonly used by technical traders to smooth out price fluctuations.
There are some differences between the two measurements, however. The primary difference between an EMA and an SMA is the sensitivity each one shows to changes in the data used in its calculation.
SMA calculates the average of price data, while EMA gives more weight to current data. The newest price data will impact the moving average more, with older price data having a lesser impact.
More specifically, the exponential moving average gives a higher weighting to recent prices, while the simple moving average assigns equal weighting to all values.
Exponential Moving Average
Since EMAs place a higher weighting on recent data than on older data, they are more reactive to the latest price changes than SMAs are, which makes the results from EMAs more timely and explains why the EMA is the preferred average among many traders.
As shown in the example below, traders with a short-term perspective may not care about which average is used, since the difference between the two averages is usually a matter of mere cents. On the other hand, traders with a longer-term perspective should give more consideration to the average they use because the values can vary by a few dollars, which is enough of a price difference to ultimately prove influential on realized returns, especially when you are trading a large quantity of stock.
As with all technical indicators, there is no one type of average a trader can use to guarantee success.
Simple Moving Average
The SMA is the most common type of average used by technical analysts and is calculated by dividing the sum of a set of prices by the total number of prices found in the series. For example, a seven-period moving average can be calculated by adding the following seven prices together and dividing the result by seven (the result is also known as an arithmetic mean average).
Example Given the following series of prices: $10, $11, $12, $16, $17, $19, $20 The SMA calculation would look like this: $10+$11+$12+$16+$17+$19+$20 = $105 7-period SMA = $105/7 = 15
Moving averages are fundamental to many technical analysis strategies, but successful traders use a combination of techniques. Investopedia’s Technical Analysis Course will show you how to identify patterns, signals, and technical indicators that drive the behavior of stock prices with over five hours of on-demand video, exercises, and interactive content.
Key Takeaways
The exponential moving average gives a higher weighting to recent prices.
The simple moving average assigns an equal weighting to all values.
As with all technical indicators, there is no one type of average a trader can use to guarantee success.
The rectangle is a classical technical analysis pattern described by horizontal lines showing significant support and resistance. It can be successfully traded by buying at support and selling at resistance or by waiting for a breakout from the formation and using the measuring principle.
Key Takeaways
A rectangle occurs when the price is moving between horizontal support and resistance levels.
The pattern indicates there is no trend, as the price moves up and down between support and resistance.
The rectangle ends when there is a breakout, and the price moves out of the rectangle.
Some traders like to trade the rectangles, buying near the bottom and selling or shorting near the top, while others prefer to wait for breakouts.
The Rectangle in Classical Technical Analysis
The rectangle formation is an example of a “price pattern” in technical analysis. Price patterns derive from the work of Richard Schabaker, considered the father of technical analysis, and Edwards and Magee, who wrote what many consider the bible on the subject.
This period of technical analysis derives from a time when charts were kept by hand on graph paper and even simple moving averages (SMA) had to be maintained by hand or with the use of a large, clunky adding machine.
Rather than modern technical analysis, which relies on indicators, such as moving average convergence divergence (MACD), technical analysts assumed that price patterns repeat themselves over and over throughout time. Pattern recognition meant pattern prediction and thus trading profit.
Many of the price patterns are based on geometrical figures. There are ascending, descending and symmetrical triangles, pennants and wedges. Occasionally, more fancifulshapes are seen, such as the head-and-shoulders formation.
The Rectangle: Supply and Demand in Balance
A price chart or graph may be thought of as an X-ray of supply and demand. Figure 1 describes a rectangle pattern where supply and demand are in approximate balance for an extended period of time. The shares move in a narrow range, hitting resistance at the rectangle’s top and finding support at its bottom. The rectangle can occur over a protracted period of time or form quickly amid a relatively wide-ranging series of bounded fluctuations. Schabaker notes that it can approach a square in its proportions.
In any case, it is a pattern which shows trader indecision, one in which the bulls and bears are approximately equally powerful.
Figure 1.
Most technicians agree, the rectangle can serve as either a reversal or continuation formation. As a reversal pattern, it ends a trend either up or down. As a continuation pattern, it signifies a pause in the prevailing trend, with the expectation that the prior trend will eventually resume. In either case, the rectangle shows a tug of war between buyers and sellers. Ultimately, either accumulation or distribution prevails, and the shares breakout or breakdown.
“Significant” Support and Resistance
The concepts of support and resistance are critical to understanding the rectangle formation.
Support is defined as any price point below the current market price where buying should emerge to create, at least temporarily, a pause in a downtrend.
Resistance, on the other hand, is any price above the current market price where selling should emerge to create, at least temporarily, a pause in an uptrend.
In a rectangle, what may be referred to as “significant” support or resistance emerges – that is, a price level returned to again and again. Whereas trendlines in technical analysis are typically drawn on a diagonal, the diagramming of support and resistance requires horizontal trendlines.
ImClone Systems: an Example of a Rectangle Formation
Figure 2 of ImClone Systems (IMCL) employs open-high-low-close bars (rather than candlesticks) and is absent of any indicators, such as MACD. The only addition is a 30-week moving average (MA), which could have been calculated in the classical era.
Figure 2.
Several observations are worth making on this chart. First, note that an intermediate uptrend line, in force for approximately one year, is broken. The break shows the uptrend has ended. Thus, the prolonged rectangle can either be a reversal or consolidation formation. Until there is a breakdown or breakout from the confines of the rectangle – roughly $37.50 to $47.50 – the pattern’s interpretation is uncertain.
Second, horizontal lines drawn on the chart denote significant support and resistance. Significant support was first established in September, tested twice in the early part of the year and retested in June. At each test of support, there was sufficient buying interest to drive the stock higher.
Significant resistance at $47.50 was first touched in August, then probed in October, April and July. At each juncture, the sellers overwhelmed buyers, and the stock receded. This vacillation between significant support and resistance creates the rectangle shape.
One final observation is the slope of the 30-week MA. Of all moving averages, this may best describe the trend. It relates to the rectangle by showing the sideways nature of the formation. In an uptrend or downtrend, the 30-week MA will slope up or down, not sideways. Note how in the early stages of the chart it sloped higher, mimicking the uptrend. Later it flattened and began to slope sideways, showing the prolonged consolidation.
Trading the Rectangle
The following are two basic strategies for trading a rectangle:
The first is to buy at support and sell at resistance (one can also sell short at resistance and cover the short sale at support). To mitigate risk, in case the stock breaks down from support, a very tight stop can be employed of perhaps 3%. For example, if one bought ImClone at $37.50, the stop-loss would be 3% lower than $37.50 or $1.12. The trader would exit the position if the stock hit $36.38 ($37.50-$1.12).
Another method to trade the rectangle is to wait for the breakout. As with all technical patterns, this breakout should ideally occur on above-normal volume. To know when to consider exiting the trade, the trader could use the measuring principle described below.
The Measuring Principle
The measuring principle allows you to set a specific minimum price target. Such a target should give you the objectivity to hold during periods of minor countertrend movement.
The measuring principle works with any well-defined technical analysis pattern, such as a rectangle or triangle. To calculate the minimum target, first establish the height of the pattern. In the case of ImClone Systems Figure 3 shows the calculation as follows:
Top:
$47.50
Bottom:
$37.50
Height:
10.00 points
Figure 3.
For a bullish breakout, once the height of the pattern has been established, add the difference to the breakout level. Since the breakout level is $47.50 and the height 10 points, the minimum target is $57.50. Of course, it may take some time to reach the target, so the trader must be patient. As well, the measuring principle is a statement of probability, not a guarantee. The trader will carefully monitor the technical picture of the stock despite the target.
How was the rectangle in IMCL resolved? Bristol Myers Squibb bid $60 a share to acquire the 83% of ImClone it did not already own. Shareholders who had seen their stock go nowhere for a year, and saw the shares close at $46.44, woke up the next morning to find their stock had opened at $64.16, well beyond the minimum target set by the measuring principle. Those who traded the rectangle, in this case, turned out not to be “square.”
The Bottom Line
In summary, the rectangle is a classical technical analysis pattern bounded by significant support and resistance and described by horizontal trendlines. The pattern can be traded by buying at support and selling at resistance or buying the breakout and employing the measuring principle to set a target.
Attribution analysis is a sophisticated method for evaluating the performance of a portfolio or fund manager. Also known as “return attribution” or “performance attribution,” it attempts to quantitatively analyze aspects of an active fund manager’s investment selections and decisions—and to identify sources of excess returns, especially as compared to an index or other benchmark.
For portfolio managers and investment firms, attribution analysis can be an effective tool to assess strategies. For investors, attribution analysis works as a way to assess the performance of fund or money managers.
Attribution analysis is an evaluation tool used to explain and analyze a portfolio’s (or portfolio manager’s) performance, especially against a particular benchmark.
Attribution analysis focuses on three factors: the manager’s investment picks and asset allocation, their investment style, and the market timing of their decisions and trades.
Asset class and weighting of assets within a portfolio figure in analysis of the investment choices.
Investment style reflects the nature of the holdings: low-risk, growth-oriented, etc.
The impact of market timing is hard to quantify, and many analysts rate it as less important in attribution analysis than asset selection and investment style.
How Attribution Analysis Works
Attribution analysis focuses on three factors: the manager’s investment picks and asset allocation, their investment style, and the market timing of their decisions and trades.
The method begins by identifying the asset class in which a fund manager chooses to invest. An asset class generally describes the type of investments that a manager chooses; within that, it can also get more specific, describing a geographical marketplace in which they originate and/or an industry sector. European fixed income debt or U.S. technology equities could both be examples.
Then, there is the allocation of the different assets—that is, what percentage of the portfolio is weighted to specific segments, sectors, or industries.
Specifying the type of assets will help identify a general benchmark for the comparison of performance. Often, this benchmark will take the form of a market index, a basket of comparable assets.
Market indexes can be very broad, such as the S&P 500 Index or the Nasdaq Composite Index, which cover a range of stocks; or they can be fairly specific, focusing on, say, real estate investment trusts or corporate high yield bonds.
Analyzing Investment Style
The next step in attribution analysis is to determine the manager’s investment style. Like the class identification discussed above, a style will provide a benchmark against which to gauge the manager’s performance.
The first method of style analysis concentrates on the nature of the manager’s holdings. If they are equities, for example, are they the stocks of large-cap or small-cap companies? Value- or growth-oriented?
American economist Bill Sharpe introduced the second type of style analysis in 1988. Returns-based style analysis (RBSA) charts a fund’s returns and seeks an index with comparable performance history. Sharpe refined this method with a technique that he called quadratic optimization, which allowed him to assign a blend of indices that correlated most closely to a manager’s returns.
Explaining Alpha
Once an attribution analyst identifies that blend, they can formulate a customized benchmark of returns against which they can evaluate the manager’s performance. Such an analysis should shine a light on the excess returns, or alpha, that the manager enjoys over those benchmarks.
The next step in attribution analysis attempts to explain that alpha. Is it due to the manager’s stock picks, selection of sectors, or market timing? To determine the alpha generated by their stock picks, an analyst must identify and subtract the portion of the alpha attributable to sector and timing. Again, this can be done by developing customize benchmarks based on the manager’s selected blend of sectors and the timing of their trades. If the alpha of the fund is 13%, it is possible to assign a certain slice of that 13% to sector selection and timing of entry and exit from those sectors. The remainder will be stock selection alpha.
Market Timing and Attribution Analysis
Though some managers employ a buy-and-hold strategy, most are constantly trading, making buy and sell decisions throughout a given period. Segmenting returns by activity can be useful, telling you if a manager’s decisions to add or subtract positions from the portfolio helped or hurt the final return—vis-à-vis a more passive buy-and-hold approach.
Enter market timing, the third big factor that goes into attribution analysis. A fair amount of debate exists on its importance, though.
Certainly, this is the most difficult part of attribute analysis to put into quantitative terms. To the extent that market timing can be measured, scholars point out the importance of gauging a manager’s returns against benchmarks reflective of upturns and downturns. Ideally, the fund will go up in bullish times and will decline less than the market in bearish periods.
Even so, some scholars note that a significant portion of a manager’s performance with respect to timing is random, or luck. As a result, in general, most analysts attribute less significance to market timing than asset selection and investment style.
Analysis of variance (ANOVA) is an analysis tool used in statistics that splits an observed aggregate variability found inside a data set into two parts: systematic factors and random factors. The systematic factors have a statistical influence on the given data set, while the random factors do not. Analysts use the ANOVA test to determine the influence that independent variables have on the dependent variable in a regression study.
The t- and z-test methods developed in the 20th century were used for statistical analysis until 1918, when Ronald Fisher created the analysis of variance method. ANOVA is also called the Fisher analysis of variance, and it is the extension of the t- and z-tests. The term became well-known in 1925, after appearing in Fisher’s book, “Statistical Methods for Research Workers.” It was employed in experimental psychology and later expanded to subjects that were more complex.
Key Takeaways
Analysis of variance, or ANOVA, is a statistical method that separates observed variance data into different components to use for additional tests.
A one-way ANOVA is used for three or more groups of data, to gain information about the relationship between the dependent and independent variables.
If no true variance exists between the groups, the ANOVA’s F-ratio should equal close to 1.
What Is the Analysis of Variance (ANOVA)?
The Formula for ANOVA is:
F=MSEMSTwhere:F=ANOVA coefficientMST=Mean sum of squares due to treatmentMSE=Mean sum of squares due to error
What Does the Analysis of Variance Reveal?
The ANOVA test is the initial step in analyzing factors that affect a given data set. Once the test is finished, an analyst performs additional testing on the methodical factors that measurably contribute to the data set’s inconsistency. The analyst utilizes the ANOVA test results in an f-test to generate additional data that aligns with the proposed regression models.
The ANOVA test allows a comparison of more than two groups at the same time to determine whether a relationship exists between them. The result of the ANOVA formula, the F statistic (also called the F-ratio), allows for the analysis of multiple groups of data to determine the variability between samples and within samples.
If no real difference exists between the tested groups, which is called the null hypothesis, the result of the ANOVA’s F-ratio statistic will be close to 1. The distribution of all possible values of the F statistic is the F-distribution. This is actually a group of distribution functions, with two characteristic numbers, called the numerator degrees of freedom and the denominator degrees of freedom.
Example of How to Use ANOVA
A researcher might, for example, test students from multiple colleges to see if students from one of the colleges consistently outperform students from the other colleges. In a business application, an R&D researcher might test two different processes of creating a product to see if one process is better than the other in terms of cost efficiency.
The type of ANOVA test used depends on a number of factors. It is applied when data needs to be experimental. Analysis of variance is employed if there is no access to statistical software resulting in computing ANOVA by hand. It is simple to use and best suited for small samples. With many experimental designs, the sample sizes have to be the same for the various factor level combinations.
ANOVA is helpful for testing three or more variables. It is similar to multiple two-sample t-tests. However, it results in fewer type I errors and is appropriate for a range of issues. ANOVA groups differences by comparing the means of each group and includes spreading out the variance into diverse sources. It is employed with subjects, test groups, between groups and within groups.
One-Way ANOVA Versus Two-Way ANOVA
There are two main types of ANOVA: one-way (or unidirectional) and two-way. There also variations of ANOVA. For example, MANOVA (multivariate ANOVA) differs from ANOVA as the former tests for multiple dependent variables simultaneously while the latter assesses only one dependent variable at a time. One-way or two-way refers to the number of independent variables in your analysis of variance test. A one-way ANOVA evaluates the impact of a sole factor on a sole response variable. It determines whether all the samples are the same. The one-way ANOVA is used to determine whether there are any statistically significant differences between the means of three or more independent (unrelated) groups.
A two-way ANOVA is an extension of the one-way ANOVA. With a one-way, you have one independent variable affecting a dependent variable. With a two-way ANOVA, there are two independents. For example, a two-way ANOVA allows a company to compare worker productivity based on two independent variables, such as salary and skill set. It is utilized to observe the interaction between the two factors and tests the effect of two factors at the same time.
