This gives rise to the belief that the values of these two moving averages differ a lot. Obviously, the two price weighting functions are intrinsically different because seemingly each price lag contributes generally very differently to the value of a moving average. To illustrate the source of confusion and help explain why SMA and LMA with the same lag time are very similar, the next figure, top panel, plots the price weighting functions of SMA(11) and LMA(16). Additional information regarding the construction of these results is available upon request. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Rather surprisingly, contrary to the common belief that these two types of moving averages are inherently different, both of them move close together. The bottom panel in the figure below shows the values of SMA(11) and LMA(16) computed using the same stock index values.īoth moving averages have the same lag time of 5 (months). Therefore, a fair comparison of the properties of the two moving averages requires using LMA and SMA with the same average lag time. However, if traders want a moving average with a smaller lag time, instead of using LMA they can alternatively decrease the window size in SMA. Apparently, LMA(16) lags behind the S&P 500 index with a shorter delay than SMA(16). Between the turning points, the index moves steadily upward or downward. This specific historical period is chosen for illustrations because over this period the trend in the S&P 500 index is clear-cut with two major turning points. The figure below, top panel, demonstrates the values of SMA(16) and LMA(16) computed using the monthly closing prices of the S&P 500 index over a 10-year period from January 1997 to December 2006. Therefore, for the same size of the averaging window, LMA has not only smaller lag time than that of SMA, but also lower smoothness. The average lag time and smoothness of LMA are given byįor a sufficiently large size of the averaging window (when n≫1), In particular, in LMA(n) the latest observation has weight n, the second latest n-1, etc. In the linearly weighted moving average the weights decrease in arithmetic progression. To correct the weighting problem in the SMA, some traders employ the linearly weighted moving average.Ī Linear (or linearly-weighted) Moving Average (LMA) is computed as Therefore, they argue, one should put more weight on the more recent price observations. Many traders believe that the most recent stock prices contain more relevant information on the future direction of the stock price than earlier stock prices. The SMA is, in fact, an equally-weighted moving average where an equal weight is given to each price observation. Obviously, increasing the size of the averaging window increases both the smoothness and the average lag time of SMA. The average lag time and smoothness of SMA are given by In this moving average, each price observation has the same weight w i=1 ( ψ i = 1/n). The Simple Moving Average (SMA) computes the arithmetic mean of n prices These are the most common types of moving averages used to time the market. Specifically, we cover “ordinary” moving averages and mention some examples of exotic moving averages. In this post we aim to give an overview of some specific types of moving averages. In my previous blog post we considered the general weighted moving average.
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