Abstract
This chapter introduces the notion of a general weighted moving average and shows that each specific moving average can be uniquely characterized by either a price weighting function or a price-change weighting function. It also demonstrates how to quantitatively assess the average lag time and smoothness of a moving average. Finally, the analysis provided in this chapter reveals two important properties of moving averages when prices trend steadily.
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Notes
- 1.
A similar idea is used in physics to compute the center of mass and in finance to compute the bond duration (Macaulay duration).
- 2.
Note that the average lag time is computed using the sequence of the weights \(\psi _i\), \(1 \le i \le n-1\). Many alternative sequences of weights can produce exactly the same value of the average lag time.
- 3.
In words, “Lag” is the required number of backshift operations applied to the time series of \(\{MA_t(n)\}\) that makes it coincide with the time series of prices \(\{P_t\}\).
- 4.
There is a large strand of econometric literature that demonstrates that volatility of financial assets is not constant over time. Specifically, there are alternating calm and turbulent periods in financial markets. Therefore, in real markets the smoothness of a moving average is not constant over time. In particular, the smoothness improves in calm periods and worsens in turbulent periods.
- 5.
It is worth emphasizing that this relationship holds only when stock prices trend steadily in one direction. This relationship does not hold when the direction of the trend changes frequently.
Reference
Ivkovic, Z., Sialm, C., & Weisbenner, S. (2008). Portfolio concentration and the performance of individual investors. Journal of Financial and Quantitative Analysis, 43(3), 613–655.
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Zakamulin, V. (2017). Basics of Moving Averages. In: Market Timing with Moving Averages. New Developments in Quantitative Trading and Investment. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-60970-6_2
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DOI: https://doi.org/10.1007/978-3-319-60970-6_2
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