Amortized moving average: Meaning, Criticisms & Real-World Uses

What Is Amortized Moving Average?

An Amortized Moving Average is a conceptual approach to analyzing price data in financial markets where the influence of older data points gradually diminishes, or "amortizes," over time. Within the realm of technical analysis, it applies the principle of amortization, typically associated with accounting for intangible assets or loan payments, to the calculation of a moving average. While not a standardized, commonly defined indicator like a Simple Moving Average (SMA) or Exponential Moving Average (EMA), the concept implies a method that assigns decreasing weight to older historical prices, thereby making the average more responsive to recent market movements.

History and Origin

The broader concept of moving averages dates back centuries, with forms of them being used by Japanese rice traders in the 18th century to analyze market trends. The modern application of moving averages in financial analysis emerged in the early 20th century, with pioneers like Richard Schabacker laying the groundwork for their use in identifying market trends⁵. Later, technicians such as Robert Edwards and John Magee further popularized them in their seminal 1948 book, "Technical Analysis of Stock Trends."⁴

While the term "Amortized Moving Average" is not explicitly tied to a singular historical invention, its underlying principle—that of diminishing influence or decay over time—is inherent in more advanced moving average calculations that developed to address the lagging nature of simple averages. As digital computing capabilities advanced, it became possible to implement sophisticated weighting schemes, allowing for calculations that could effectively "amortize" the impact of older data points, making the average more reflective of current conditions.

Key Takeaways

An Amortized Moving Average is a conceptual form of moving average where the weight or influence of past data points decreases over time, similar to asset amortization.
It is not a widely standardized indicator but embodies principles found in weighted moving averages, which prioritize recent data.
The primary goal is to make the moving average more responsive to current market conditions compared to simple averages.
This approach can help identify emerging trend lines and potential shifts in momentum more quickly.
Like all moving averages, it is a lagging indicator, meaning it is based on past data, despite its responsiveness to recent price action.

Formula and Calculation

Since "Amortized Moving Average" is not a universally standardized term with a single, agreed-upon formula, its calculation would conceptually involve a weighting method where older data points are given progressively less importance. This is analogous to how the principal portion of a loan payment increases over time while the interest portion decreases, or how the book value of an intangible asset is reduced over its useful life.

One could conceptualize an Amortized Moving Average as a type of Weighted Moving Average (WMA) where the weights are specifically designed to decay or "amortize" over time. A general representation of a weighted moving average is:

\text{WMA}_n = \frac{\sum_{i=1}^{n} (P_i \times w_i)}{\sum_{i=1}^{n} w_i}

Where:

(\text{WMA}_n) = Weighted Moving Average for n periods
(P_i) = Price at period i
(w_i) = Weight assigned to the price at period i
(n) = Total number of periods in the calculation

For an Amortized Moving Average, the (w_i) values would be structured to decline as i increases (i.e., as data points get older). For example, a simple linear amortization could assign a weight of n to the most recent price, n-1 to the previous, and so on, down to 1 for the oldest. More complex amortization schemes could involve exponential decay, similar to the calculation of an Exponential Moving Average, which already applies a greater weight to more recent prices. The precise "amortization" function would define the behavior of the average.

Interpreting the Amortized Moving Average

Interpreting an Amortized Moving Average would follow the general principles of interpreting other types of moving averages, but with an emphasis on its heightened responsiveness to recent asset prices. A rising Amortized Moving Average would suggest a strengthening uptrend, as it would quickly reflect recent bullish price action. Conversely, a falling Amortized Moving Average would indicate a downtrend.

Traders and analysts use moving averages to identify the direction and strength of a trend. When the Amortized Moving Average crosses above a longer-term moving average, it might signal a buy opportunity, indicating that short-term momentum is gaining strength relative to the longer-term trend. Conversely, a cross below could signal a sell or a shift to a bearish outlook. Its responsiveness would make it potentially useful for identifying these shifts earlier than a simple average, helping in assessing support and resistance levels and generating trading signals.

Hypothetical Example

Consider a hypothetical stock, "DiversiCo Inc." (DCO), with the following closing prices over 5 days:

Day 1: $100
Day 2: $102
Day 3: $105
Day 4: $103
Day 5: $107

Let's imagine a simple Amortized Moving Average that gives the most recent day a weight of 5, the previous day a weight of 4, and so on, down to 1 for the oldest day in a 5-day period.

To calculate the 5-day Amortized Moving Average for Day 5:

Multiply each day's price by its assigned weight:
- Day 1: $100 * 1 = $100
- Day 2: $102 * 2 = $204
- Day 3: $105 * 3 = $315
- Day 4: $103 * 4 = $412
- Day 5: $107 * 5 = $535
Sum the weighted prices: $100 + $204 + $315 + $412 + $535 = $1566
Sum the weights: 1 + 2 + 3 + 4 + 5 = 15
Divide the sum of weighted prices by the sum of weights: $1566 / 15 = $104.40

The 5-day Amortized Moving Average for DCO on Day 5 is $104.40. This value, compared to a Simple Moving Average for the same period (which would be $(100+102+105+103+107)/5 = $103.40), shows a higher value due to the greater emphasis on more recent, higher prices. This responsiveness is a key characteristic of an Amortized Moving Average.

Practical Applications

While not a standard indicator with a predefined calculation, the conceptual Amortized Moving Average aligns with principles applied in various quantitative finance and financial modeling contexts. In practice, similar weighting schemes are employed to develop responsive indicators for identifying market trends.

One area of application could be in algorithmic trading systems where specific decay functions are applied to price series to generate dynamic trading signals. For instance, quantitative analysts might design proprietary indicators that give exponentially decaying weight to past observations to create a highly adaptive moving average that responds quickly to changes in market volatility. Such customized indicators aim to filter out market "noise" while quickly reflecting significant shifts in price momentum.

Beyond individual security analysis, the underlying concept of smoothing data by giving more weight to recent observations is also employed in broader economic analysis. For example, economists at institutions like the Federal Reserve Bank of San Francisco conduct research that analyzes trends in economic data, often employing methods to filter out short-term fluctuations and highlight underlying patterns, which implicitly involves giving greater consideration to recent information in time series analysis.

#³# Limitations and Criticisms

As a conceptual rather than formally defined indicator, the main limitation of an Amortized Moving Average lies in the lack of a standardized formula, which means different implementations could produce vastly different results. This makes it difficult to compare analyses across different practitioners or platforms.

More generally, like all forms of moving averages, an Amortized Moving Average is a lagging indicator. It is based on past price data and, therefore, cannot predict future price movements with certainty. While its "amortizing" nature aims to make it more responsive, it will always react after a price change has occurred. This inherent lag can lead to delayed signals, potentially causing traders to enter or exit positions late, especially in fast-moving or choppy markets.

Critics of technical analysis often argue that relying solely on historical price patterns to predict future outcomes is ineffective in efficient markets. The CFA Institute has discussed the ongoing debate between fundamental and technical analysis, noting that proponents of strong-form market efficiency believe all information is already reflected in current prices, making it impossible to consistently profit from historical patterns. So²me academic studies have also questioned the consistent profitability of technical trading rules over time, suggesting that any perceived profits may decline in subsequent periods due to factors like data snooping.

#¹# Amortized Moving Average vs. Exponential Moving Average

The Amortized Moving Average and the Exponential Moving Average (EMA) share a fundamental similarity: both prioritize recent price data over older data, aiming to be more responsive to current market conditions than a Simple Moving Average. However, the key difference lies in their definition and methodology.

An Exponential Moving Average (EMA) is a widely recognized and precisely defined technical indicator. It uses an exponentially weighted calculation, where the weighting factor decreases geometrically for older prices. This gives significantly more importance to the most recent closing prices, making it react more quickly to new information and market shifts. The EMA has a specific smoothing factor formula and a clear iterative calculation, ensuring consistent results across different platforms and analyses.

An Amortized Moving Average, on the other hand, is a more conceptual term. It refers to any moving average where the influence of older data is "amortized" or reduced over time, but it does not specify a single, universal calculation method. While an EMA could be considered a type of amortized moving average due to its decaying weighting scheme, the term "Amortized Moving Average" itself lacks the specific formulaic rigor and widespread adoption of the EMA. It implies a principle of diminishing returns for historical data rather than a fixed statistical calculation. Essentially, the EMA is a specific implementation of the concept that an Amortized Moving Average represents.

FAQs

What is the main purpose of an Amortized Moving Average?

The main purpose of an Amortized Moving Average is to create a more responsive average of price data by giving less weight or influence to older data points. This allows it to reflect recent market movements and emerging trend lines more quickly than traditional simple moving averages.

Is an Amortized Moving Average a standard technical indicator?

No, "Amortized Moving Average" is not a standard, universally recognized technical analysis indicator with a fixed formula, unlike the Simple Moving Average or Exponential Moving Average. It is more of a conceptual term describing a weighting approach where the impact of past data diminishes over time.

How does an Amortized Moving Average differ from an Exponential Moving Average?

An Amortized Moving Average is a broad concept where older data points have less influence. An Exponential Moving Average (EMA) is a specific, well-defined type of weighted moving average that achieves this "amortization" effect by applying exponentially decreasing weights to older prices. Therefore, an EMA could be considered one form of an amortized moving average.