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Questioning the Essence of Moving Averages

“The previous day's closing price and the 20-day moving average were the same. Today’s closing price was higher than yesterday’s, but the moving average today fell below yesterday’s. Why is that?”

The role of the moving average is to smooth price movements and make trends easier to understand. However, in situations like the problem, even though prices are rising, the moving average can be falling, making it unclear which direction the trend is in.

Answer
“Because today’s close is lower than the close 20 days ago.”

Explanation

The moving average is defined as the average of the closing prices over the past N days, plotted by “moving” it to today’s price, and connected by a line. Hence it is a “moving” average. For daily charts, it is the average of the closing prices of the past N candles.

Another role of the moving average is to compare the average purchase price (or selling price) in the past with the current price to see how much the buyers and sellers are making or losing, and how that changes.

However, moving averages have drawbacks.

・They treat all past N days’ prices in the same proportion
・Prices before the past N days are not reflected

Here begins the problem’s explanation. To simplify, let’s consider the same issue with a 5-day moving average.

Let the closing prices over 6 days be A, B, C, D, E, F.

Day 1 A
Day 2 B
Day 3 C
Day 4 D
Day 5 E
Day 6 F

Then,

5-day moving average → (A+B+C+D+E) ÷ 5

6-day moving average → (B+C+D+E+F) ÷ 5

That’s how it is.

What is the difference between these two?

In this case, A drops out and F is added.

If you replace this with the problem’s case, it means the price on day 1 drops out and the price on day 21 is newly added.

So, even if today’s price is higher than yesterday’s moving average, if the price 20 days ago was higher than today, the moving average will fall.

Whether the moving average turns upward depends on whether today’s price is higher than the price from N days ago.

In the problem’s case, it says “the closing price of the previous day and the moving average value are the same,” but that does not affect whether the moving average turns upward. However, it does relate to the EMA (Exponential Moving Average), so I’ll discuss that next time.

Do you know the definition of EMA?

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