**Market Data Questions**

# Exponential Moving Averages Calculation

Can you help me understand how to convert trend value % into period exponential moving averages (EMAs)? For example, you say that a 10% Trend is roughly equal to a 19-period EMA. What about the rest of them?

If you are running any sort of TA platform, then the 10% Trend and 5% Trend are what others call a 19-day and 39-day Exponential Moving Average (EMA). If you are doing your analysis in a spreadsheet calculation spreadsheet from the data page on our web site. To build the formulae from scratch:

10%T(today) = 0.1 x Price(today) + 0.9 x 10%T(yesterday)

5%T(today) = 0.05 x Price(today) + 0.95 x 5%T(yesterday)

The formula for converting an EMA’s smoothing constant to a number of days is:

2

———-

n + 1

where n is the number of days. Thus, a 19-day EMA would fit into the formula as follows:

2 2

————- = ———- = 0.10, or 10%

19 + 1 20

Even if a charting program calls an EMA a “19-day” or any other period of time, in the background the software is still going to be making the coversion detailed above and doing the math as we describe.

You can read one of the original pieces ever written about this concept by going to http://www.mcoscillator.com/reports/special/McClellan_MTAaward.pdf. There, we excerpt from P.N. Haurlan’s pamphlet, “Measuring Trend Values”.

The reason why we use the old terminology of “10% Trend” instead of calling it a 19-day EMA is two-fold.m First, it is the original terminology, and so it is usually more appropriate to keep the correct names for things even if the rest of the world changes. Second, it is slightly misleading to use a certain time period when talking about EMAs.

In a 19-day Simple Moving Average (SMA), the data point from 20 days ago drops out completely and has no further bearing on the indicator value.

But in an EMA, old data never completely goes away; it just becomes decreasingly relevant to the current indicator reading.

So to say that it is a 19-day indicator implies that nothing older than 19 days is still in the data, and that is not quite the case.