THE HAnDbook of TEcHnIcAl AnAlySISis calculated by multiplying the latest closing price by an exponential weighting
ratio of X and adding this to (1 − X) of rolling average. For example, if we wanted
to calculate a 10 percent EMA of daily prices, we take the exponential weighting
ratio 0.1 (which represents 10 percent) and multiply it by the latest closing price.
We then add this value to 0.9 of yesterday’s weighted moving average. The process
is repeated to create the exponential moving average. Hence there is no actual
drop-off of old values after the inception date. Put simply:
10 percent EMA Rolling value of = (Latest Close×+0 1. ) (Previous EMAA 0 9×. )Note that instead of dealing in percentages and ratios, we can redefine them in
terms of time periods, via the following formula:
Periods=[(2/Exponential Weighting Ratio)− 1 ]Hence, a 25-period EMA is equivalent to a (2/0.25)−1 = 8−1 = 7 period EMA.
Rearranging the equation we get:
Exponential Weighting Ratio 2/ Periods 1=[ ( + )]Hence, a 49-period EMA is equivalent to a 2/(50 + 1) = 0.04 ~ 4 percent EMA.
It should be noted that the moving average convergence-divergence (MACD) also
uses EMAs for both of its moving averages. Hence, Gerald Appel’s 7.5 percent and
15 percent EMAs would be equivalent to:
7 5 percent EMA 2/0 075 1 100 percent 25 66
26 period EM. : [(. )−×] =.
=− AA (rounding up)15 percent EMA 2/0 150 1 100 percent 12 33
12 period E: [(. )−×] =.
=− MMA rounding down( )Calculating the EMA is relatively easy. Let us assume that we use yesterday’s EMA
value of $30 as our starting value. (Most platforms use yesterday’s SMA of the same
lookback period as the starting point since no EMA is available.) The closing price to-
day is $28, and the closing prices for the next two days are $26 and $24, respectively.
figure 11.11 Calculation of the Linearly Weighted Moving Average of the CBOE
Interest Rate 10-Year Treasury Note.