Moving Average (MA), Weighted MA, and Exponential MA

moving-average-(ma),-weighted-ma,-and-exponential-ma
 


Date


 


Closing Price of AAPL


 


Weighting


 


June 26


 


$22.73


 


5/15


 


June 25


 


$22.59


 


4/15


 


June 24


 


$22.57


 


3/15


 


June 23


 


$22.71


 


2/15


 


June 20


 


$22.73


 


1/15


The weighted average is calculated by multiplying the given price by its associated weighting and totaling the values. The formula for the WMA is as follows:




WMA

=

Price

1

×

n


Price

2

×

(

n



1

)




 Price

n

n

×

(

n


1

)

2

where:

n

=

Time period

begin{aligned} &text{WMA} = frac{ text{Price}_1 times n text{Price}_2 times ( n – 1 ) cdots text{ Price}_n }{ frac{ n times ( n 1 ) }{ 2} } \ &textbf{where:} \ &n = text{Time period} \ end{aligned}

WMA=2n×(n 1)Price1×n Price2×(n1)  Pricenwhere:n=Time period

The denominator of the WMA is the sum of the number of price periods as a triangular number. In the example from the table above, the weighted five-day moving average would be $90.62:




(

9

0

.

9

0

×

5

1

5

)

 


 

(

9

0

.

3

6

×

4

1

5

)

 


 

(

9

0

.

2

8

×

3

1

5

)


(

9

0

.

8

3

×

2

1

5

)

 


 

(

9

0

.

9

1

×

1

1

5

)

=

$

9

0

.

6

2

begin{aligned} ( 90.90 times tfrac{ 5 }{ 15 } ) & ( 90.36 times tfrac{ 4 }{ 15 } ) ( 90.28 times tfrac{ 3 }{ 15 } ) \ & ( 90.83 times tfrac{ 2 }{ 15 } ) ( 90.91 times tfrac{ 1 }{ 15 } ) = $90.62 \ end{aligned}

(90.90×155)   (90.36×154)   (90.28×153) (90.83×152)   (90.91×151)=$90.62

In this example, the recent data point was given the highest weighting out of an arbitrary 15 points. You can weigh the values out of any value you see fit. The lower value from the weighted average above relative to the simple average suggests that recent selling pressure could be more significant than some traders anticipate. For most traders, the most popular choice when using weighted moving averages is to use a higher weighting for recent values. (For more information, see: Moving Average Tutorial.)

Exponential Moving Averages

Exponential moving averages (EMAs) are also weighted toward the most recent prices, but the rate of decrease between one price and its preceding price is not consistent. The difference in the decrease is exponential. Rather than every preceding weight being 1.0 smaller than the weight in front of it, there might be a difference between the first two period weights of 1.0, a difference of 1.2 for the two periods after those periods, and so on. The formula for EMA is




EMA

=

Price

t

×

k


SMA

y

×

(

1



k

)

where:

t

=

Today

k

=

2

Number of days in period


1

SMA

=

Simple Moving Average of closing price

for the number of days in the period

y

=

Yesterday

begin{aligned} &text{EMA} = text{Price}_t times k text{SMA}_y times ( 1 – k ) \ &textbf{where:} \ &t = text{Today} \ &k = frac { 2 }{ text{Number of days in period} 1 } \ &text{SMA} = text{Simple Moving Average of closing price} \ &text{for the number of days in the period} \ &y = text{Yesterday} \ end{aligned}

EMA=Pricet×k SMAy×(1k)where:t=Todayk=Number of days in period 12SMA=Simple Moving Average of closing pricefor the number of days in the periody=Yesterday

Calculating an EMA involves three steps. The first step is to determine the SMA for the period, which is the first data point in the EMA formula. Then, a multiplier is calculated by taking 2 divided by the number of periods plus 1. The final step is to take the closing price minus the prior day EMA times the multiplier plus the prior day EMA. (For related reading, see: How is the Exponential Moving Average (EMA) Formula Calculated?)

Which Moving Average is More Effective?

Because an exponential moving average (EMA) uses an exponentially weighted multiplier to give more weight to recent prices, some believe it is a better indicator of a trend compared to a WMA or SMA. Some believe that the EMA is more responsive to changes in trends. On the other hand, the more basic smoothing provided by the SMA may render it more effective for finding simple support and resistance areas on a chart. In general, moving averages smooth price data that can otherwise be visually noisy.

The functions of an EMA and a WMA are similar, they rely more heavily on the most recent prices and placing less value on older prices. Traders use these EMAs and WMAs over SMAs if they are concerned that the effects of lags in data may reduce the responsiveness of the moving average indicator.

All moving averages have a significant drawback in that they are lagging indicators. Since moving averages are based on prior data, they suffer a time lag before they reflect a change in trend. A stock price may move sharply before a moving average can show a trend change. A shorter moving average suffers from less lag than a longer moving average.

Still, this lag is useful for certain technical indicators known as moving average crossovers. The technical indicator known as the death cross occurs when the 50-day SMA crosses below the 200-day SMA, and it is considered a bearish signal. An opposite indicator, known as the golden cross, is created when the 50-day SMA crosses above the 200-day SMA, and it is considered a bullish signal. (For related reading, see: How to Use a Moving Average to Buy Stocks.)

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