指數移動平均線(Exponential Moving Average, EMA)

計算方式

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Today EMA = (Today CP * K) + Yesterday EMA * (1 - K)

Today EMA: 今日 EMA
Today CP: 今日收盤價
K: 加權指數 (Something / N + 1)
N: 時間週期
Something: 平滑因子,通常預設為 2

舉例陽明(2609) 111/02/18 的 5 EMA

加權指數
K = 平滑因子 / (時間週期 + 1)
= Something / (N + 1)
= 2 / (5 + 1)
= 2 / 6
= 0.333333333

今日 EMA
Today EMA = (今日收盤價 * 加權指數) + 昨日 EMA * (1 - 加權指數)
= (Today CP * K) + Yesterday EMA * (1 - K)
= (116.50 * 0.333333333) + 111.53 * (1 - 0.333333333)
= 38.833332945 + 111.53 * 0.666666667
= 38.833332945 + 74.35333337051
= 113.18666631551 約等於 133.19

舉例陽明(2609) 111/02/18 的 10 EMA

加權指數
K = 平滑因子 / (時間週期 + 1)
= Something / (N + 1)
= 2 / (10 + 1)
= 2 / 11
= 0.181818182

今日 EMA
Today EMA = (今日收盤價 * 加權指數) + 昨日 EMA * (1 - 加權指數)
= (Today CP * K) + Yesterday EMA * (1 - K)
= (116.50 * 0.181818182) + 110.24 * (1 - 0.181818182)
= 21.181818203 + 110.24 * 0.818181818
= 21.181818203 + 90.19636361632
= 111.37818181932 約等於 111.38

舉例陽明(2609) 111/02/18 的 20 EMA

加權指數
K = 平滑因子 / (時間週期 + 1)
= Something / (N + 1)
= 2 / (20 + 1)
= 2 / 21
= 0.095238095

今日 EMA
Today EMA = (今日收盤價 * 加權指數) + 昨日 EMA * (1 - 加權指數)
= (Today CP * K) + Yesterday EMA * (1 - K)
= (116.50 * 0.095238095) + 109.94 * (1 - 0.095238095)
= 11.0952380675 + 109.94 * 0.904761905
= 11.0952380675 + 99.4695238357
= 110.5647619032 約等於 110.57

範例資料

日期 開盤價 最高價 最低價 收盤價 成交量 5EMA 10EMA 20EMA
111/02/18 112.00 118.00 111.00 116.50 103,926 113.19 111.38 110.57
111/02/17 113.00 114.50 111.50 112.00 39,731 111.53 110.24 109.94
111/02/16 113.50 113.50 112.00 112.50 30,104 111.30 109.85 109.73
111/02/15 112.00 112.50 110.50 111.00 31,536 110.70 109.26 109.43
111/02/14 111.50 115.50 110.50 110.50 71,168 110.55 108.88 109.27
111/02/11 114.00 115.00 112.00 112.00 55,575 110.57 108.52 109.14
111/02/10 113.50 114.50 111.50 114.00 42,037 109.86 107.74 108.84
111/02/09 114.00 115.50 111.00 112.00 62,258 107.79 106.35 108.30
111/02/08 109.00 116.50 108.50 112.50 155,773 105.68 105.10 107.91
111/02/07 100.50 108.00 100.00 108.00 59,599 102.27 103.45 107.42
111/01/26 96.10 99.90 96.10 98.60 51,052 99.41 102.44 107.36
111/01/25 99.00 99.10 95.10 95.10 48,479 99.81 103.30 108.28
111/01/24 97.00 101.00 96.50 99.90 48,844 102.17 105.12 109.67
111/01/21 103.00 103.50 99.00 99.00 65,444 103.31 106.28 110.70
111/01/20 104.00 105.50 103.50 104.00 28,239 105.46 107.90 111.93
111/01/19 105.00 107.50 103.00 104.00 51,633 106.19 108.76 112.77
111/01/18 104.50 108.00 104.00 106.50 31,750 107.29 109.82 113.69
111/01/17 106.00 106.50 104.50 105.50 30,165 107.68 110.56 114.44
111/01/14 105.00 107.50 103.00 107.50 55,764 108.77 111.68 115.39
111/01/13 108.50 109.50 105.00 105.00 47,851 109.41 112.61 116.22
111/01/12 113.50 114.00 107.50 108.00 54,098 111.61 114.31 117.40
111/01/11 112.00 115.00 110.50 112.00 41,157 113.42 115.71 118.39
111/01/10 111.50 114.50 109.00 111.50 47,052 114.13 116.53 119.06
111/01/07 115.50 116.00 111.00 113.50 37,537 115.45 117.65 119.85
111/01/06 113.50 117.00 113.50 114.50 35,949 116.42 118.57 120.52
111/01/05 115.00 117.00 113.50 115.00 35,370 117.39 119.48 121.16
111/01/04 115.00 116.00 113.50 115.50 36,842 118.58 120.47 121.80
111/01/03 120.00 120.50 113.00 114.50 106,847 120.12 121.58 122.47

範例資料: 陽明(2609) 111/02/18 ~ 111/01/03 個股股價行情
資料來源: https://stock.wearn.com/cdata.asp?Year=111&month=02&kind=2609