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| RSI:
Calculation Underlies Meaningful Interpretation |
RSI is probably J. Welles Wilder Jr.'s best-known
indicator. It can be found on virtually every technical analysis website
and is included with almost all software packages. RSI stands for
Relative Strength Index, but the name is misleading. Most relative
strength calculations compare a stock against an index -- such as
comparing Intel (INTC) to the Semiconductor or $SOX index. Wilder's RSI
compares a stock's gains to its losses over a set period of time. The
result is an RSI graph usually presented as a panel above or below the
price chart.
When Wilder first articulated RSI in his 1978 book, New Concepts in
Technical Analysis (ISBN 0-894959-027-8), his methodology involved
the use of a Hewlett-Packard programmable calculator. The swing trader
of that time would have had to follow the logic of a 10-column
spreadsheet to understand how the indicator was constructed. The swing
trader of 2004 has a noticeable advantage. With a stroke of the computer
key, presto, RSI appears above or below the price chart.
On reflection, however, this ability to effortlessly conjure up RSI can
also be a disadvantage. Without understanding the mathematical
construction of the indicator, it is easy to use it mechanically. Worse,
its implications can be misinterpreted, which may lead to poor trading
decisions. In future articles I will devote attention to a detailed discussion of how RSI can:
-- Serve as a leading indicator of an upcoming reaction
or reversal by limning out "a failure swing."
-- Trace out price patterns difficult to detect on the underlying price
chart.
-- Signal bearish or bullish momentum divergence and therefore the
probability of trend reversal.
-- Mimic trendlines on the underlying price chart by establishing key
support and resistance levels.
Many times during these discussions, I will refer back
to the mathematical reasoning behind RSI and I will now explain that
calculation.
The formula for RSI is:
RSI = 100 – [100/1 +RS]
RS = Average of n periods closes up/Average of n periods closes down.
RSI provides meaningful information on a chart of any length, and I have
used it on 5 minute, hourly, daily, weekly and monthly charts.
"N" in the RS formula is the number of periods used in the
calculation. Wilder himself suggested 14 periods as the default, but a 9
and 21 period RSI are also commonly used by traders.
If you're not mathematically inclined, finding RS can sound daunting,
but is actually simple. The first step is to assemble 14 periods of data
for any stock or index. In the example below of Intel, I started my RSI
calculation on November 1st and collected 14 days of closing prices,
since I wanted to do a daily RSI computation.
The next step was to total all the up closes, or daily gains, during the
14 days. As the spreadsheet below shows, Intel gained 17 cents on
November 2nd, 6 cents on November 3rd, 21 cents on November 4th etc. The
sum of these gains for all fourteen days was $2.77. To find out the average
gain for the period, one simply divides $2.77 by 14 to get 19.8
cents.
The same process is repeated for the down days. Total declines in the
14-day period were 50 cents, making the average decline 3.6 cents.
Next, you need to figure out RS. RS is calculated by dividing the
average up closes (19.8) by the average down closes
(3.6). This simple calculation (19.8/3.6) yields a result of 5.50.
The formula asks us to then add 1.0 to 5.5, giving us a result of 6.5.
To resolve the brackets we divide 100/6.5 and find that the answer is
15.38.
The final step is to subtract 15.38 from 100. The 100 is included in the
formula to insure that the final result always oscillates between zero
and 100. When 15.38 is deducted from 100, we have calculated the RSI of
84.62. That RSI indicates Intel is extremely overbought and is prone to
profit taking or a "reaction." (Note that Stockcharts further
smoothes this raw RSI number by adding additional data points so its RSI
and the one you calculate will be slightly different.)
One of Wilder's goals in creating RSI was to eliminate unnecessary
calculations. Once the 14th day's numbers were established, he used a
10-column spreadsheet to compute subsequent RSI values. An example of
the 10- column spreadsheet with RSI calculations is provided below. The
math takes some practice. The logic itself, however, doesn't change. RSI
for days 15-19 (November 19-26) is presented in the spreadsheet.
| A |
B |
C |
D |
E |
F |
G |
H |
I |
J |
| Date |
Close |
Up |
Down |
Up
Avg. |
Down
Avg. |
Cell
E/F |
1.0+"G" |
100/"H" |
(100-Cell
I) = RSI |
| 11/1 |
$22.44 |
|
|
|
|
|
|
|
|
| 11/2 |
$22.61 |
0.17 |
|
|
|
|
|
|
|
| 11/3 |
$22.67 |
0.06 |
|
|
|
|
|
|
|
| 11/4 |
$22.88 |
0.21 |
|
|
|
|
|
|
|
| 11/5 |
$23.36 |
0.48 |
|
|
|
|
|
|
|
| 11/8 |
$23.23 |
|
-0.13 |
|
|
|
|
|
|
| 11/9 |
$23.08 |
|
-0.15 |
|
|
|
|
|
|
| 11/10 |
$22.86 |
|
-0.22 |
|
|
|
|
|
|
| 11/11 |
$23.17 |
0.21 |
|
|
|
|
|
|
|
| 11/12 |
$23.69 |
0.52 |
|
|
|
|
|
|
|
| 11/15 |
$23.77 |
0.08 |
|
|
|
|
|
|
|
| 11/16 |
$23.84 |
0.08 |
|
|
|
|
|
|
|
| 11/17 |
$24.32 |
0.48 |
|
|
|
|
|
|
|
| 11/18 |
$24.80 |
0.48 |
|
|
|
|
|
|
|
| 14
Day Totals |
2.77 |
|
0.198 |
0.036 |
5.50 |
6.50 |
15.38 |
84.62 |
| 11/19 |
$24.16 |
|
-0.64 |
0.184 |
0.079 |
2.33 |
3.33 |
30 |
70.00 |
| 11/22 |
$24.10 |
|
-0.06 |
0.171 |
0.078 |
2.19 |
3.19 |
31.55 |
68.65 |
| 11/23 |
$23.37 |
|
-0.73 |
0.158 |
0.124 |
1.28 |
2.28 |
43.86 |
56.14 |
| 11/24 |
$23.61 |
0.24 |
|
0.164 |
0.115 |
1.42 |
2.42 |
41.32 |
58.68 |
| 11/26 |
$23.21 |
|
-0.40 |
0.152 |
0.135 |
1.12 |
2.12 |
47.16 |
52.84 |
Below is a chart of Intel covering the period of the spreadsheet,
November 1st -26th. In addition to RSI, I have also placed parabolic SAR
and ADX, two of Wilder's other popular indicators, on the chart. Note
that on November 12th RSI went above the overbought 70 level. That
warned the swing trader INTC was significantly overbought. By itself, it
was not a sell signal, because a stock can get and stay overbought for a
long period of time when a strong uptrend is in place. It did caution,
however, to be very alert for a reaction and be prepared to nail down
profits.
Intel stayed overbought for several days and reached a closing peak
of $24.80 on November 18th. RSI at that point was an extreme 84.62. Note
how the large series of up days and the very small number of down days
led to this extreme reading.
On November 19th, Intel declined 64 cents, creating a large black
candle. RSI gave a sell signal as it declined from above 70 to below
that level. The slower moving ADX, while remaining on a buy signal, saw
+DI fall below the black ADX line, often signaling a peak. The following
day INTC lost another 6 cents. The parabolic SAR dots switched from
below the share price to above it, signifying that profits should
immediately be taken on INTC (the Swing Trader exited its position in
INTC on this day with an 8.1% gain). According to Wilder's indicators,
however, since ADX was on a buy signal, INTC should not be shorted.
Note how the RSI declined on subsequent days as the price fell. As the
average gains in the last fourteen days approached the average losses,
RSI trended down toward the 50 level, the point at which gains and
losses over the 14 days are in perfect balance.
Understanding how RSI is constructed leads to more effective use of the
indicator.
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