The document discusses various mathematical indicators used in technical analysis for stocks including moving averages, exponential moving averages, rate of change indicator, and relative strength index. It provides formulas to calculate exponential moving averages and the relative strength index. Sample calculations and charts are shown to illustrate how to calculate a 5-day exponential moving average and 7-day rate of change indicator. Moving averages are used to represent short, medium, and long term trends in stock prices.

1. MATHEMATICAL INDICATORS
Technical Analysis

2.  Moving Average
 Exponential Moving Average
 Rate of Change Indicator
 Relative Strength Index
 Moving Average Convergence and Divergence

3. EXPONENTIAL MOVING AVERAGE
 EMA can be calculated by using the following
formula,
 EMA = (current closing price – previous EMA) *
Factor + previous EMA
 Where , Factor = 2/n+1
 N = number of days for which the average is to be
calculated.

4. CALCULATE 5 DAYS EMA
Days Closing Price
1 33
2 35
3 37.5
4 36
5 39
6 40
7 40.5
8 38.5
9 41
10 42

5. CONT
 If we calculating the five day exponential moving
average, the correct five day EMA will be available
from the sixth day onwards.
 A moving average represents the underlying trend
in the share price movement.
 Five day or ten day average would indicate the
short term trend
 A 50 day average would indicate the medium term
trend and
 200 day average would represent the long term
trend.

6. CON..
 The moving averages are plotted on the price
charts
 The curved line joining these moving average
represent trend line.
 When the price of share intersects and moves
above or below this trend line, it may be taken as
first sign of trend reversal.

7. CHART SHOWING FIVE DAYS EMA
0
10
20
30
40
50
1 2 3 4 5 6 7 8 9 10
ClosingPrice
Exponential Moving Average
Series1
Series2

8. PROBLEM 2
Days Closing Price
1 25
2 26
3 25.5
4 24.5
5 26
6 26
7 26.5
8 26.5
9 26
10 27

9. RATE OF CHANGE INDICATOR
 Oscillators
 Oscillators are the mathematical indicators calculated
with the help of the closing price data.
ROC oscillator which measures the rate of change of the
current price as compared to the price a certain number
of days or weeks back.
To calculate 7 day rate of change, each day’s price is
divided by the price which prevailed 7 days ago and
then 1 is subtracted from this price ratio.

10. -0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
1 2 3 4 5 6 7 8 9 10 11
ROC Chart
1 2 3 4 5 6 7

11.  ROC values may be positive, negative or zero
 When the ROC line is above the zero line, the price
is rising and when it is below the zero line the price
is falling.
 One should buy a share that is oversold and sell a
share that is overbought.
 Many analyst use zero line for identifying buying
and selling opportunities.

12. RELATIVE STRE

13. RELATIVE STRENGTH INDEX
 A powerful indicator that signal buying and selling
opportunities ahead of the market.
 RSI for a share is calculated by using the following
formula
 RSI = 100- [100/(1+RS)]
 Where,
 RS = Average Gain per day/ Average loss per day

14.  Most commonly used time period is 14 days.
 For the calculation of 14 day RSI, the gain per day
or loss per day is arrived at by comparing the
closing price of a day with that of the previous day
for a period of 14 days.
 The gains are added up and divided by 14 to get
the average gain per day.
 Similarly, the absolute losses are added up and
divided by 14 to get the average losses.
 The ratio between these values (average gains /
average losses) is known as relative strength (RS).

15. RSI
Day Closing Price
1 130
2 132
3 130
4 135
5 137
6 134
7 136
8 140
9 140
10 142
11 139
12 141
13 145
14 143
15 145