MATHEMATICAL INDICATORS

Technical Analysis

Moving Average

Exponential Moving Average

Rate of Change Indicator

Relative Strength Index

Moving Average Convergence and Divergence

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.

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

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.

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.

CHART SHOWING FIVE DAYS EMA

0

10

20

30

40

50

1 2 3 4 5 6 7 8 9 10

Clo

sin

g P

ric

e

Exponential Moving Average

Series1

Series2

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

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.

-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

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.

RELATIVE STRE

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

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).

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