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1. 1.1 About the topic
What is Beta ?
Beta measures the responsiveness of a stock's price to changes in the overall stock market.
On comparison of the benchmark index for e.g. NSE Nifty to a particular stock returns, a
pattern develops that shows the stock's openness to the market risk. This helps the investor
to decide whether he wants to go for the riskier stock that is highly correlated with the
market (beta above 1), or with a less volatile one (beta below 1).
For example, if a stock's beta value is 1.3, it means, theoretically this stock is 30% more
volatile than the market. Beta calculation is done by regression analysis which shows
security's response with that of the market.
By multiplying the beta value of a stock with the expected movement of an index, the
expected change in the value of the stock can be determined. For example, if beta is 1.3
and the market is expected to move up by 10%, then the stock should move up by 13%
(1.3 x 10).
Beta is the key factor used in the Capital Asset Price Model (CAPM) which is a model
that measures the return of a stock. The volatility of the stock and systematic risk can be
judged by calculating beta. A positive beta value indicates that stocks generally move in
the same direction with that of the market and the vice versa. Risk is an important
consideration in holding any portfolio. The risk in holding securities is generally
associated with the possibility that realised returns will be less than the returns expected.
Risks can be classified as Systematic risks and Unsystematic risks.
Unsystematic risks:
These are risks that are unique to a firm or industry. Factors such as management
capability, consumer preferences, labour, etc. contribute to unsystematic risks.
Unsystematic risks are controllable by nature and can be considerably reduced by
sufficiently diversifying one's portfolio.
Systematic risks:
These are risks associated with the economic, political, sociological and other macro-level
changes. They affect the entire market as a whole and cannot be controlled or eliminated
merely by diversifying one's portfolio.
What is Beta?
The degree to which different portfolios are affected by these systematic risks as
compared to the effect on the market as a whole, is different and is measured by Beta. To

2. put it differently, the systematic risks of various securities differ due to their relationships
with the market. The Beta factor describes the movement in a stock's or a portfolio's
returns in relation to that of the market returns. For all practical purposes, the market
returns are measured by the returns on the index (Nifty, Mid-cap etc.), since the index is a
good reflector of the market.
Many investors look for beta of a stock to measure the relative risk attached to it. As we
know and discussed in the article “How to hedge your portfolio using Nifty future?" that
beta (β) is the price sensitivity of an underlying asset with respect to the Index. The beta
calculation evaluates the performance of the historical prices of the equity with respect to
that of Index. This relative performance is further used to measure the risk attached with
the equity in the form of beta.
A β >1 indicates higher relative risk and the β < 1 signifies the lower relative risk.
You can calculate the β of any stock in Excel, provided you have data of historical prices
of the stock in consideration and the Index.
Let us calculate the β of a stock with the help of steps as shown in the following example:
(1) Select the equity and the Index:
The first step is to identify the stock whose beta is to be calculated with respect to the
market Index.
I am taking AXIS Bank Ltd as a stock in consideration and S&P CNX NIFTY as the
Index.
(2) Collect the historical prices of the stock and the Index for a period of time: Now, the
next step is to download the historical prices of both the stock and the Index for same
period of time. Well, the selection of the time period depends on the outlook of the
investor. If he is planning to invest in a stock for long term purposes then he should
collect data for longer duration say a year or two and if he is thinking to sell the stock in a
short time then he can look for data for shorter duration.

3. Well, in this example I am taking last two months data of the historical prices of the stock
AXIS Bank Ltd and last two months data S & P CNX NIFTY, which is shown in the table
below:
(You can find the historical price data in www.nseindia.com)
S.No Date Close price of AXIS Bank Close price of S&P NIFTY
1 10-Apr-15 568.05 8780.35
2 13-Apr-15 566 8834
3 15-Apr-15 550.2 8750.2
4 16-Apr-15 550.8 8706.7
5 17-Apr-15 533.7 8606
6 20-Apr-15 518.25 8448.1
7 21-Apr-15 523.2 8377.75
8 22-Apr-15 540.1 8429.7
9 23-Apr-15 538.2 8398.3
10 24-Apr-15 527.25 8305.25
11 27-Apr-15 524.2 8213.8
12 28-Apr-15 535 8285.6
13 29-Apr-15 551.95 8239.75
14 30-Apr-15 567.8 8181.5
15 04-May-15 568.35 8331.95
16 05-May-15 565.85 8324.8
17 06-May-15 543.3 8097
18 07-May-15 527.35 8057.3

4. 19 08-May-15 540.8 8191.5
20 11-May-15 551.1 8325.25
21 12-May-15 532.35 8126.95
22 13-May-15 558.5 8235.45
23 14-May-15 555.85 8224.2
24 15-May-15 562.05 8262.35
25 18-May-15 567.5 8373.65
26 19-May-15 561.45 8365.65
27 20-May-15 558.25 8423.25
28 21-May-15 570.45 8421
29 22-May-15 568.65 8458.95
30 25-May-15 562.1 8370.25
31 26-May-15 564.25 8339.35
32 27-May-15 577.8 8334.6
33 28-May-15 574.65 8319
34 29-May-15 585.4 8433.65
35 01-Jun-15 578.45 8433.4
36 02-Jun-15 553.1 8236.45
37 03-Jun-15 550.9 8135.1
38 04-Jun-15 556.4 8130.65
39 05-Jun-15 548.4 8114.7
40 08-Jun-15 553.6 8044.15
41 09-Jun-15 558.7 8022.4
42 10-Jun-15 564.5 8124.45
43 11-Jun-15 546.75 7965.35

5. (3) Calculate the percentage change in price:
The daily percentage change in prices is calculated both for stock AXIS Bank Ltd and
index S&P CNX NIFTY. This is calculated by current day’s price minus previous day’s
price and then divides the result by previous day’s price.
Percentage change (% change) = [(current day’s price – previous day’s price)/ previous
day’s price] x 100
Calculating the daily percentage change in the table below:
A B C D E F
S.No Date Close Price of AXIS bank % change in AXIS Bank price Close
price of S&P NIFTY % change in NIFTY price
1 10-Apr-15 568.05 8780.35
2 13-Apr-15 566 -0.4% 8834 0.6%
3 15-Apr-15 550.2 -2.8% 8750.2 -0.9%
4 16-Apr-15 550.8 0.1% 8706.7 -0.5%
5 17-Apr-15 533.7 -3.1% 8606 -1.2%
6 20-Apr-15 518.25 -2.9% 8448.1 -1.8%
7 21-Apr-15 523.2 1.0% 8377.75 -0.8%
8 22-Apr-15 540.1 3.2% 8429.7 0.6%
9 23-Apr-15 538.2 -0.4% 8398.3 -0.4%
10 24-Apr-15 527.25 -2.0% 8305.25 -1.1%
11 27-Apr-15 524.2 -0.6% 8213.8 -1.1%
12 28-Apr-15 535 2.1% 8285.6 0.9%
13 29-Apr-15 551.95 3.2% 8239.75 -0.6%
14 30-Apr-15 567.8 2.9% 8181.5 -0.7%

6. 15 04-May-15 568.35 0.1% 8331.95 1.8%
16 05-May-15 565.85 -0.4% 8324.8 -0.1%
17 06-May-15 543.3 -4.0% 8097 -2.7%
18 07-May-15 527.35 -2.9% 8057.3 -0.5%
19 08-May-15 540.8 2.6% 8191.5 1.7%
20 11-May-15 551.1 1.9% 8325.25 1.6%
21 12-May-15 532.35 -3.4% 8126.95 -2.4%
22 13-May-15 558.5 4.9% 8235.45 1.3%
23 14-May-15 555.85 -0.5% 8224.2 -0.1%
24 15-May-15 562.05 1.1% 8262.35 0.5%
25 18-May-15 567.5 1.0% 8373.65 1.3%
26 19-May-15 561.45 -1.1% 8365.65 -0.1%
27 20-May-15 558.25 -0.6% 8423.25 0.7%
28 21-May-15 570.45 2.2% 8421 0.0%
29 22-May-15 568.65 -0.3% 8458.95 0.5%
30 25-May-15 562.1 -1.2% 8370.25 -1.0%
31 26-May-15 564.25 0.4% 8339.35 -0.4%
32 27-May-15 577.8 2.4% 8334.6 -0.1%
33 28-May-15 574.65 -0.5% 8319 -0.2%
34 29-May-15 585.4 1.9% 8433.65 1.4%
35 01-Jun-15 578.45 -1.2% 8433.4 0.0%
36 02-Jun-15 553.1 -4.4% 8236.45 -2.3%
37 03-Jun-15 550.9 -0.4% 8135.1 -1.2%
38 04-Jun-15 556.4 1.0% 8130.65 -0.1%
39 05-Jun-15 548.4 -1.4% 8114.7 -0.2%

7. 40 08-Jun-15 553.6 0.9% 8044.15 -0.9%
41 09-Jun-15 558.7 0.9% 8022.4 -0.3%
42 10-Jun-15 564.5 1.0% 8124.45 1.3%
43 11-Jun-15 546.75 -3.1% 7965.35 -2.0%
(4) Understand the concept of Variance and Covariance:
Before, we proceed further in calculating the β of AXIS Bank Ltd, it is important to first
understand the concept of variance and co-variance
Variance: It is the measurement of the spread between the numbers in a data. It actually
measures the distance between each number in a data set from the mean of the data set.
Where,
N = total number of data sets
x = price of particular date
µ = mean of N number of data sets
Covariance: It is the degree or the extent by which the returns of two risky assets move
with respect to each other. A positive covariance indicates that the returns of assets move
together while the negative covariance means that the returns move in the opposite
direction.

8. (5) The calculation of beta:
It is the covariance of returns of AXIS Bank Ltd and the returns of S&P CNX NIFTY (for
the period April 10, 2015 to June 11, 2015) divided by the variance of the returns of the
S&P CNX NIFTY for the similar period.
Beta of AXIS Bank Ltd = COVARIANCE of returns of AXIS Bank Ltd and the returns of
S&P CNX NIFTY/ VARIANCE of the returns of the S&P CNX NIFTY
You can get the results by using following formula in excel:
Beta of AXIS Bank Ltd = COVAR (D2:D43, F2:F43) / VAR (F2:F43)
Where D2:D43 is the returns of AXIS Bank Ltd.
F2:F43 shows the returns of S&P CNX NIFTY
Beta of AXIS Bank Ltd = (1.66 x 10-4) / (1.28 x 10-4)
Beta of AXIS Bank Ltd = 1.3
This means that for 1 unit change in the price of the S&P CNX NIFTY the price change in
AXIS Bank will be 1.3 units.
(5) Assess the reliability of risk: Now we will understand that to what extent knowing the
values of S&P CNX NIFTY helps you predict the values of AXIS Bank. This can be
calculated using R- square, here is the formula in excel to calculate it:

9. R- Squared = RSQ (F2:F43, D2:D43)
R- Squared = 0.485 or 48.5%
R2 is 0.485
48.5% of AXIS Bank’s price movement can be explained by the price movements of
benchmark index S&P CNX NIFTY. Therefore, we can say that the price movements of
AXIS Bank is 48.5% correlated to the price movements in S&P CNX NIFTY
Conclusion: Although it is a time consuming exercise but it gives an investor an idea
about the risk of associated with the particular asset. Apart from calculating beta we can
also get to know the extent of correlation in between the equity and the index and hence
let us know the reliability of the risk. The main disadvantage is that the β calculation does
not reflect the recent changes. In the end, we can say that this is a useful tool to assess the
risk element attached to the asset and investor should apply this tool before investing in
any equity.