Description
Beta shows how a price of a security responds to market forces, The more responds to the price of a security is to changes in the market, the higher will be its beta.
Calculation of beta(?)
? Beta measures non diversifiable risk.
? Beta shows how a price of a security
responds to market forces.
? The more responds to the price of a security
is to changes in the market, the higher will be
its beta.
? Beta is calculated by relating the returns on
a security with the returns of the market
? Market return is measured by the average
return of a large sample of stocks such as
BSE or NSE index.
? The beta for overall market is equal to 1.00.
Beta can be positive or negative.
? However all betas are positive and most
betas lie somewhere between .4 and 1.9.
? Stocks having betas of less than 1 will of
course be less responsive to changing returns
in the market and therefore are considered
less risky .
Methods of beta calculation
? Direct method
? Market model
Direct method
? Beta is the ratio of covariance between
market return and the security’s return
to the market return variance.
? ?=Covj,m/?m
2
? j- security’s return
? m- market return
CASE
Returns on Sensex and Jaya Infotech
Beta Calculation for Jaya Infotech Limited
Covj,m=4666.30/5=933.26
?m
2
=5288.23/5=1057.65
? ?=Covj,m/?m
2
=933.26/1057.65=0.88
Market model
Estimates for Regression Equation
The value of ? and ? in the regression equation are given by the
following equations:
2 2
( ) ( )
( )
N X Y X Y
N X X
S - S S
b =
S - S
2
(5)(4, 774.49) (27.42)(19.73)
(5)(5, 438.58) (27.42)
23,872.45 541.00 23,331.45
0.88
27,192.90 751.86 26, 441.04
Alpha
Alpha 3.95 (0.88)(5.48) 0.89
j
j
Y X
-
b =
-
-
= = =
-
= a = - b
= a = - = -
Alpha
? It is the return when market is flat or
market return is zero.
Return
? rj=Ln (pt /pt-1)
? Pt-Price of today
? Pt-1-price of previous day
or
? Todays security return={(Todays price
– Previous day price)/ Previous day
price)} X 100
CASE-2
NSE index(x) Bajaj Auto
OCT 5 1998 904.95 597.8
6 845.75 570.8
7 874.25 582.95
8 847.95 559.85
9 849.1 554.6
12 835.8 545.1
13 816.75 519.15
14 843.55 560.7
15 835.55 560.95
16 839.5 597.4
Index return (x) x2 stock return Y2 XY
-6.54 42.77 -4.52 20.43 29.56
3.37 11.36 2.13 4.54 7.18
-3.01 9.06 -3.96 15.68 11.92
0.14 0.02 -0.94 0.88 -0.13
-1.57 2.46 -1.71 2.92 2.68
-2.28 5.2 -4.76 22.66 10.85
3.28 10.76 8 64 26.24
-0.95 0.9 0.04 0.0016 -0.04
0.47 0.22 6.5 42.25 3.06
Total=-7.09 82.75 0.78 173.36 91.32
? ?= 1.19
? Alpha=1.02
Thank You……..
doc_768267814.ppt
Beta shows how a price of a security responds to market forces, The more responds to the price of a security is to changes in the market, the higher will be its beta.
Calculation of beta(?)
? Beta measures non diversifiable risk.
? Beta shows how a price of a security
responds to market forces.
? The more responds to the price of a security
is to changes in the market, the higher will be
its beta.
? Beta is calculated by relating the returns on
a security with the returns of the market
? Market return is measured by the average
return of a large sample of stocks such as
BSE or NSE index.
? The beta for overall market is equal to 1.00.
Beta can be positive or negative.
? However all betas are positive and most
betas lie somewhere between .4 and 1.9.
? Stocks having betas of less than 1 will of
course be less responsive to changing returns
in the market and therefore are considered
less risky .
Methods of beta calculation
? Direct method
? Market model
Direct method
? Beta is the ratio of covariance between
market return and the security’s return
to the market return variance.
? ?=Covj,m/?m
2
? j- security’s return
? m- market return
CASE
Returns on Sensex and Jaya Infotech
Beta Calculation for Jaya Infotech Limited
Covj,m=4666.30/5=933.26
?m
2
=5288.23/5=1057.65
? ?=Covj,m/?m
2
=933.26/1057.65=0.88
Market model
Estimates for Regression Equation
The value of ? and ? in the regression equation are given by the
following equations:
2 2
( ) ( )
( )
N X Y X Y
N X X
S - S S
b =
S - S
2
(5)(4, 774.49) (27.42)(19.73)
(5)(5, 438.58) (27.42)
23,872.45 541.00 23,331.45
0.88
27,192.90 751.86 26, 441.04
Alpha
Alpha 3.95 (0.88)(5.48) 0.89
j
j
Y X
-
b =
-
-
= = =
-
= a = - b
= a = - = -
Alpha
? It is the return when market is flat or
market return is zero.
Return
? rj=Ln (pt /pt-1)
? Pt-Price of today
? Pt-1-price of previous day
or
? Todays security return={(Todays price
– Previous day price)/ Previous day
price)} X 100
CASE-2
NSE index(x) Bajaj Auto
OCT 5 1998 904.95 597.8
6 845.75 570.8
7 874.25 582.95
8 847.95 559.85
9 849.1 554.6
12 835.8 545.1
13 816.75 519.15
14 843.55 560.7
15 835.55 560.95
16 839.5 597.4
Index return (x) x2 stock return
Y2 XY-6.54 42.77 -4.52 20.43 29.56
3.37 11.36 2.13 4.54 7.18
-3.01 9.06 -3.96 15.68 11.92
0.14 0.02 -0.94 0.88 -0.13
-1.57 2.46 -1.71 2.92 2.68
-2.28 5.2 -4.76 22.66 10.85
3.28 10.76 8 64 26.24
-0.95 0.9 0.04 0.0016 -0.04
0.47 0.22 6.5 42.25 3.06
Total=-7.09 82.75 0.78 173.36 91.32
? ?= 1.19
? Alpha=1.02
Thank You……..
doc_768267814.ppt