Question

Based on the following information, calculate the Beta (β) of ASEA Brown Boveri (ABB) a leading Swiss heavy equipment manufacturer specializing in robotics and automation technology.

	Returns
Year	ABB	DJIA-Market
2015	8.60%	10.50%
2016	-15.30%	-14.40%
2017	22.90%	18.70%
2018	33.10%	25.50%
2019	16.60%	15.90%

Answer 1

ABB [ Y ]	DJIA - Market [ X ]	Y2	X2	XY
8.60	10.50	73.96	110.25	90.3
-15.30	-14.40	234.09	207.36	220.32
22.90	18.70	524.41	349.69	428.23
33.10	25.50	1095.61	650.25	844.05
16.60	15.90	275.56	252.81	263.94
65.9	56.2	2203.63	1570.36	1846.84

Correlation co-efficient : -

r = n Σ XY - ( ΣX) (ΣY) / √ n Σ X2 - (ΣX)2 √ n Σ Y2 - (Σ Y)2

   = ( 5 * 1846.84) - ( 56.2 * 65.9 ) / √ ( 5 * 1570.36) - (56.2)2  √ (5 * 2203.63) - (65.9)2

= 9234.2 - 3703.58 / √ 7851.8 - 3158.44 √ 11018.15 - 4342.81

= 5530.62 / √ 4693.36 √ 6675.34

= 5530.62 / ( 68.5081 * 81.7027).

= 0.988

Calculation of Standerd deviation - DJIA

=   √ N ΣX2 - (ΣX)2 / N2

= √ 5 * 1570.36 - (56.2)2 / 25

=  √ 7851.8 -3158.44 / 25

=  √ 4693.36 / 25

=  √ 187.73

= 13.70

Calculation of Standerd deviation - ABB

=   √ N ΣY2 - (ΣY)2 / N2

= √ 5 * 2203.63 - (65.9)2 / 25

=  √ 11018.15 -4342.81 / 25

= √ 6675.34 / 25

= √267.01

= 16.34

Calculation of Beta :-

= Correlation co-efficient * Std dev (ABB) * std dev (DJIA) / [std dev of (DJIA) ]2

= (0.98 ) (16.34 * 13.70) / (13.70)2

= 219.38084 / 187.69

= 1.16