Question

. Given the sample of returns of the Top Black Asphalt Company and the S&P 500 index, calculate Top Black's covariance and beta. I Year Rs(Top Black) +15% + 6% -10% 0 ( Rm(Market) +8% +2% -7% 3% 2% 0% 1 4% )

Answer 1

Lets Consider Rs (Top Black) as x and Rm( Market) as y

Year	Rs (Top Black)/ x	Rm (Market)/y	(x-7)	$1585203197362_image.png$	F*G
1	15%	8%	12%	6%	1%
2xxxxxx	6%	2%	3%	0%	0%
3	-10%	-7%	-13%	-9%	1%
4	0%	3%	-3%	1%	0%
5	4%	2%	1%	0%	0%
Mean/sum	3%	2%			2%

Covariance - £ (x – X) (y – 5) n-1

Therefore, Covariance = 2% / 4

Covariance = 0.465%

Now Beta, we also need variance of benchmark

Year	Rm (Market)/y	$1585203596467_image.png$	(メーカー
1	8%	6%	0%
2	2%	0%	0%
3	-7%	-9%	1%
4	3%	1%	0%
5	2%	0%	0%
Mean/sum	2%		1%

Variance - Σy -y)

Variance = 1%/5

Variance = 0.23%

And Beta = Covariance/Variance

Beta = 0.465% / 0.23%

Beta = 1.98