Question

The table below shows daily returns on XYZ and Market.

	Return of XYZ	Return of Market
Monday	5%	-4%
Tuesday	-3%	3%
Wednesday	6%	10%
Thursday	-10%	-5%
Friday	8%	7%

1. Find Expected returns of XYZ and Market.

2. What is the covariance of XYZ and the Market?

3. Find the Beta of XYZ.

Answer 1

Expected return of XYZ = [5%-3%+6%-10%+8%]/5 = 6%/5 = 1.2%

Expected return of market = [-4%+3%+10%-5%+7%]/5 = 11%/5 = 2.2%

Days (i)	Return of XYZ (ii)	Return of Market (iii)	Return of XYZ - Expected return of XYZ (iv)	Return of market - Expected return of market (v)	(vi) = (iv)*(v)	(vii) = (v)^2
Monday	5%	-4%	3.80%	-6.20%	-0.2356%	0.3844%
Tuesday	-3%	3%	-4.20%	0.80%	-0.0336%	0.0064%
Wednesday	6%	10%	4.80%	7.80%	0.3744%	0.6084%
Thursday	-10%	-5%	-11.20%	-7.20%	0.8064%	0.5184%
Friday	8%	7%	6.80%	4.80%	0.3264%	0.2304%
					1.2380%	1.7480%

Covariance of XYZ & market = Σ{[Return of XYZ - Expected return of XYZ]*[Return of market - Expected return of market]/N = 1.238%/5 = 0.2476%

Variance of market = Σ{[(Return of market - Expected return of market)^2]}/N = 1.748%/5 = 0.3496%

Beta of XYZ = Covariance of XYZ & market/Variance of market = 0.2476%/0.3496% = 0.7082