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

1. Expected returns are basically the average of the given returns:

XYZ = 5% - 3% + 6% - 10% + 8% / 5

= 6%/5 = 1.2%

Market returns = -4% + 3% + 10% - 5% + 7% / 5

= 11%/5 = 2.2%

2. Covariance = Sum of ( (Xi - Xmean) ( Yj - Ymean)) / n-1

= ( (5-1.2)*(-4-2.2) + (-3-1.2)*(3-2.2) + (6-1.2)*(10-2.2) + (-10-1.2)*(-5-2.2) + (8-1.2)*(7-2.2)) / 5-1

= ( 3.8*-6.2 + -4.2*0.8 + 4.8*7.8 + -11.2*-7.2 + 6.8*4.8)/4

= (-23.56 - 3.36 + 37.44 + 80.64 + 32.64)/4

= 123.8/4

= 30.95

3. Beta of XYZ = Covariance/ variance of XYZ

Varience = Sum of (xi - xmean)^2 / n-1

= (3.8^2 + -4.2^2 + 4.8^2 + -11.2^2 + 6.8^2) / 5-1

= (14.44 + 17.64 + 23.04 + 125.44 + 46.24) /4

= 226.8/4

= 56.7

Beta = 30.95/56.7

= 0.546

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