Question

Consider the following 2 stocks:

	Closing Prices
	Stock A	Stock B
Year 1	33.75	112.09
Year 2	31.69	115.74
Year 3	29.17	115.89
Year 4	25.64	120.75
Year 5	27.97	125.12
Year 6	30.36	127.46
Year 7	32.74	110.49
Year 8	35.09	111.26
Year 9	31.89	106.99
Year 10	33.56	105.17
Year 11	30.12	108.25

1. If correlation between the returns was -.301, calculate the covariance of returns

Answer 1

Covariance between two stocks x and y is calculated as correlation(x,y)*standard deviation of x* standard deviation of y

Standard deviation of x is calculated as sqrt((summation of (Xi-X)^2)/(n-1)); where Xi is the individual stock price, X is mean of the given stock prices and n is the number of values in the sample.

Mean= 33.75+31.69+....30.12/11= 31.09

= sqrt((33.75-31.09)^2+(31.69-31.09)^2+....(30.12-31.09)^2)/(11-1))

= 2.78

Standard deviation of y is calculated similarly.

Mean= 112.09+115.74+....108.25/11= 114.47

= sqrt((112.09-114.47)^2+(115.74-114.47)^2+....(108.25-114.47)^2)/(11-1))

= 7.34

So, Covariance= (-0.301*2.78*7.34)= -6.15