Question

Based on the following information determine the covariance and correlation between the returns of the two stocks.

State of Economy	Probability of State of Economy	Return of X	Return of Y
Bear	0.10	-0.02	0.034
Normal	0.65	0.138	0.062
Bull	0.25	0.218	0.092

Answer 1

For calculation of covariance and coefficient of the stocks we have to make following calculations:

state of the economy	probability related to state of the economy (pi)	return of stock X (Rx )	(pi)* (Rx )	(Rx ) - Average return	[(Rx ) - Average return]2	(pi) * [(Rx ) - Average return]2
Bear	.10	-.02	-.002	-.1622	.0263	.00263
Normal	.65	.138	.0897	-.0042	.00001764	.000011466
Bull	.25	.218	.0545	.0758	.00575	.0014375
		Average Return =	.1422		Total =	.004078966

Now variancec= .004078966

Standard deviation = .004078966 = .0639

state of the economy	probability related to state of the economy (pi)	return of stock Y (Rx )	(pi)* (RY)	(RY) - Average return	[(RY) - Average return]2	(pi) * [(RY) - Average return]2
Bear	.10	.034	.0034	-.0327	.001069	.000106929
Normal	.65	.062	.0403	-.0047	.00002209	.0000143585
Bull	.25	.092	.023	.0253	.00064	.0002673225
		Average Return =	.0667		Total =	.0003886

Now variancec= .0003886

Standard deviation = .0003886 = .0197

Now Cov _x,y = p_i  [(R_x ) - Average return ] [(R_Y) - Average return]

State of the economy	pi	[(Rx ) - Average return ] [(RY) - Average return]	pi  [(Rx ) - Average return ] [(RY) - Average return]
Bear	.10	.0053 = (-.1622 * -.0327)	.00053
Normal	.65	.00001974	.0000128
Bull	.25	.00192	.00048
		Cov x,y =	.0010228

Now Cov _x,y = .0010228

Correlation = Cov _x,y / Standard deviation of X * Standard deviation of Y

= .0010228/ .0639*.0197

=.0010228/ .00125883 = 0.8125

So, Correlation between two stocks = 0.8125

this shows both stocks have positive and strong correlation which means they move in same direction.