Question

Consider the following two stocks.

	Probabilities (pi )	Stock "a"	Stock "b"
Recession	p1= 31%	-4%	4%
Normal	p2= 26%	7%	-4%
Boom	p3= 43%	11%	26%

Expected Return

r¯a = 5.31

r¯b = 11.38

Standard Deviation

SDa = 6.44

SDb = 13.05

Question:

Using the correct answers from the previous questions, what is the correlation between the two stocks? Enter your answer rounded to 2 decimal places.

Corr(a, b) = ?

Answer 1

Correlation between 2 stocks can be computed with help of below formula -

= Covariance(x,y ) / standard deviation of x * standard deviation of y

and

Here,

Expected Return

r¯a = 5.31

r¯b = 11.38

covariance = 0.31 ( - 0.04 - 0.0531 ) * ( 0.04 - 0.1138 ) + 0.26 ( 0.07 - 0.0531) * ( - 0.04 - 0.1138) + 0.43 ( 0.11 - 0.0531 ) * ( 0.26 - 0.1138)

= 0.31 ( - 0.0931 ) ( - 0.0738) + 0.26 ( 0.0169) ( 0.0738) + 0.43 ( 0.0569) ( 0.1462)

= 0.002129942 + 0.000324277 + 0.003577075

= 0.006031294

Standard Deviation

SDa = 6.44

SDb = 13.05

= 0.006031294 / 0.0084042

= 0.717652364

= 0.72 (approx)

Corr(a, b) = 0.72

Hope it helps!