Given the returns for two stocks with the following information, calculate the correlation coefficient of the returns for the two stocks. Assume the expected return for Stock 1 is 10.8 percent and 9.7 percent for Stock 2. Do not round intermediate computations.

The correlation coefficient of the returns for the two stocks is 0.231

Explanation:

From the question given, we apply the method called co variance

Co variance is referred to as when the co-movement of variables are measured.  

The co variance is defined as:

ρ₁,₂=Cov₁,₂/σ₁ x σ₂

The Expected return of stock 1 μ1= 0.4 x 9+0.5 x 11+0.1 x 17=10.8%

The Expected return of stock 1 μ2=0.4 x 11+0.5 x 8+0.1 x 13=9.7%

The Variance of stock 1 σ²₁ is:

1 σ²₁=0.092 x 0.4+0.112 x 0.5+0.172 x 0.1−0.1082σ12=0.092 x 0.4+0.112 x 0.5+0.172 x 0.1−0.1082

=0.012180-0.011664 =0.000516

The standard deviation of stock 1 σ₁ =2√0.0005162 =0.022716 =2.2716%

Thus,

The Variance of stock 2 σ²₂ is:

2 σ²₂= 0.112 x 0.4+0.082 x 0.5+0.132 x 0.1−0.09722 =0.009730-0.009409=0.000321

The standard deviation of stock 2 σ₂ =2√0.000321 =0.017916=1.792%

Cov₁,₂=0.4 x (0.09−0.108)x (0.11−0.097)+0.5 x(0.11−0.108)x(0.08−0.097)+0.1 x(0.17−0.108)x(0.13 8)x(0.13−0.097) =-0.000094-0.000017+0.000205 =0.000094

Therefore,

ρ₁,₂=0.000094/((0.017916)x(0.022716)) =0.231

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