Consider the following probability distribution for stocks A and B: $$\begin{array} { c c c c }
\text { State } & \text { Probability } & \text { Return on Stock A } & \text { Return on Stock B } \
1 & 0.10 & 10 \% & 8 \% \
2 & 0.20 & 13 \% & 7 \% \
3 & 0.20 & 12 \% & 6 \% \
4 & 0.30 & 14 \% & 9 \% \
5 & 0.20 & 15 \% & 8 \% \
\hline
\end{array}$$ The coefficient of correlation between A and B is

Question

Consider the following probability distribution for stocks A and B: $$\begin{array} { c c c c } 
\text { State } & \text { Probability } & \text { Return on Stock A } & \text { Return on Stock B } \
1 & 0.10 & 10 \% & 8 \% \
2 & 0.20 & 13 \% & 7 \% \
3 & 0.20 & 12 \% & 6 \% \
4 & 0.30 & 14 \% & 9 \% \
5 & 0.20 & 15 \% & 8 \% \
\hline
\end{array}$$ The coefficient of correlation between A and B is

Quizplus · Accepted Answer

The correct answer is A because the coefficient of correlation between A and B is 0.46. This can be calculated using the following formula:```ρ(A, B) = Cov(A, B) / (σA * σB)```where:* ρ(A, B) is the coefficient of correlation between A and B* Cov(A, B) is the covariance between A and B* σA is the standard deviation of A* σB is the standard deviation of BThe covariance between A and B can be calculated using the following formula:```Cov(A, B) = E[(A - μA)(B - μB)]```where:* E is the expected value operator* μA is the mean of A* μB is the mean of BThe standard deviation of A can be calculated using the following formula:```σA = √(E[(A - μA)^2])```The standard deviation of B can be calculated using the following formula:```σB = √(E[(B - μB)^2])```Using these formulas, we can calculate the coefficient of correlation between A and B to be 0.46.

Consider the Following Probability Distribution for Stocks a and B