$\begin{array}{c}
\begin{array}{c}
\underline{\text { Year }} \
1 \
2 \
3 \
4
\end{array}
\begin{array}{c}
\underline{\text {Stock X}}\
-27 \% \
6 \% \
34 \%\
11\%
\end{array}
\begin{array}{c}
\underline{\text { Market } }\
-7 \% \
11 \% \
18 \% \
10\%
\end{array}
\end{array}$

-A risky security has a variance of 0.034596 and a covariance with the market of 0.0216. The variance of the market is 0.023716. What is the correlation of this risky security to the market?
A) 0.47
B) 0.96
C) 0.75
D) 0.37
E) 0.58

Question

$\begin{array}{c}
\begin{array}{c}
\underline{\text { Year }} \
1 \
2 \
3 \
4
\end{array}
\begin{array}{c}
\underline{\text {Stock X}}\
-27 \% \
6 \% \
34 \%\
11\%
\end{array}
\begin{array}{c}
\underline{\text { Market } }\
-7 \% \
11 \% \
18 \% \
10\%
\end{array}
\end{array}$
  
-A risky security has a variance of 0.034596 and a covariance with the market of 0.0216. The variance of the market is 0.023716. What is the correlation of this risky security to the market?
A) 0.47
B) 0.96
C) 0.75
D) 0.37
E) 0.58

Quizplus · Accepted Answer

The correlation coefficient ($r$) between two variables can be calculated using the formula $r = \frac{cov(X,Y)}{\sqrt{var(X) \cdot var(Y)}}$, where $cov(X,Y)$ is the covariance between the two variables, and $var(X)$ and $var(Y)$ are the variances of the respective variables. Plugging in the given values: $r = \frac{0.0216}{\sqrt{0.034596 \cdot 0.023716}}$, which calculates to approximately 0.75.

-A Risky Security Has a Variance of 0