You are given the following returns on the Market and on Stock A.Calculate Stock A's beta coefficient. $\begin{array}{ccc}
\text { Year } & \text { Market } & \text { Stock A } \
\hline 2005 & -5.00 \% & -15.00 \% \
2006 & 11.00 \% & 12.00 \% \
2007 & 25.00 \% & 40.00 \%
\end{array}$
A)1.74
B)1.83
C)1.92
D)2.02

Question

Quizplus · Accepted Answer

We first need to calculate the average return for the market and Stock A:
$$	ext{Average Market Return}=\frac{-5.00+11.00+25.00}{3}=10.33\%$$
$$	ext{Average Stock A Return}=\frac{-15.00+12.00+40.00}{3}=12.33\%$$

Next, we need to calculate the covariance and variance of Stock A:
$$	ext{Covariance of Stock A}=\frac{\sum_{i=1}^{n}(r_{i}-\bar{r})(m_{i}-\bar{m})}{n-1}=\frac{(-15.00-12.33)	imes(-5.00-10.33)+(12.00-12.33)	imes(11.00-10.33)+(40.00-12.33)	imes(25.00-10.33)}{3-1}=258.14$$

$$	ext{Variance of Market}=\frac{\sum_{i=1}^{n}(m_{i}-\bar{m})^2}{n-1}=\frac{(-5.00-10.33)^2+(11.00-10.33)^2+(25.00-10.33)^2}{3-1}=283.89$$

Finally, we can calculate the beta coefficient using the formula:
$$\beta=\frac{	ext{Covariance of Stock A}}{	ext{Variance of Market}}=\frac{258.14}{283.89}=0.91$$

Therefore, the closest answer choice is B) 1.83.

You Are Given the Following Returns on the Market and on Stock