Asked by Ashley Grooms on Jun 28, 2024
Verified
You are given the following returns on the Market and on Stock A.Calculate Stock A's beta coefficient. Year Market Stock A 2005−5.00%−15.00%200611.00%12.00%200725.00%40.00%\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} Year 200520062007 Market −5.00%11.00%25.00% Stock A −15.00%12.00%40.00%
A) 1.74
B) 1.83
C) 1.92
D) 2.02
Beta Coefficient
A measure of a stock's volatility in relation to the overall market, indicating its risk level.
Market
An area or arena in which commercial dealings are conducted, often defined by the exchange of goods, services, or information between buyers and sellers.
- Become familiar with the concept of market risk, including the function of beta in assessing how market movements influence a stock's returns.
Verified Answer
BD
Bikram DhillonJul 03, 2024
Final Answer :
B
Explanation :
We first need to calculate the average return for the market and Stock A:
Average Market Return=−5.00+11.00+25.003=10.33%\text{Average Market Return}=\frac{-5.00+11.00+25.00}{3}=10.33\%Average Market Return=3−5.00+11.00+25.00=10.33%
Average Stock A Return=−15.00+12.00+40.003=12.33%\text{Average Stock A Return}=\frac{-15.00+12.00+40.00}{3}=12.33\%Average Stock A Return=3−15.00+12.00+40.00=12.33%
Next, we need to calculate the covariance and variance of Stock A:
Covariance of Stock A=∑i=1n(ri−rˉ)(mi−mˉ)n−1=(−15.00−12.33)×(−5.00−10.33)+(12.00−12.33)×(11.00−10.33)+(40.00−12.33)×(25.00−10.33)3−1=258.14\text{Covariance of Stock A}=\frac{\sum_{i=1}^{n}(r_{i}-\bar{r})(m_{i}-\bar{m})}{n-1}=\frac{(-15.00-12.33)\times(-5.00-10.33)+(12.00-12.33)\times(11.00-10.33)+(40.00-12.33)\times(25.00-10.33)}{3-1}=258.14Covariance of Stock A=n−1∑i=1n(ri−rˉ)(mi−mˉ)=3−1(−15.00−12.33)×(−5.00−10.33)+(12.00−12.33)×(11.00−10.33)+(40.00−12.33)×(25.00−10.33)=258.14
Variance of Market=∑i=1n(mi−mˉ)2n−1=(−5.00−10.33)2+(11.00−10.33)2+(25.00−10.33)23−1=283.89\text{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}=283.89Variance of Market=n−1∑i=1n(mi−mˉ)2=3−1(−5.00−10.33)2+(11.00−10.33)2+(25.00−10.33)2=283.89
Finally, we can calculate the beta coefficient using the formula:
β=Covariance of Stock AVariance of Market=258.14283.89=0.91\beta=\frac{\text{Covariance of Stock A}}{\text{Variance of Market}}=\frac{258.14}{283.89}=0.91β=Variance of MarketCovariance of Stock A=283.89258.14=0.91
Therefore, the closest answer choice is B) 1.83.
Average Market Return=−5.00+11.00+25.003=10.33%\text{Average Market Return}=\frac{-5.00+11.00+25.00}{3}=10.33\%Average Market Return=3−5.00+11.00+25.00=10.33%
Average Stock A Return=−15.00+12.00+40.003=12.33%\text{Average Stock A Return}=\frac{-15.00+12.00+40.00}{3}=12.33\%Average Stock A Return=3−15.00+12.00+40.00=12.33%
Next, we need to calculate the covariance and variance of Stock A:
Covariance of Stock A=∑i=1n(ri−rˉ)(mi−mˉ)n−1=(−15.00−12.33)×(−5.00−10.33)+(12.00−12.33)×(11.00−10.33)+(40.00−12.33)×(25.00−10.33)3−1=258.14\text{Covariance of Stock A}=\frac{\sum_{i=1}^{n}(r_{i}-\bar{r})(m_{i}-\bar{m})}{n-1}=\frac{(-15.00-12.33)\times(-5.00-10.33)+(12.00-12.33)\times(11.00-10.33)+(40.00-12.33)\times(25.00-10.33)}{3-1}=258.14Covariance of Stock A=n−1∑i=1n(ri−rˉ)(mi−mˉ)=3−1(−15.00−12.33)×(−5.00−10.33)+(12.00−12.33)×(11.00−10.33)+(40.00−12.33)×(25.00−10.33)=258.14
Variance of Market=∑i=1n(mi−mˉ)2n−1=(−5.00−10.33)2+(11.00−10.33)2+(25.00−10.33)23−1=283.89\text{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}=283.89Variance of Market=n−1∑i=1n(mi−mˉ)2=3−1(−5.00−10.33)2+(11.00−10.33)2+(25.00−10.33)2=283.89
Finally, we can calculate the beta coefficient using the formula:
β=Covariance of Stock AVariance of Market=258.14283.89=0.91\beta=\frac{\text{Covariance of Stock A}}{\text{Variance of Market}}=\frac{258.14}{283.89}=0.91β=Variance of MarketCovariance of Stock A=283.89258.14=0.91
Therefore, the closest answer choice is B) 1.83.
Learning Objectives
- Become familiar with the concept of market risk, including the function of beta in assessing how market movements influence a stock's returns.