Use the following to answer questions 1-3: Standard Deviation Beta Security X 0.
ID: 2649676 • Letter: U
Question
Use the following to answer questions 1-3:
Standard Deviation Beta
Security X 0.35 1.45
Security Y 0.28 1.06
Security Z 0.44 1.22
1. Which of the following is correct?
A) Security Z has the greatest total risk because it has the largest standard deviation.
B) Security X has the greatest total risk because it has the largest beta.
C) Security X has the greatest diversifiable risk because it has the largest beta.
D) Security Y has the lowest total risk because it has the lowest beta.
E) An equally-weighted portfolio of XYZ will have the same market risk as the market portfolio.
2. Which security has the greatest systematic risk?
A) Z because it has the largest standard deviation.
B) X because it has the largest beta coefficient.
C) Z because it has a high beta and the largest standard deviation.
D) Y because it has the greatest diversifiable risk.
E) It is not possible to tell given the information above.
3. Which security has the greatest required return?
A) Y because it has the largest standard deviation.
B) X because it has the largest beta coefficient.
C) Z because it has the highest ratio of standard deviation to beta.
D) Y because it has the lowest beta coefficient.
E) It is not possible to tell given the information above
Explanation / Answer
This question requires understanding and application of CAPM model and types of risk associated with financial securities.
According to CAPM Model, Expected rate of Return = Risk free rate + Beta * Market Risk premium.
Total Risk (or Standard deviation) = Systematic Risk (Beta) + Non-systematic (diversifiable risk)
Now, let us look at the questions.
Q1. Statement A is true.
As explained above, total risk or volatility is mathematically measured by standard deviation. Hence, higher the standard deviation, higher would be the total risk.
In this question, Z has the highest standard deviation and hence highest total risk.
Q2. Statement B is true.
Beta is measure of systematic risk. This is also known as market risk and cannot be removed by virtue of diversification. Highest Beta if for security X and hence that holds the highest systematic risk.
Q3. Statement B is true.
Based on the CAPM equation, required return is driven by risk free rate, Beta and Market risk premium. Except beta, other two variables would be same for all the three stocks. Hence, higher the Beta, higher would be the required rate of return. Hence, X having the highest beta, will have the highest required rate of retrun.
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