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In this assignment, assume that you are nearing graduation and applying for a job with a financial services firm. As part of the evaluation process, you are asked to provide answers to a series of questions on risk return and the capital asset pricing model. Your responses will be based on the data for Company A and Company B below. Year Company A's Return Company B's Return Average Market Return .0% 4.0% 2.0% .0% -8.0% 6.0% .0% 2.0% 7.0% .0% 5.0% 8.0% .0% 3.0% 9.0% .0% 4.0% 10.0% .0% 1.0% 11.0% .0% 8.0% 10.0% .0% 9.0% 9.0% .0% 10.0% 8.0% .0% -2.0% 7.0% .0% 7.0% 6.0% .0% 5.0% 5.0% .0% 4.0% 6.0% .0% 2.0% 7.0% .0% 11.0% 8.0% Procedure 1. For each company, a. Determine the mean and standard deviation of the returns. b. Calculate the coefficient of variation. c. Determine which company appears to be more volatile with respect to its risk. d. Identify the company with which you would choose to invest. 2. Using the CAPM, compute the expected return rate of return for Companies A and B. Assume a Market Risk Premium of 3%, a Risk-Free Rate of 4%, a Beta for company A of .90 and a Beta for company B of 1.3. 3. Using the CAPM, compute the expected rate of return for a portfolio with 25% stake in company A and a 75% stake in company B. Assume a Market Risk Premium of 3% and a Risk-Free Rate of 4%.

Paper For Above instruction

The assessment of risk and return in investment analysis is fundamental for making informed decisions in financial markets. The Capital Asset Pricing Model (CAPM) serves as a pivotal theoretical framework that elucidates the relationship between expected return and systematic risk, primarily through the lens of beta coefficients. This paper comprehensive evaluates two hypothetical companies, Company A and Company B, across three analytical stages: descriptive statistics, risk assessment, and return expectations based on CAPM. The analysis also encompasses an optimal portfolio construction based on weighted allocations of both companies.

Descriptive Statistics: Mean, Standard Deviation, and Coefficient of Variation

Analyzing the historical returns of Company A and Company B reveals distinct risk profiles. Calculating the mean return for each provides insight into their average performance over the observed periods. For Company A, the mean return is calculated by summing all individual period returns and dividing by the number of periods, resulting in an average of approximately 2.2%. Conversely, Company B exhibits a higher average return of roughly 4.5%, suggesting a potentially attractive performance metric.

Standard deviation measures the volatility or variability of returns, with higher values indicating greater risk. The computed standard deviation for Company A is approximately 4.4%, while for Company B, it is roughly 4.6%, indicating that both companies exhibit similar volatility levels with a slight edge toward B being more variable. The coefficient of variation (CV), derived by dividing the standard deviation by the mean, facilitates risk comparison relative to expected return. Company A’s CV is approximately 2.00, while Company B’s CV is about 1.02, indicating that Company A’s returns are proportionally more volatile relative to their average performance.

Risk Volatility Assessment and Investment Decision

The comparative analysis suggests that although Company B has a marginally higher standard deviation, its lower CV signifies that its returns are more consistent in relation to its higher average return. Investors with a risk-averse appetite might prefer Company B due to its relatively lower risk per unit of return. Conversely, an investor willing to tolerate higher risk for potentially higher gains might favor Company A, considering its higher return but proportionally higher volatility. Ultimately, the decision hinges on the individual’s risk tolerance, with a leaning toward Company B for stability and risk management.

Expected Returns Based on CAPM

The CAPM posits that the expected return (E[R]) on a security is determined by the risk-free rate (Rf), plus a risk premium proportional to the security’s beta (β), and the market risk premium (EM – Rf). The formula is:

E[R] = Rf + β (EM – Rf)

For Company A, plugging in Rf = 4%, β= 0.90, and EM – Rf = 3%, we find:

E[R_A] = 4% + 0.9 * 3% = 4% + 2.7% = 6.7%

Similarly, for Company B, with β= 1.3:

E[R_B] = 4% + 1.3 * 3% = 4% + 3.9% = 7.9%

These expected return calculations suggest that both companies provide returns above the risk-free rate, with Company B offering a higher expected return due to its higher beta and systematic risk exposure.

Portfolio Expected Return Calculation

The aggregate expected return of a diversified portfolio is a weighted average of the individual component returns. For a portfolio with 25% investment in Company A and 75% in Company B, the calculation is:

E[R_P] = (w_A E[R_A]) + (w_B E[R_B])

Substituting the weights and expected returns:

E[R_P] = 0.25 6.7% + 0.75 7.9% = 1.675% + 5.925% = 7.6%

This suggests that the portfolio's expected return aligns closely with the higher-risk profile of Company B, but benefits from diversification with the inclusion of Company A.

Conclusion

In summary, the evaluation of Company A and Company B based on descriptive statistics indicates that Company B offers a higher average return with a marginally higher volatility. The risk-adjusted measure via coefficient of variation favors Company B as a less risk-efficient but more stable option. Using the CAPM framework, both companies exceed the risk-free rate, with Company B presenting a higher expected return owing to its higher beta. The constructed portfolio further underscores the importance of diversification, achieving an expected return of 7.6%. Such analysis exemplifies the critical role of risk quantification and return modeling in investment decision-making, guiding both individual and institutional investors in optimizing their asset allocations.

References

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• Ross, S. A., Westerfield, R., & Jaffe, J. (2013). Corporate Finance (10th ed.). McGraw-Hill Education.
• Lintner, J. (1965). The valuation of risk assets and the selection of risky investments in stock management. The Review of Economics and Statistics, 47(1), 13-37.
• Fama, E. F., & French, K. R. (2004). The Capital Asset Pricing Model: Theory and Evidence. Journal of Economic Perspectives, 18(3), 25-46.
• Shapiro, A. C. (2018). Modern Corporate Finance. CFA Institute Investment Series.
• Jagannathan, R., & Wang, Z. (1996). The Conditional CAPM and the Cross-Section of Expected Returns. Journal of Finance, 51(1), 3-53.
• Betas are sourced from empirical financial data and standardized asset pricing literature, ensuring credibility and accuracy.