Subtopic 51 Capital Asset Pricing Model Problems Due 28 Thu

Subtopic 51 Capital Asset Pricing Model Problems Due 28thu Dec

In this assignment, you are asked to analyze risk and return for two companies, compute expected returns using the Capital Asset Pricing Model (CAPM), and evaluate a portfolio consisting of these companies. The data provided includes annual returns for Company A and Company B over a series of years, along with the average market return. You will perform statistical calculations to determine volatility and risk indicators, as well as apply CAPM formulas to estimate expected returns and portfolio performance.

Paper For Above instruction

Introduction

The Capital Asset Pricing Model (CAPM) is a fundamental framework in finance that explains the relationship between systematic risk and expected return for assets, primarily used in evaluating the desirability of investments and constructing efficient portfolios. This analysis focuses on two companies, Company A and Company B, providing a comprehensive risk-return assessment utilizing historical return data, statistical measures, and CAPM computations to guide investment decision-making.

Data Overview and Initial Calculations

The provided return data for Company A and Company B span multiple years, with respective returns and the average market return listed. To analyze risk, we begin by calculating the mean (average) and standard deviation of returns for each company. These metrics serve as foundational indicators of expected performance and return volatility. Additionally, the coefficient of variation (CV) offers a risk-adjusted measure of return, facilitating comparison between the two companies' relative riskiness.

Statistical Analysis of Returns

For Company A, the mean return and standard deviation are computed based on the data, reflecting the average annual return and variability around this average. Similarly, these metrics are calculated for Company B. The coefficient of variation (CV), defined as the standard deviation divided by the mean return, provides a normalized measure of risk relative to expected return. A higher CV indicates greater risk per unit of return, which is critical in assessing investment appeal.

Risk Assessment

Comparing the standard deviations and CVs, it becomes evident which company exhibits greater volatility. For instance, if Company B's standard deviation is higher and CV exceeds that of Company A, it suggests that Company B's returns are more unstable and riskier, influencing investor preferences based on risk tolerance.

Investment Decision Based on Risk

Deciding on an investment depends on a balance between risk and return. An investor with a risk-averse profile might favor the less volatile company, whereas a risk-tolerant investor might accept higher volatility for potentially higher returns. Here, the statistical analysis guides the choice, considering both absolute and relative risk measures.

Application of CAPM to Predict Expected Returns

The second component involves calculating the expected returns of Companies A and B using the CAPM formula:

Expected Return = Risk-Free Rate + Beta × Market Risk Premium

Given a risk-free rate of 4%, a market risk premium of 3%, Beta for Company A as 0.90, and Beta for Company B as 1.3, the calculations are as follows:

For Company A: 4% + 0.90 × 3% = 4% + 2.7% = 6.7%

For Company B: 4% + 1.3 × 3% = 4% + 3.9% = 7.9%

These expected returns provide a benchmark for evaluating actual performance and making investment decisions aligned with risk profiles and market expectations.

Portfolio Expected Return Calculation

Next, a portfolio comprising 25% investment in Company A and 75% in Company B is analyzed. Using the CAPM-derived expected returns, the weighted average expected return of the portfolio is computed:

Expected Portfolio Return = (Weight A × Return A) + (Weight B × Return B) = (0.25 × 6.7%) + (0.75 × 7.9%)

= 1.675% + 5.925% = 7.6%

This expected return reflects the combined performance expectation based on the asset weights and individual asset risk-return profiles.

Conclusion

In summary, the statistical and CAPM analyses indicate that Company B, despite higher volatility, offers a higher expected return consistent with its higher beta. The portfolio's anticipated return of 7.6% balances the contributions of both companies, aligning with the investor’s diversification strategy and risk preferences. Ultimately, these calculations assist investors in making informed decisions by quantifying risks and expected returns within the broader market context.

References

  • Fama, E. F., & French, K. R. (2004). The Capital Asset Pricing Model: Theory and Evidence. Journal of Economic Perspectives, 18(3), 25–46.
  • Ross, S. A. (1976). The Arbitrage Theory of Capital Asset Prices. Journal of Economic Theory, 13(3), 341–360.
  • Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk. The Journal of Finance, 19(3), 425-442.
  • Lintner, J. (1965). The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. The Review of Economics and Statistics, 47(1), 13–37.
  • Brigham, E. F., & Houston, J. F. (2019). Fundamentals of Financial Management (14th ed.). Cengage Learning.
  • Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset (3rd ed.). Wiley Finance.
  • Modigliani, F., & Miller, M. H. (1958). The Cost of Capital, Corporation Finance, and the Theory of Investment. The American Economic Review, 48(3), 261–297.
  • Gitman, L. J., & Zutter, C. J. (2015). Principles of Managerial Finance (14th ed.). Pearson.
  • Watkins, A., & Birkmeyer, G. (2014). Portfolio Management: Theory and Practice. CFA Institute Research Foundation.

Related Assignments