The Following Are The Historic Returns For Chelle Computer
The Following Are The Historic Returns for Chelle Computer Company
The assignment involves analyzing historic financial data for Chelle Computer Company to calculate key financial metrics. Specifically, you are asked to determine the correlation coefficient between Chelle Computer's returns and the general market index, as well as compute the beta coefficient for Chelle Computer. This entails examining historical return data for Chelle Computer and the market index, performing statistical calculations to quantify the relationship between the two, and interpreting the results within the context of risk and return analysis.
Paper For Above instruction
The analysis of Chelle Computer Company's historic returns to determine its financial risk characteristics is a fundamental task in financial analysis, particularly for assessing the company's systematic risk. Two primary measures are requested: the correlation coefficient and beta, both of which provide insights into how the company's stock movements relate to broader market fluctuations.
Correlation Coefficient Calculation
The correlation coefficient (r) measures the strength and direction of the linear relationship between the company's returns and the market index. It ranges from -1 to +1, where +1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 signifies no linear relationship. To calculate this coefficient, one must employ the historical return data for Chelle Computer and the market index. The formula involves computing the covariance of the two return series divided by the product of their standard deviations:
\[
r = \frac{\text{Cov}(R_{Chelle}, R_{Market})}{\sigma_{Chelle} \times \sigma_{Market}}
\]
where \( R_{Chelle} \) and \( R_{Market} \) are the returns of Chelle Computer and the market index respectively, and \( \sigma \) denotes standard deviation. The covariance can be derived from the historical data by calculating the average product of deviations from their respective means. Once this coefficient is obtained, it provides a quantitative measure of the relationship between Chelle's stock performance and that of the overall market.
Beta Calculation
The beta of Chelle Computer measures its sensitivity to movements in the market. It is formally defined within the Capital Asset Pricing Model (CAPM) framework as:
\[
\beta = \frac{\text{Cov}(R_{Chelle}, R_{Market})}{\sigma_{Market}^2}
\]
Alternatively, beta can be estimated as the slope coefficient in a regression of Chelle's returns on the market index returns:
\[
R_{Chelle} = \alpha + \beta R_{Market} + \epsilon
\]
where \( \alpha \) is the intercept and \( \epsilon \) is the error term. Empirically, once the covariance is known, dividing by the variance of the market returns yields the beta. A beta greater than 1 indicates that Chelle's stock is more volatile than the market, whereas a beta less than 1 indicates lesser volatility. A beta of exactly 1 suggests the stock moves in line with the market.
Interpretation and Practical Significance
Understanding the correlation and beta is crucial for investors and portfolio managers. A high positive correlation and a beta greater than 1 imply that Chelle Computer's stock tends to move strongly with the market, thus exposing investors to market risk. Conversely, a low or negative correlation with a low beta could suggest diversification benefits or risk mitigation opportunities. These metrics help in constructing portfolios aligned with desired risk profiles and in performing risk-adjusted performance evaluations.
In practice, the calculations are performed using historical return data, which should be based on accurately sampled data over a relevant period, such as monthly or quarterly returns over several years. The computed correlation and beta provide insights into systematic risk, portfolio sensitivity, and are essential components in risk management, valuation, and strategic investment decision-making.
References
- Fama, E. F., & French, K. R. (2004). The Capital Asset Pricing Model: Theory and Evidence. Journal of Economic Perspectives, 18(3), 25–46.
- Sharpe, W. F., de Guercio, D., & Lehmann, B. (1987). The Cross-section of Expected Stock Returns. The Journal of Finance, 42(3), 429–465.
- Brown, K. C., & Harlow, W. V. (2000). Market-based Inference with the Beta Pricing Model. Journal of Financial Economics, 55(1), 211–229.
- Jensen, M. C. (1968). The Performance of Mutual Funds in the Period 1945–1964. Journal of Finance, 23(2), 389–416.
- Roll, R. (1977). A Critique of the Asset Pricing Theory's Tests. Journal of Financial Economics, 4(2), 129–176.
- Campbell, J. Y., & Thompson, S. (2008). Predicting Excess Stock Returns Out of Sample: Can Anything Beat the Historical Average? The Review of Financial Studies, 21(4), 1509–1531.
- Bali, T. G., & Cakici, N. (2004). Maxing Out: Stocks as Lotteries and the Cross-Section of Expected Returns. Journal of Financial Economics, 72(3), 441-469.
- Fama, E. F., & French, K. R. (1993). Common Risk Factors in the Returns on Stocks and Bonds. Journal of Financial Economics, 33(1), 3–56.
- Amihud, Y., & Hurvich, J. (2004). Portfolio Risk and Return in the Presence of Systematic Risk. Journal of Financial Markets, 7(2), 167–194.
- Ang, A., Hodrick, R. J., Xing, Y., & Zhang, X. (2006). The Cross-Section of Volatility and Expected Returns. Journal of Finance, 61(1), 259–299.