The Following Are The Historic Returns For The Chelle Comput

The Following Are The Historic Returns For The Chelle Computer Comp

The provided data entails the historic returns of Chelle Computer Company alongside a general market index across various years. Additionally, the assignment requires calculating key financial metrics such as the correlation coefficient between Chelle Computer and the market index, and the beta coefficient for Chelle Computer. Beyond this, the task involves evaluating two mutual funds using the Capital Asset Pricing Model (CAPM) to determine their expected returns, interpret their valuation status, and analyze the security market line under different market conditions. Lastly, performance assessment based on current market returns and stock returns is also part of the assignment.

Paper For Above instruction

Analyzing the historical returns of a company along with market data allows investors and analysts to estimate critical measures of risk and return, which are instrumental in making informed investment decisions. This paper presents a detailed analysis of the Chelle Computer Company’s historic returns, computes its statistical measures related to market risk, evaluates mutual funds through CAPM, and discusses implications regarding market valuation and performance.

Historical Returns and Their Significance

Historical returns provide a valuable window into the performance of a company's stock over time. For Chelle Computer, the data includes annual returns juxtaposed with a market index, facilitating calculations of covariance, correlation, and beta. These measures help quantify the systematic risk that the stock shares with the entire market. Systematic risk, or market risk, cannot be diversified away and is pertinent in understanding how the stock is likely to behave relative to market movements.

Calculating Correlation Coefficient

The correlation coefficient between Chelle Computer and the market index can be computed using the historical return data. The formula involves the covariance of the stock and index returns divided by the product of their standard deviations:

Correlation (r) = Covariance (C_xy) / (σ_x * σ_y)

By calculating the covariance of the respective return series and their standard deviations, the correlation coefficient can be determined. A coefficient close to 1 indicates a strong positive relationship, whereas a value near -1 indicates a strong negative relationship. The actual numerical calculation involves the sum of the products of deviations from the mean divided by n-1, as per standard statistical procedures.

Calculating Beta

Beta measures the sensitivity of the stock's returns relative to changes in the market index. It is computed as:

Beta = Covariance (C_xy) / Variance of the market (σ²_market)

A beta greater than 1 indicates that the stock tends to be more volatile than the market, while a beta less than 1 suggests lower volatility. The calculation again relies on covariance and variance derived from historical return data.

Expected Returns of Mutual Funds Using CAPM

The Capital Asset Pricing Model (CAPM) provides a framework to estimate the expected return of an asset based on its beta, the risk-free rate, and the expected market risk premium:

Expected Return = R_f + β *(E(R_m) - R_f)

Given a risk-free rate of 3.9% and market risk premium of 6.1%, the expected returns for Funds T and U can be calculated as follows:

• Fund T: 3.9% + 1.20 * 6.1% = 3.9% + 7.32% = 11.22%
• Fund U: 3.9% + 0.80 * 6.1% = 3.9% + 4.88% = 8.78%

Valuation Assessment of Funds T and U

By comparing these expected CAPM-based returns with the forecasted returns (9.0% for Fund T and 10.0% for Fund U), we observe that the actual forecasted returns for both funds exceed their CAPM estimates. This suggests that the funds may be undervalued because they are projected to yield higher returns than what their market risk justifies. Alternatively, if these forecasted returns are accurate and the CAPM estimates are correct, investors might perceive them as offering attractive prospects given their risk profiles.

Security Market Line (SML) Analysis

The security market line depicts the relationship between beta and expected returns in efficient markets. For the two different market conditions presented:

• Condition 1: R_f = 0.08; R_m (proxy) = 0.12
• Condition 2: R_f = 0.06; R_m (true) = 0.15

We can derive the SML equations for each:

For condition 1: Expected return = 0.08 + β*(0.12 - 0.08) = 0.08 + 0.04β

For condition 2: Expected return = 0.06 + β*(0.15 - 0.06) = 0.06 + 0.09β

Comparing these lines indicates how market conditions affect the risk-return trade-off, with the steeper slope under the second condition implying increased compensation per unit of beta.

Performance Evaluation Based on Current Market Returns

With the current market return of 12%, and the stock returns for Rader Tire at 11%, the analysis involves assessing whether the actual returns align with the expected returns based on beta. If a stock's actual return surpasses the CAPM predicted return given its beta, it suggests superior performance relative to its risk profile. Conversely, underperformance may indicate inefficiency or mispricing.

If Rader Tire's return is below the expected return based on its beta, it suggests underperformance. The market index's return at 12% aligns with the market risk, but the individual stock's return determines if it is outperforming or underperforming relative to its systematic risk exposure.

Conclusion

Overall, calculating the correlation coefficient and beta provides foundational insight into the systematic risk associated with Chelle Computer. The investment valuation analysis, aided by CAPM estimates, offers perspective on whether the funds are attractively priced. Analyzing market lines under various conditions reveals the influence of macroeconomic factors. Finally, performance evaluation against market returns informs ongoing investment strategies and risk management approaches. These measures collectively underpin informed decision-making in financial analysis and investment management.

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