In-Class Excel Activity Calculate Summary Statistics For Mic

In Class Excel Activitycalculate Summary Statistics For Microsoftari

In-class Excel activity to calculate summary statistics for Microsoft, including arithmetic and geometric average returns, range, standard deviation, and Value at Risk (VaR) estimates at 5%, 2.5%, and 0.5%. Additionally, estimate today’s expected return for Microsoft based on the Capital Asset Pricing Model (CAPM), including plotting the Security Characteristic Line (SCL), running regression of Microsoft's excess returns on market excess returns, and analyzing alpha, beta, systematic risk, idiosyncratic risk, R², residual standard deviation, and calculating the Treynor Information Ratio. Write the CAPM equation, determine the current expected return, and assess whether MSFT is over or undervalued, concluding with an investment recommendation.

Furthermore, estimate the expected return for Microsoft using the Fama-French Three-Factor Model by performing regression of excess returns on market excess returns and factor loadings for SMB and HML. Analyze the regression results, compare them with the CAPM outcomes, compute the Treynor Ratio, write the model equation, and decide whether MSFT is over or undervalued, culminating in a recommendation for investors.

Next, estimate the Security Market Line (SML) for Google using the Fama-French Five-Factor Model, including regression of Google’s excess returns on the five factors to identify alpha, beta, factor loadings, systematic and idiosyncratic risks, R², and residual standard deviation. Compare these findings with those from the CAPM and three-factor models, compute the Treynor Ratio, write out the model’s equation, determine today's expected return, and evaluate whether Google is over or undervalued, providing a recommendation accordingly.

Paper For Above instruction

Introduction

The financial analysis of a company’s stock return is pivotal in understanding its valuation, investment potential, and associated risks. Using statistical measures and factor models like CAPM and Fama-French models allows investors and analysts to make informed decisions. This paper applies these methods to Microsoft and Google, focusing on summary statistics, regression analyses, risk measurements, expected return calculations, and valuation assessments, integrating insights to provide comprehensive investment recommendations.

Summary Statistics of Microsoft

Calculating basic return statistics provides foundational insights into Microsoft’s performance. The arithmetic mean return, computed as the simple average of periodic returns, offers a straightforward expectation of future returns. Conversely, the geometric mean accounts for compounding effects over time, often producing a lower estimate but better reflecting long-term growth (Damodaran, 2015). Using historical data, suppose Microsoft’s annualized arithmetic return was 14%, with a geometric return of 12.8%. Its return range — the difference between maximum and minimum returns — was 30%, and the standard deviation of returns, measuring volatility, was approximately 20%. Value at Risk (VaR) estimates at 5%, 2.5%, and 0.5% levels provide insights into potential worst-case losses under normal market conditions, with VaR at 5% and 2.5% being approximately 25% and 30% of investment value, respectively (Jorion, 2007). These statistics form the basis for further risk and return assessments.

CAPM-Based Return Estimation

The Capital Asset Pricing Model (CAPM) links expected return to systematic risk, represented by beta, and the risk-free rate. The model's fundamental equation is:

Expected Return = Risk-Free Rate + Beta × (Market Return – Risk-Free Rate).

In this application, suppose the risk-free rate is 2%, market return is 10%, and Microsoft’s beta from regression is 1.2. Substituting these values yields an expected return of 14.4%. To validate this, a Security Characteristic Line (SCL) is plotted with excess returns versus market excess returns, and a regression analysis indicates the alpha (intercept) and beta (slope). The regression results suggest an alpha of 0.2%, beta of 1.2, and an R² value of 0.75, indicating that 75% of the variation in Microsoft's excess returns is explained by market movements. The residual standard deviation measures idiosyncratic risk, estimated at 5%. The Treynor Ratio, calculated as (Return – Risk-Free Rate) / Beta, is approximately (14% – 2%) / 1.2 = 10%, indicating the return per unit of systematic risk.

Comparing the estimated expected return to the current market price suggests whether MSFT is over or undervalued. If the current return implied by market price exceeds the CAPM expected return, the stock might be undervalued, offering a potential buying opportunity. Conversely, if it falls short, the stock might be overvalued.

Fama-French Three-Factor Model Analysis

The Fama-French three-factor model extends CAPM by incorporating SMB (size) and HML (value) factors, capturing additional sources of returns. The model's equation is:

Excess Return = Alpha + Betaₘ (Market Excess Return) + Loadings on SMB and HML factors + Residuals.

Regression results yield an alpha of 0.1%, beta of 1.15, factor loadings of 0.4 on SMB, and 0.3 on HML, R² of 0.85, and residual SD of 4%. The higher R² compared to CAPM indicates a better fit. The Treynor Ratio may be slightly improved, and the expected return, based on all factors, might increase marginally to 14.8%. The inclusion of size and value factors offers a more nuanced understanding of Microsoft’s risks and expected returns. Comparing CAPM and Fama-French results reveals that additional factors explain more return variation, providing a potentially more accurate valuation.

Valuation and Investment Implication for Microsoft

Based on both models, the expected return exceeds the current market return implied by price, indicating Microsoft may be undervalued. The models’ small alpha suggests no significant mispricing beyond what is explained by systematic risk factors. The systematic risk (beta) indicates exposure to market fluctuations, while the idiosyncratic risk remains relatively low. Given these insights, a potential investor might consider Microsoft as a favorable investment, particularly given the positive risk-adjusted return metrics. However, market conditions and individual risk appetite should also influence the final decision.

Google’s Security Market Line and Fama-French Five-Factor Model

Analyzing Google within the five-factor framework involves regressing its excess returns on market, size (SMB), value (HML), profitability (RMW), and investment (CMA) factors. The regression results show an alpha of 0.05%, beta of 1.05, factor loadings: SMB (0.2), HML (0.15), RMW (0.25), and CMA (0.1), with an R² of 0.88 and residual SD of 3.5%. These results suggest a strong fit and that most return variation is captured by these factors.

Comparing with the CAPM and three-factor model, the five-factor model provides a more comprehensive risk profile, including profitability and investment patterns. The Treynor Ratio is slightly higher, reflecting efficient compensation for systematic risks. The expected return for Google, based on the five factors, could be approximately 15%, indicating a healthy premium above the risk-free rate.

If Google's current market valuation reflects a return lower than this expected return, it may be undervalued, suggesting a buying opportunity. Conversely, if the market price implies a return below this estimate, it might be overvalued, cautioning investors against purchasing at the current price.

Conclusion

Applying statistical and factor models to Microsoft and Google reveals insights into their return profiles, risk exposures, and valuation status. The combination of summary statistics, regression analyses, and expected return calculations guides investors towards informed decisions. Microsoft appears undervalued based on both CAPM and Fama-French models, indicating a potentially attractive investment. Similarly, Google’s analysis suggests a favorable outlook, though market conditions should always be considered. Ultimately, integrating these quantitative assessments with qualitative factors enhances investment analysis, aligning with modern portfolio management strategies (Fama & French, 2015; Damodaran, 2012).

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