Group Project Fin 320 Fall 2020 Part I Total Points 375 ✓ Solved

group Project Fin 320 Fall 2020 Part I Total Points 375 T

This project involves portfolio return/risk calculations using annual data for the S&P 500 Index and Gold over a 29-year period. It requires calculating expected returns, standard deviations, correlations, plotting security graphs, constructing efficient portfolios, identifying optimal and minimum variance portfolios, and analyzing effects of correlation changes on diversification. Additionally, for Part II, the project involves weekly return analyses of market and international ETFs, CAPM estimations, and risk decomposition. The task includes creating various plots, tables, and calculations supporting the assessment of investment opportunities and securities pricing according to CAPM and Market Model principles.

Paper For Above Instructions

Part I: Portfolio Return and Risk Analysis

The core of Part I involves constructing a comprehensive analysis of two risky securities—the S&P 500 Index and Gold—using historical data to estimate returns, risks, and their correlation. With these estimates, one can visualize the securities on an expected return versus standard deviation graph, draw capital allocation lines (CAL), construct portfolios with different weights, and identify optimal investment mixes.

First, the data collection involves obtaining annual historical values for the S&P 500 and Gold from the spreadsheet "GroupProject1Data.xls" covering from 1976 to 2003. Additionally, an estimate of the annual risk-free rate is required, which should be chosen based on recent U.S. Treasury rates corresponding to a one-year investment horizon, available from relevant financial sources with date and category noted.

Next, calculating annual returns involves deriving the percentage change in prices year-over-year for both securities across 28 years (1976-2003). From these returns, statistical measures such as the mean (average return), standard deviation (as a proxy for risk), and correlation between S&P 500 and Gold are computed, summarized in a table and attached as Exhibit 1.

Using expected return and risk estimates, the securities are plotted on an Expected Return – Standard Deviation graph. The risk-free asset is also plotted, and the Capital Allocation Line (CAL) is drawn for each security. These visualizations, enclosed as Exhibit 2, facilitate understanding of risk-return tradeoffs and portfolio choices.

Constructing risky portfolios involves calculating combined expected returns and risks with varying weights from 0% to 100% in 5% increments, resulting in 21 portfolios. These calculations are documented in an accompanying spreadsheet (Exhibit 3). The later step involves charting these portfolios, the risk-free asset, and identifying the minimum variance portfolio and the optimal risky portfolio on a graph (Exhibit 4). This helps in visualizing the efficient frontier and capital allocation strategies.

The analysis then proceeds to applying the optimal risky portfolio to achieve specific target returns between 2% and 10%. Calculations determine the portfolio weights in risky and risk-free assets and the resulting standard deviation, which are annotated on the graph. Further, a sensitivity analysis investigates future scenarios assuming different correlations (e.g., 0.30), recalculating the efficient frontier and optimal portfolios to observe how correlation impacts diversification benefits and risk reduction (Exhibits 5 and 6). These assessments highlight how correlation influences portfolio risk and diversification strategies.

Part II: Market and Capital Asset Pricing Model Analysis

Part II transitions to weekly return data on the S&P 500 and two international ETFs, aiming to estimate the CAPM parameters and decompose risks. Weekly prices are used to compute weekly returns, from which mean returns, standard deviations, and variances are calculated, summarized in a table and documented as Exhibit 1.

The analysis continues with plotting securities on the expected return versus standard deviation graph and constructing the Capital Market Line (CML) based on the weekly risk-free rate (1.5% annually divided by 52 weeks). This visual illustrates the position of the securities relative to the CML and tests their compliance with CAPM expectations.

Subsequently, the Market Model involves calculating excess returns (subtracting the weekly risk-free rate) and fitting regression trendlines for each security versus the market (S&P 500). From these regressions, alpha and beta estimates are obtained and recorded as shown in Exhibit 3. Beta indicates systematic risk, while alpha assesses abnormal performance.

Decomposition of total risk into market (systematic) and firm-specific (idiosyncratic) components involves calculating the market risk as beta squared times the variance of the market, and firm-specific risk as the residual component. These results enable comparisons of the risk profiles of the securities across different risk categories. The risk analysis supports insights into which securities are riskier overall versus in terms of systematic factors, and how diversification impacts those risks.

The Security Market Line (SML) is then constructed using the risk-free rate, beta estimates, and expected returns, with securities plotted accordingly. This determines whether securities are fairly valued under CAPM assumptions, guiding buy or sell recommendations for international ETFs if they lie above or below the SML. The graphs and calculations are documented as Exhibit 5.

Conclusion

This comprehensive project integrates statistical calculations, graphical visualizations, portfolio optimization techniques, and CAPM estimations to assess risk and return characteristics of various securities. It emphasizes the importance of diversification, correlation effects, and valuation models in making informed investment decisions.

References

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