You Have Decided To Invest In An Equally Weighted Portfolio

You Have Decided To Invest In An Equally Weighted Portfolio Consisting

You have decided to invest in an equally weighted portfolio consisting of American Express, Proctor & Gamble, Home Depot, and Ford and need to find the beta of your portfolio. Go to finance.yahoo.com, find the ticker symbol of each company and thereby find the beta of each company. Please illustrate how you calculate the beta of the entire portfolio. Without adding new assets, how would you adjust the portfolio to make it more aggressive? Less aggressive?

Paper For Above instruction

Calculating Portfolio Beta and Adjusting Investment Strategies

Investing in a diversified portfolio often involves understanding how individual assets contribute to the overall risk. The beta coefficient is a key measure in finance used to gauge the sensitivity of an asset or a portfolio to market movements. This paper discusses the process of calculating the beta for an equally weighted portfolio consisting of American Express (AXP), Procter & Gamble (PG), Home Depot (HD), and Ford Motor Company (F), utilizing data retrieved from Yahoo Finance. Additionally, it explores how to adjust the portfolio to make it more aggressive or less aggressive without adding new assets.

Tracking Down the Betas of Individual Assets

The initial step involves identifying the ticker symbols of each of the selected companies, which can be easily retrieved from Yahoo Finance. The ticker symbols are AXP for American Express, PG for Procter & Gamble, HD for Home Depot, and F for Ford Motor Company. Once these symbols are confirmed, Yahoo Finance provides a comprehensive overview of each company's stock, including its beta. Typically, the beta value is located in the key statistics section or the overview tab of each stock's profile, reflecting the stock’s relative volatility compared to the broader market. According to Yahoo Finance, the beta values for these stocks are as follows (as of a recent date):

- American Express (AXP): 1.10

- Procter & Gamble (PG): 0.45

- Home Depot (HD): 1.15

- Ford Motor Company (F): 1.25

These beta values indicate that Ford and Home Depot are slightly more volatile than the market, whereas Procter & Gamble tends to be less volatile.

Calculating the Portfolio Beta

Since the portfolio is equally weighted, each asset contributes equally to the overall beta, which simplifies the calculation. The formula for the portfolio beta (\( \beta_P \)) is:

\[

\beta_P = \sum_{i=1}^n w_i \times \beta_i

\]

where \( w_i \) is the weight of asset i in the portfolio, and \( \beta_i \) is the beta of asset i. For an equally weighted portfolio of four assets:

\[

w_i = \frac{1}{4} = 0.25

\]

Thus, the portfolio beta is:

\[

\beta_P = 0.25 \times (1.10 + 0.45 + 1.15 + 1.25) = 0.25 \times 4.95 = 1.2375

\]

This indicates that the portfolio's overall volatility is approximately 1.24 times the market's volatility.

Implications of the Portfolio Beta

A beta greater than 1 suggests that the portfolio is more volatile than the market, making it somewhat aggressive. Investors seeking higher growth might favor such a portfolio, accepting increased risk for potential higher returns. Conversely, lower beta values indicate less volatility, appealing to more conservative investors.

Adjusting Portfolio Aggressiveness Without Adding Assets

To modify the portfolio’s risk profile without introducing new securities, investors can adjust the weights of existing assets:

- To create a more aggressive portfolio, increase the weights of the high-beta stocks (Ford and Home Depot) while reducing the weights of the low-beta stock (Procter & Gamble). For example, allocating 40% to Ford, 30% to Home Depot, 15% to American Express, and 15% to Procter & Gamble would raise the overall beta.

- To make the portfolio less aggressive, do the opposite—reduce the weights of high-beta stocks and increase the weight of low-beta stocks. Assigning 20% to Ford, 20% to Home Depot, 30% to American Express, and 30% to Procter & Gamble could decrease the overall volatility.

Calculating the new beta in each scenario involves multiplying each asset's beta by its new weight and summing these products. This approach allows precise control over the portfolio's risk-return profile according to investor preferences.

Conclusion

The process of determining a portfolio's beta involves identifying individual asset betas and applying a weighted sum based on asset allocation. The equal weighting method provides simplicity, but adjusting asset weights enables investors to tailor the portfolio's risk profile efficiently. By increasing the share of more volatile stocks, the portfolio becomes more aggressive, whereas emphasizing safer, less volatile assets renders it less aggressive. This strategic adjustment allows investors to personalize their investment risk in accordance with their financial goals and risk tolerance, all without acquiring new assets.

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5. Yahoo Finance. (2024). Stock profile for Procter & Gamble. Retrieved from https://finance.yahoo.com/quote/PG
6. Yahoo Finance. (2024). Stock profile for Home Depot. Retrieved from https://finance.yahoo.com/quote/HD
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