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Investment weights illustrate how each investment contributes to the overall portfolio value. They represent the proportion of the total investment that each individual component makes up. By understanding these weights, we can better grasp the impact an investment has on the overall portfolio.
To calculate investment weights, follow these simple steps:

• Determine the dollar value of each investment.
• Add all the investment values to find the total portfolio value.
• Divide each individual investment's value by the total portfolio value.

In our example, the total portfolio is valued at \( \\( 75,000 \). The investment of \( \\) 35,000 \) makes up approximately \( 0.467 \) or \( 46.7\% \) of the portfolio. Meanwhile, the investment of \( \$ 40,000 \) constitutes \( 0.533 \) or \( 53.3\% \). These weights affect how much each stock's risk (or beta) contributes to the portfolio beta.

Portfolio risk refers to the overall risk that a portfolio of investments carries in relation to the broader market. By looking at a portfolio's beta, we can understand how volatile the portfolio is likely to be compared to the overall market.
A key component of portfolio risk evaluation is how investments within a portfolio interact with each other and with the market. This interaction is captured by the beta coefficient. A portfolio with a beta greater than 1 is more volatile than the market, while a beta less than 1 indicates less volatility.
In the given exercise, combining both stocks gives a weighted beta that represents the entire portfolio's exposure to market risk. Calculating portfolio beta helps investors decide whether their investment strategy aligns with their risk tolerance and investment goals.

The beta coefficient is a measure of an investment's sensitivity to market movements. It quantifies how much an investment's return is expected to change in response to a change in the overall market return.
Here's a brief guide to understanding beta:

• A beta of 1 indicates that the investment's price is expected to move with the market.
• A beta greater than 1 suggests higher volatility than the market.
• A beta less than 1 implies less volatility compared to the market.

In our example, one stock has a beta of 0.8, which means it's expected to be less volatile than the market. The other stock has a beta of 1.4, indicating it should be more volatile. The portfolio's overall beta is calculated as a weighted average of these individual betas, indicating the portfolio's sensitivity compared to the overall market.

Weighted average is a mathematical technique that takes into account the relative importance of each component. It's commonly used when some elements of a set contribute more than others.
To calculate a weighted average:

• Multiply each component by its corresponding weight.
• Add these results together.
• The sum is your weighted average.

In finance, it's used to determine values like the portfolio beta. By applying weights to each stock's beta, we calculate how each stock affects the overall beta. This gives us a more accurate picture of the portfolio's risk relative to market fluctuations. In the exercise, after determining weights, they were used to scale each beta before summing them, resulting in a portfolio beta of approximately 1.12. This weighted approach ensures that larger investments influence the beta more.