To solve these calculations, let’s understand the method for calculating the expected increase and expected decrease in a firm’s stock price based on its beta coefficient.

Formula

The expected change in value of a firm’s shares due to a change in the market portfolio is calculated as: $\text{Expected Change} = \text{Beta} \times \text{Market Change}$ In this case:

• If the market increases by 10%, we multiply each company’s beta by $+10\%$.
• If the market decreases by 10%, we multiply each company’s beta by $-10\%$.

Part 1: Expected Decrease in Stock Value with a 10% Market Drop

Let’s calculate the expected decrease for each company if the market drops by 10%.

1. Apple Inc. (Beta = 1.09): $\text{Expected Decrease} = 1.09 \times (-10\%) = -10.90\%$

2. Dell Technologies (Beta = 1.16): $\text{Expected Decrease} = 1.16 \times (-10\%) = -11.60\%$

3. Microsoft (Beta = 1.02): $\text{Expected Decrease} = 1.02 \times (-10\%) = -10.20\%$

4. American Electric Power Co. (Beta = 0.49): $\text{Expected Decrease} = 0.49 \times (-10\%) = -4.90\%$

5. Duke Energy Corp. (Beta = 0.88): $\text{Expected Decrease} = 0.88 \times (-10\%) = -8.80\%$

6. Centerpoint Energy (Beta = 1.34): $\text{Expected Decrease} = 1.34 \times (-10\%) = -13.40\%$

Summary Table

Here’s a table of the expected decrease in share value:

Part 2: Analyzing Volatility

The beta coefficient is a measure of volatility. Stocks with a higher beta are generally more volatile relative to the market.

In this case, Centerpoint Energy (Beta = 1.34) is the most volatile, while American Electric Power Co. (Beta = 0.49) is the least volatile among these firms.

Questions and Next Steps

1. Would you like to see how the increase values relate to different investment risk strategies?
2. Do you need an explanation on the concept of beta in more detail?
3. Would you like a further breakdown of each industry and why certain sectors tend to have higher or lower beta values?
4. Do you want to see calculations for other hypothetical market changes (e.g., a 5% increase)?
5. Should we explore other factors besides beta that could influence stock volatility?

Tip

Stocks with a beta higher than 1.0 tend to have more pronounced price changes relative to the market, while those below 1.0 tend to be less responsive.