Let's answer each part step by step.

a. Expected Change in Stock Values Based on Beta

The beta coefficient ($\beta$) of a stock measures its sensitivity to market movements. A beta of 1.00 implies that the stock moves in line with the S&P 500. A beta greater than 1 means the stock is more volatile than the market, while a beta less than 1 implies the stock is less volatile.

Given the S&P 500's expected change is 14.29%, we can calculate the expected change in each stock using the formula:

$\text{Expected Change in Stock} = \text{Beta} \times \text{Market Change}$

For each company:

1. Savoy Corp.: $0.94 \times 14.29\% = 13.4326\%$
2. Hokie Industries: $1.18 \times 14.29\% = 16.9022\%$
3. Alison Records: $1.89 \times 14.29\% = 27.0081\%$
4. Expo Enterprises: $0.39 \times 14.29\% = 5.5731\%$

So, the expected changes are:

• Savoy Corp.: 13.43%
• Hokie Industries: 16.90%
• Alison Records: 27.01%
• Expo Enterprises: 5.57%

b. Outperforming Stock in a Market Decline of 21.44%

In a market drop, stocks with lower beta values typically decline less than those with higher beta values. Therefore, the stock with the lowest beta should outperform others in a downturn.

The change in stock value for a market decline of 21.44% would be calculated similarly to part (a):

1. Savoy Corp.: $0.94 \times (-21.44\%) = -20.1536\%$
2. Hokie Industries: $1.18 \times (-21.44\%) = -25.2992\%$
3. Alison Records: $1.89 \times (-21.44\%) = -40.5216\%$
4. Expo Enterprises: $0.39 \times (-21.44\%) = -8.3616\%$

Expo Enterprises, with the lowest beta (0.39), would likely outperform the others in a market decline, as it would experience the smallest percentage drop (-8.36%).

Summary

• If the S&P 500 rises by 14.29%:

  • Savoy Corp.: +13.43%
  • Hokie Industries: +16.90%
  • Alison Records: +27.01%
  • Expo Enterprises: +5.57%

• If the S&P 500 drops by 21.44%, Expo Enterprises should outperform the others, as it would experience the smallest decline due to its lower beta.

Would you like more details on any part?

Here are 5 related questions to consider:

1. How does beta influence stock volatility relative to the market?
2. Why might a company have a beta higher or lower than 1?
3. What types of stocks or industries typically have low beta values?
4. How can investors use beta to manage portfolio risk?
5. What are the limitations of using beta as the sole measure of a stock's risk?

Tip: In a diversified portfolio, mixing high-beta and low-beta stocks can help balance potential returns and risks.