Math Problem Statement

If a stock's beta is 0.8 during a period when the market portfolio was down by 10%, then, a priori, we could expect this individual stock to:

Question 8 options:

a)

gain, but less than 10%

b)

lose, but less than 10%

c)

lose more than 10%

d)

gain more than 10%

Solution

The beta of a stock measures its sensitivity to market movements. A beta of 1 indicates that the stock tends to move in sync with the market. A beta below 1, such as 0.8, suggests that the stock is less volatile than the market. Here’s the expected behavior in this case:

Since the stock's beta is 0.8, and the market portfolio has dropped by 10%, we can calculate the expected percentage change in the stock's value as follows:

Expected change in stock=β×Market change=0.8×(10%)=8%\text{Expected change in stock} = \beta \times \text{Market change} = 0.8 \times (-10\%) = -8\%

This indicates that the stock would be expected to lose 8%, which is less than the market's 10% drop.

Correct Answer:

b) lose, but less than 10%

Would you like further details or have any questions?


Here are some related questions to deepen understanding:

  1. How would the expected return change if the beta were 1.2 instead of 0.8?
  2. What does a beta of 0 signify for a stock's behavior relative to the market?
  3. How would the answer change if the market increased by 10% instead of decreasing?
  4. What is the significance of beta values greater than 1 in terms of risk?
  5. How does beta impact a portfolio’s diversification strategy?

Tip: Beta values close to 1 indicate that a stock moves closely with the market, while values far from 1 suggest higher or lower volatility relative to the market.

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Math Problem Analysis

Mathematical Concepts

Financial Mathematics
Stock Beta
Market Sensitivity Analysis

Formulas

Expected change in stock = beta × Market change

Theorems

Beta coefficient interpretation in financial markets

Suitable Grade Level

Undergraduate Finance / Economics