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:
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:
- How would the expected return change if the beta were 1.2 instead of 0.8?
- What does a beta of 0 signify for a stock's behavior relative to the market?
- How would the answer change if the market increased by 10% instead of decreasing?
- What is the significance of beta values greater than 1 in terms of risk?
- 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
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