Financial Risk Manager Part 1
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An analyst runs a simulation to estimate the future value of an investment of $10,000 today over a 40-year period. He uses random monthly returns that are normally distributed. How does the analyst’s situation create a discretization error bias?
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NNikitesh
A
By using normally distributed returns
B
By using a simulation period that’s too long (40 years)
C
By assuming that returns are random
D
By assuming that returns are generated on a monthly basis instead of a continuous basis
Explanation:
Explanation
Discretization error bias occurs when a continuous process is approximated using discrete intervals. In this scenario:
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Continuous vs. Discrete Returns: In reality, asset returns are generated continuously over time, but the analyst is modeling them using discrete monthly intervals.
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Monthly Basis Assumption: By assuming returns are generated on a monthly basis rather than continuously, the analyst introduces discretization bias. This means the simulation only captures price changes at monthly intervals, missing the continuous evolution of returns that would occur in reality.
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Why Other Options Are Incorrect:
- Option A: Using normally distributed returns relates to distributional assumptions, not discretization bias.
- Option B: The length of the simulation period (40 years) doesn't create discretization bias; it's the frequency of measurement that matters.
- Option C: Assuming returns are random is a different modeling assumption unrelated to discretization.
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Impact of Discretization Bias: When returns are modeled discretely (e.g., monthly), the simulation may underestimate or overestimate certain properties like volatility, path dependency, or extreme events that could occur between the discrete measurement points.
Key Insight: Discretization bias is specifically about the frequency of measurement or modeling intervals, not about distributional assumptions or randomness.
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