Financial Risk Manager Part 1
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A financial analyst at a technology company is evaluating the risk profile of a new investment product using historical data. The analyst is considering applying a resampling technique to estimate the distribution of potential returns. The analyst debates whether to use Monte Carlo simulation or bootstrapping for the analysis. Which of the following statements about bootstrapping is correct?
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TTanishq
A
Bootstrapping requires that the data be independent and identically distributed (i.i.d.).
B
In bootstrapping, data must be resampled without replacement to preserve statistical integrity.
C
Bootstrapping can only be applied to data that is normally distributed.
D
Bootstrapping involves resampling with replacement from the original dataset.
Explanation:
Explanation
Bootstrapping is a statistical technique that involves repeatedly resampling with replacement from an original dataset to estimate the distribution of a statistic. This method allows analysts to assess the variability of a statistic without making strict assumptions about the underlying data distribution.
Why Option D is Correct:
- Bootstrapping specifically involves resampling with replacement from the original dataset
- Each bootstrap sample can be the same size as the original dataset
- Each observation in the original dataset has the same probability of appearing in each bootstrap sample
- This process helps create a sampling distribution of the statistic for estimating measures like confidence intervals
Why Other Options are Incorrect:
Option A is incorrect: While having i.i.d. data is ideal for many statistical methods, bootstrapping can be applied even when data does not strictly meet these criteria. However, caution is needed when applying bootstrapping to dependent data.
Option B is incorrect: Bootstrapping specifically involves resampling with replacement. Resampling without replacement would be a different type of resampling method, not bootstrapping.
Option C is incorrect: One of the main advantages of bootstrapping is that it does not assume any specific distribution of the data, including normal distribution. It can be applied to data with any distribution, making it a flexible tool in statistical analysis.
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