Financial Risk Manager Part 1
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The application of statistical correlation models to access financial correlation is limited because of the following reasons:
I. The Spearman and the Kendall models work best with cardinal observations and consider the extreme value of outliers.
II. Both the Spearman and the Kendall approaches take the order of the elements into consideration while ignoring numerical values.
III. The Kendall τ works best with only a few concordant and discordant pairs.
IV. Among all models, the Pearson approach is the best statistical model and is widely used because it measures nonlinear relationships and financial variables are mostly nonlinear.
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NNikitesh
A
I and IV
B
III and IV
C
II and III
D
II, III and I
Explanation:
Correct Answer: C (II and III)
Explanation:
Statement I is incorrect: The Spearman and Kendall models are actually ordinal correlation measures, not cardinal. They work with ranks rather than actual numerical values, which makes them less sensitive to outliers, not more sensitive. Cardinal observations refer to actual numerical values with meaningful intervals.
Statement II is correct: Both Spearman's rank correlation and Kendall's tau are ordinal correlation measures. They consider the order/rank of observations while ignoring the actual numerical values. This is a limitation when applying them to financial data where the actual magnitude of values matters.
Statement III is correct: Kendall's tau works by comparing pairs of observations. When there are many tied pairs (neither concordant nor discordant), these pairs are omitted from the calculation. Working with only a few concordant and discordant pairs can distort the Kendall tau coefficient, making it less reliable.
Statement IV is incorrect: The Pearson correlation coefficient measures linear relationships, not nonlinear relationships. Financial variables often exhibit nonlinear relationships, which is why Pearson correlation may not be the best model for financial applications. Additionally, Pearson correlation is sensitive to outliers.
Why this matters for financial risk management:
- Financial data often contains outliers and exhibits nonlinear relationships
- Ordinal correlations (Spearman, Kendall) ignore the magnitude of price movements, which is crucial in finance
- The limitations of these statistical correlation models highlight the need for more sophisticated approaches like copulas or tail dependence measures in financial risk modeling
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