Financial Risk Manager Part 1
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An investor is analyzing the data of two assets X and Y for a period of 7 years. He applied all three statistical models to measure the correlation coefficient. The results were as follows:
- Pearson correlation coefficient = -0.8501
- Spearman correlation coefficient = -0.9
- Kendall's τ = -0.4
He again analyzed the same data but changed two values of asset X without affecting its ranking. What would be the impact of this change on the results?
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A
The Spearman results would change but the results of Pearson and Kendall approaches would remain unchanged.
B
The Pearson and the Kendall results would change but the Spearman results would remain unchanged.
C
The Kendall results would change but the results of the Spearman and Pearson approaches would remain unchanged.
D
The Pearson results would change but the results of the Spearman and the Kendall approaches would remain unchanged.
Explanation:
Explanation
Understanding the Correlation Measures
Pearson Correlation Coefficient:
- Measures linear correlation between two variables
- Assumes normal distribution of data
- Sensitive to exact values in the dataset
- Calculated using the actual data values
Spearman Correlation Coefficient:
- Rank-based correlation measure
- Measures monotonic relationship (whether variables move in the same direction)
- Not sensitive to exact values - only depends on the ranking order
- Calculated using the ranks of data points
Kendall's Tau (τ):
- Rank-based correlation measure
- Measures ordinal association between variables
- Not sensitive to exact values - only depends on concordant/discordant pairs
- Based on the relative ordering of data points
Impact of Changing Values Without Affecting Ranking
When the investor changes two values of asset X without affecting its ranking:
-
Pearson correlation WILL change - Since Pearson uses actual data values, any change in the values (even if ranking remains the same) will affect the linear correlation calculation.
-
Spearman correlation WILL NOT change - Spearman only cares about the relative ranking order. Since the ranking remains unchanged, the Spearman correlation remains the same.
-
Kendall's tau WILL NOT change - Kendall's tau is also rank-based and depends on concordant/discordant pairs. Since the relative ordering remains the same, Kendall's tau remains unchanged.
Why Other Options Are Incorrect
- Option A: Incorrect because Spearman results would NOT change
- Option B: Incorrect because Kendall results would NOT change
- Option C: Incorrect because Kendall results would NOT change
Key Takeaway
Rank-based correlation measures (Spearman and Kendall) are robust to changes in data values as long as the relative ranking order remains unchanged, while Pearson correlation is sensitive to any changes in the actual data values.
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