Financial Risk Manager Part 1

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:

1. 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.

2. Spearman correlation WILL NOT change - Spearman only cares about the relative ranking order. Since the ranking remains unchanged, the Spearman correlation remains the same.

3. 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.