medium · FRM Part 1 Quantitative Analysis
An analyst is comparing the 'information ratio' of two active managers using a bootstrap to determine if the difference is significant. Manager A has a higher ratio, but Manager B has a much longer track record.
What will the bootstrap standard errors likely reflect?
- The bootstrap standard error will be biased for Manager B, since a longer track record always contains more undetected market 'regime shifts'.
- Manager A will show a smaller standard error because a higher measured 'active return' itself reduces the underlying noise in that manager's tracking error.
- The standard errors will end up exactly equal, since both managers are being evaluated using performance data drawn from the very same overlapping market cycle.
- Manager B will likely have a smaller bootstrap standard error because their estimate is based on a larger sample size, which increases the precision.
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