hard · FRM Part 1 Valuation and Risk Models
An analyst estimates 1-day 95% VaR of a daily-return series two ways: (i) the basic historical-simulation order statistic and (ii) an age-weighted (BRW) historical simulation that assigns exponentially declining weights with decay λ=0.98 to older observations. Recent volatility has been markedly HIGHER than the full-sample average.
Holding the data set fixed, which statement best describes the expected effect of switching from (i) to (ii)?
- Age-weighting raises the estimated VaR because it places more weight on recent, higher-volatility returns, moving probability mass into the tail loss estimate.
- Age-weighting lowers the estimated VaR because exponential decay discards the most extreme historical losses, which are typically the oldest.
- Age-weighting leaves the VaR unchanged because reweighting observations does not alter which return sits at the 5th percentile.
- Age-weighting raises the estimated VaR only if the decay factor exceeds the RiskMetrics standard of λ=0.94.
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