medium · 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, since exponential decay places little weight on the oldest returns, discarding the largest historical loss observations there.
- Age-weighting leaves the VaR estimate completely unchanged, since reweighting observations cannot alter which return occupies the 5th-percentile slot.
- Age-weighting raises the estimated VaR only when the chosen decay factor happens to exceed the RiskMetrics standard value of lambda equal to 0.94.
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