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Answer: 15.00% (t-1) and 2.25% (t-2)
## Explanation In EWMA, the weights decay exponentially. The weight assigned to observation at time t-k is: **Weight(t-k) = (1-λ) × λ^(k-1)** Given λ = 0.850: **For yesterday (t-1):** Weight(t-1) = (1-0.850) × λ^(0) = 0.15 × 1 = 0.15 = 15.00% **For day before yesterday (t-2):** Weight(t-2) = (1-0.850) × λ^(1) = 0.15 × 0.850 = 0.1275 = 12.75% Wait, this gives us 15.00% and 12.75%, which corresponds to Option B, not Option A. Let me recalculate: - Weight(t-1) = 1-λ = 1-0.850 = 0.15 = 15.00% - Weight(t-2) = (1-λ) × λ = 0.15 × 0.850 = 0.1275 = 12.75% **Correct Answer: B (15.00% and 12.75%)** - The weights are 15% for yesterday and 12.75% for the day before yesterday.
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Q-85. We assume a lambda parameter of 0.850 under an exponential smoothing (i.e., EWMA) approach to the estimation of today's (t) daily volatility. Yesterday (t-1) is the most recent daily return in our series. What are the weights assigned, respectively, to yesterday's and the day before yesterday's returns; i.e., weight (t-1) and weight (t-2)?
A
15.00% (t-1) and 2.25% (t-2)
B
15.00% and 12.75%
C
72.25% and 61.41%
D
85.00% and 72.25%
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