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Answer: A variance estimated from the EWMA model is a weighted average of the prior day's estimated variance and the prior day's squared return.
The correct answer is D. The EWMA (Exponentially Weighted Moving Average) estimate of variance is a weighted average of the variance rate estimated for the prior day and the prior day's observed squared return. This method gives more weight to recent observations, which makes it particularly useful for capturing the changing nature of financial market volatility. Option A is incorrect because the EWMA model is not a special case of the GARCH (1,1) model with the long-run volatility set to zero. Instead, the EWMA model is a simplified version of GARCH where the long-term variance is assumed to be zero, and the sum of the weights of the other parameters equals 1. Option B is incorrect because the GARCH (1,1) model does not only consider the prior day's estimated variance and squared return but also includes a weight assigned to the long-run average variance rate. Option C is incorrect because the comparison of weights assigned to the prior day's estimated variance between the GARCH (1,1) and EWMA models can only be made under specific parameter configurations, and it is not universally true that GARCH (1,1) assigns a higher weight than EWMA.
Author: LeetQuiz Editorial Team
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A junior risk analyst is in the process of evaluating the variability of a particular market factor. The analyst is considering whether to apply the Exponentially Weighted Moving Average (EWMA) model or the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model, specifically the GARCH (1,1) variant. Which of the following statements is correct?
A
The EWMA model is a special case of the GARCH (1,1) model with the additional assumption that the long-run volatility is zero.
B
A variance estimated from the GARCH (1,1) model is a weighted average of the prior day's estimated variance and the prior day's squared return.
C
The GARCH (1,1) model assigns a higher weight to the prior day's estimated variance than the EWMA model.
D
A variance estimated from the EWMA model is a weighted average of the prior day's estimated variance and the prior day's squared return.
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