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Answer: Daily returns prior to the most recent day are reflected in the EWMA calculation by the previous variance rate estimate.
D is correct. The EWMA formula is: \( \lambda = (1 - \alpha) \lambda_{t-1} + \alpha r_{t-1}^2 \). Under the EWMA approach, when a new return is observed, the variance rate estimate is updated using this return. When the next new return is observed, the previously observed return is not needed, as it is reflected in the previously calculated variance rate estimate. In this way, the term \( \lambda_{t-1} \) in the formula contains information on all past returns. A, B, and C are incorrect, as per the above explanation.
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A junior market risk analyst is studying the Exponentially Weighted Moving Average (EWMA) method for estimating volatility. This method is known for applying different weights to past returns, with more recent returns receiving higher weights, making them more influential on the volatility estimate. The analyst observes that the squared return of the most recent day plays a crucial role in updating the EWMA calculation. Which of the following statements correctly describes an aspect of this method?
A
Daily returns prior to the most recent day have no influence on the current variance rate estimate in the EWMA calculation.
B
Daily returns prior to the most recent day are reflected in the EWMA calculation by the smoothing parameter (^).
C
Daily returns prior to the most recent day are reflected in the EWMA calculation by the most recent day's squared return.
D
Daily returns prior to the most recent day are reflected in the EWMA calculation by the previous variance rate estimate.
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