Explanation

D is correct. The EWMA (Exponentially Weighted Moving Average) formula is:

$$\sigma_n^2 = (1 - \lambda) r_{n-1}^2 + \lambda \sigma_{n-1}^2$$

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 because it is already reflected in the previously calculated variance rate estimate
• The term $\sigma_{n-1}^2$ in the formula contains information on all past returns through the recursive nature of the calculation

Why other options are incorrect:

• A: Incorrect - Daily returns prior to the most recent day DO influence the current variance rate estimate through the recursive nature of the EWMA formula
• B: Incorrect - While λ (lambda) is the smoothing parameter that determines the decay rate, it doesn't directly reflect past returns; past returns are captured through the previous variance estimate
• C: Incorrect - The most recent day's squared return only captures information about that specific day, not about prior days' returns

The key insight is that EWMA uses an exponentially decaying weighting scheme where older observations have progressively smaller weights, and this information is efficiently captured through the recursive updating of the variance estimate.