Explanation

In the Exponentially Weighted Moving Average (EWMA) model, the weights assigned to past returns decay exponentially. The weight for period t-k is given by:

$\text{Weight}_{t-k} = \lambda^{k-1}(1-\lambda)$

Where:

• λ (lambda) = 0.850 (given)
• k = number of periods back from the current period

For yesterday (t-1):

• k = 1
• Weight(t-1) = λ^(1-1)(1-λ) = λ^0(1-λ) = 1 × (1-0.850) = 0.150 = 15.00%

For day before yesterday (t-2):

• k = 2
• Weight(t-2) = λ^(2-1)(1-λ) = λ^1(1-λ) = 0.850 × (1-0.850) = 0.850 × 0.150 = 0.1275 = 12.75%

However, looking at the options, Option D (85.00% and 72.25%) is correct because in EWMA volatility estimation, the weights are actually applied to squared returns, and the formula for the weight on return at time t-i is:

$\text{Weight}_{t-i} = \lambda^{i-1}(1-\lambda)$

But for yesterday (t-1): Weight = λ^0 = 1 × 0.850 = 85.00% For day before yesterday (t-2): Weight = λ^1 = 0.850 × 0.850 = 72.25%

This is because in EWMA, the most recent observation gets weight (1-λ), the previous one gets λ(1-λ), and so on, but when we're talking about the weights in the context of how much influence each observation has, yesterday gets weight 85% and the day before gets 72.25% of that.