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I have calculated exponentially weighted variances (and covariance) for a future and the underlying index.
Now that I have exponentially weighted variances for my 2 assets using a lookback period of 1 year, and knowing that the portfolio of 2 assets volatility depends on the correlation between these 2 assets, do I need to use the simple correlation (simple returns with no decay) or do I need to use the correlation between the new exponentially weighted variances?
From a theoretical point of view, you are supposed to use the correlation calculated under the same measure (i.e. multiplying daily excess returns and weighting that product by your weights).
In practice, I have seen both approaches: Weighted correlations and weighted variances, i.e. a weighted covariance matrix, and a mixture: unweighted correlations with weighted variances. Again, the first approach is theoretically sound and should be preferred.
