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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?

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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.

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  • $\begingroup$ How do you overcome the issue of historical data? RiskMetrics uses a 1 year lookback period so I first need 1 year to calculate the first asset variances. Then I need another year to calculate the weighted variance (another 262 array with t = 1 to 262). Then only I can can calculate correlations on these weighted variances and I need another year. Is this how this works? I am a bit confused. $\endgroup$ – tweedi Mar 31 at 17:13
  • $\begingroup$ You have to base all estimates (variances and correlations) off the same time window. $\endgroup$ – Kermittfrog Mar 31 at 20:31
  • $\begingroup$ Thanks, I managed to re-calculate everything. I first needed one year (252d) of data to calculate the first exponentially weighted variances and covariances. For the rest of the time series I used the recursive formulas for the new exponentially weighted variance and covariance. All variances and covariances are indeed estimated based on the same time window. $\endgroup$ – tweedi Apr 2 at 14:28

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