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Apologies in advance if this question has been asked already.

I am estimating basis risk for different term points in the curve. Imagine i have three time series (1-month, 3-month, 1-year). I believe they are NOT independent of each other. I have estimated the absolute daily change for each one of them (% change didn't work as some time series switch from negative to positive, or the other way around). I could generate a variance/covariance matrix of the absolute daily change in these three time series, and calculate some sort of a 'portfolio' standard deviation (assuming equal weights). This standard deviation would be in basis points, as mentioned above. For instance, 2 bps. I could also generate some sort of an expected value (average) for this portfolio, for instance 10 bps.

The question that I have is: how do I interpret the standard deviation in the context of each separate time series? If i want to estimate tail risk for this portfolio, is it accurate to (assuming normal distribution), to just estimate 2 standard deviations from the mean and analyze the tail risk from that data point? What would 4 basis points mean for each time series, i.e., how do I transform this portfolio tail risk to each time series, given that it is not proportional (%) change, but rather absolute change?

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If $v$ is a vector of DV01 ezposures versus your various risk factors/buckets and $\Sigma$ is your covariance matrix tegen portfolio (delta-normal) Var is given by $$\alpha \sqrt{v^T \Sigma v }$$ where $\alpha$ is some point from the inverse cumulative normal.this gives you risk in cash (money) terms rather than % losses.

There are other ways to measure tail risks of course, both in metrics and methodology, but this looks like what you're after

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