I have 1000 scenarios (time series) of length 15 years x 12 months = 180 months for one asset's return. The model that underlies the scenarios is unknown.

I want to say something about the projected/expected annualised volatility (for short: annualized volatility*) of the asset's return. However, I see quite a few options:

  1. the average of 1000 standard deviations of 180 returns, multiplied by sqrt(12)

  2. the square root of the average of 1000 variances of 180 returns, multiplied by sqrt(12)

  3. the standard deviation of 180,000 returns, multiplied by sqrt(12)

  4. the standard deviation of 1000 cumulative returns, divided by sqrt(15)

  5. ?

Is there one generally accepted method?

*See, for example: https://am.jpmorgan.com/nl/en/asset-management/institutional/insights/portfolio-insights/ltcma/interactive-assumptions-matrices/


One extreme case to consider. Suppose in 500 scenarios all 180 monthly returns are +1% and in 500 scenarios all 180 monthly returns are -1%.

Another extreme case. Suppose all even-month returns are +1% and all odd-month returns are -1%.



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