New answers tagged returns
You would calculate return for each single position and for each segment of time. Following that you would geometrically link all these separate returns.
You need to model the underlyings, price the derivatives, and then measure risk.
It doesn't make sense to use the (co)variance(s) of asset values; if you did, by cutting an investment's share of the allocation by half, you would also cut its variance by a factor of 4. In a meaningful portfolio design, the volatility (variance) of an asset, by itself, is the same no matter how much or how little of your portfolio you put in it. Why ...
Each of these can be used, but each has serious drawbacks. No. 1 is inaccurate unless you use $N>>10$ years of data. But decades of data may not be available or may no longer be relevant to today's economy. No. 2 is good except that the CAPM has been rejected by empirical tests. More advanced models from Asset Pricing Theory may be helpful (FF3, FF5, ...
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