Optimal Portfolio Allocation to Minimize Volatility with Independent Assets
By
ibobev
Toasted to a respectable shade. No regrets, no crumbs left.
Summary
This article presents a mathematical optimization problem about portfolio allocation to minimize volatility. It discusses how to allocate $100 between two independent assets with different volatility levels, explaining that putting all money in the less volatile asset is not optimal, nor is putting all in the more volatile one. The article formalizes the problem using random variables X and Y with finite variance, and promises to derive the optimal allocation formula and generalize it to multiple assets. The core concept is finding the weighting that minimizes portfolio variance when combining independent assets with different risk profiles.
Key quotes
· 5 pulledSuppose you have $100 to invest in two independent assets, A and B, and you want to minimize volatility.
Putting all your money on A would be the worst thing to do, but putting all your money on B would not be the best thing to do.
The optimal allocation would be some mix of A and B, with more (but not all) going to B.
We will formalize this problem and determine the optimal allocation, then generalize the problem to more assets.
Let X and Y be two independent random variables with finite variance and assume at least one of X and Y is no
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