If we put a % of our wealth into asset X, with systematic risk of x, and

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If we put a % of our wealth into asset X, with systematic risk of βx, and b% of our wealth into asset Y, with systematic risk of βy, then the beta of the resulting portfolio, βp, is simply the weighted average of the betas of individual securities: Prove the equation portfolio bate βP = a βx + b βy.
Portfolio
A portfolio is a grouping of financial assets such as stocks, bonds, commodities, currencies and cash equivalents, as well as their fund counterparts, including mutual, exchange-traded and closed funds. A portfolio can also consist of non-publicly...
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