prove the Benefits of portfolio diversification mathematically

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Answer :- According to the Markowitz's portfolio theory (Modern portfolio theory), investors are mainly concerned with two properties of an asset: risk and return, but by diversification of portfolio, it is possible to trade off between them.

The risks to which a security / portfolio is exposed are divided into two groups, diversifiable and non-diversifiable: -

The diversifiable risk can be eliminated through a portfolio consisting of large number of well diversified securities. Whereas, the non-diversifiable risk is attributable to factors that affect businesses like interest rate changes, inflation, political changes etc. As diversifiable risk can be eliminated by an investor through diversification, the non-diversifiable risk is the only risk a business should be concerned with.

Alpha measures the unsystematic risk, also referred to as diversifiable risk. Alpha measures the magnitude of the security's response to changes in other securities. The unsystematic risk can be eliminated through a portfolio consisting of large number of well diversified securities.

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Prove the benefits of diversification mathematically

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prove the Benefits of portfolio diversification mathematically

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