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##### Overview:

Portfolio diversification is the most fundamental concept of risk management. The allocation of financial resources in stocks, bonds, riskless, assets, oil and other assets determine the expected return and risk of a portfolio. Taking account of covariances and expected returns, investors can create a diversified portfolio that maximizes expected return for a given level of risk. An important mission of financial institutions is to provide portfolio-diversification services.

Fabozzi et al. Foundations of Financial Markets and Institutions, chapters 8 and 13

Jeremy Siegel, Stocks for the Long Run, chapters 1 and 2

Optimal Portfolio Diversification

in General Case

Drop assumption of equal weighting, independence and equal variance

Put xi dollars in i th asset, I=1,..,n, where the xi sum to \$1.

Portfolio expected value

Portfolio variance (two assets) =

Beta

The CAPM implies that the expected return on the ith asset is determined from its beta.

Beta (i) is the regression slope coefficient when the return on the ith asset is regressed on the return on the market.

Fundamental equation of the CAPM: