Assume that two investors each hold a portfolio, and that portfolio is their only asset.Investor A's portfolio has a beta of minus 2.0, while Investor B's portfolio has a beta of plus 2.0.Assuming that the unsystematic risks of the stocks in the two portfolios are the same, then the two investors face the same amount of risk.However, the holders of either portfolio could lower their risks, and by exactly the same amount, by adding some "normal" stocks with beta = 1.0.

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The two investors face the same amount of systematic risk due to the opposite betas of their portfolios. However, both investors could lower their risks by adding normal stocks with a beta of 1.0, as the systematic risks of the stocks in their portfolios would be diversified. Therefore, the risk reduction would be the same for both investors.

Assume That Two Investors Each Hold a Portfolio, and That