Unsystematic risk is the risk inherent to a particular asset whereas systematic risk is the risk that affects all the assets in the market.
The market portfolio does not have unsystematic risk, it only has systematic risk. This is because, under CAPM, the market portfolio is defined as the value weighted portfolio of all the assets in the market thus it is completely diversified and thus all unsystematic (diversifiable) risk has been removed.
On the other hand, the investment portfolio of any individual investor will have at least some level of unsystematic risk. This is because, unless the investor replicates the market portfolio , the diversification of the portfolio will not be ideal and thus some level of diversifiable risk will still be there in the portfolio.
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