Which of the following statements about asset pricing models is most accurate?
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Diversification reduces unsystematic, or unique risk. With the risk-free asset and a portfolio of risky assets, the equation for the expected standard deviation is linear: wAsA . A combination of the risk free asset and a portfolio always gives more return for a given level of risk. Risk tends to be reduced, but assuming that assets are not perfectly positively correlated, an investor can achieve the benefits of diversification by adding just one security (Markowitz). Studies have shown that approximately 18-30 stocks are needed for proper diversification. The main point is that the number of stocks required is small and is significantly less than all securities (and significantly less than 1,000 securities).
An equally weighted portfolio of a risky asset and a risk-free asset will exhibit:
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A risk free asset has a standard deviation of returns equal to zero and a correlation of returns with any risky asset also equal to zero. As a result, the standard deviation of returns of a portfolio of a risky asset and a risk-free asset is equal to the weight of the risky asset multiplied by its standard deviation of returns. For an equally weighted portfolio, the weight of the risky asset is 0.5 and the portfolio standard deviation is 0.5 × the standard deviation of returns of the risky asset.
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