answers to final BA 472.docx - 7-2 The expected return for one security is determined from a probability distribution consisting of the likely outcomes

answers to final BA 472.docx - 7-2 The expected return for...

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7-2. The expected return for one security is determined from a probability distribution consisting of the likely outcomes, and their associated probabilities, for the security. The expected return for a portfolio is calculated as a weighted average of the individual securities’ expected returns. The weights used are the percentages of total investable funds invested in each security. 7-3. The Markowitz model is based on the calculations for the expected return and risk of a portfolio. Another name associated with expected return is simply “mean,” and another name associated with the risk of a portfolio is the “variance.” Hence, the model is sometimes referred to as the mean-variance approach. 7-5. Each security in a portfolio, in terms of dollar amounts invested, is a percentage of the total dollar amount invested in the portfolio. This percentage is a weight, and the general assumption is that these weights sum to 1.0, accounting for all of the portfolio funds. 7-7. Markowitz was the first to formally develop the concept of portfolio diversification. He showed quantitatively why, and how, portfolio diversification works to reduce the risk of a portfolio to an investor. In effect, he showed that diversification involves the relationships among securities. 7-8. With regard to risk, the whole is not equal to the sum of the parts. We cannot simply add up the individual (weighted) standard deviations of the securities in the portfolio, and obtain portfolio risk. If we could, the whole would be equal to the sum of the parts. ] 7-9. In the Markowitz model, three factors determine portfolio risk: individual variances, the covariances between securities, and the weights (percentage of investable funds) given to each security. 7-10. The correlation coefficient is a relative measure of risk ranging from -1 to +1. The covariance is an absolute measure of risk. Since COV AB = ρ AB σ A σ B , COV AB ρ AB = ───── σ A σ B 7-11. For 10 securities, there would be n (n-1) covariances, or 90. Divide by 2 to obtain unique covariances; that is, [n(n-1)] / 2, or in this case, 45. 7-12. With 30 securities, there would be 900 terms in the variance-covariance matrix. Of these 900 terms, 30 would be variances, and n (n - 1), or 870, would be covariances. Of the 870 covariances, 435 are unique. Final Exam Study Guide page 1
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7-13. A stock with a large risk (standard deviation) could be desirable if it has high negative correlation with other stocks. This will lead to large negative covariances which help to reduce the portfolio risk. 7-14. This statement is CORRECT. As the number of securities in a portfolio increases, the importance of the covariance relationships increases while the importance of each individual security’s risk decreases. 15 Investors should typically expect stock and bond returns to be positively related, as well as bond and bill returns. Note, however, that correlations can change depending upon the time period used to measure the correlation. Stocks and gold have been negatively related, and stocks and real estate are typically negatively related.
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  • Spring '14
  • MilanP.Sigetich
  • Modern portfolio theory

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