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CHAPTER 7 AN INTRODUCTION TO PORTFOLIO MANAGEMENT Answers to Questions 1. Investors hold diversified portfolios in order to reduce risk, that is, to lower the variance of the portfolio, which is considered a measure of risk of the portfolio. A diversified portfolio should accomplish this because the returns for the alternative assets should not be correlated so the variance of the total portfolio will be reduced. 2. The covariance is equal to Σ E[(R i - E(R i ))(R j - E(R j ))] and shows the absolute amount of comovement between two series. If they constantly move in the same direction, it will be a large positive value and vice versa. Covariance is important in portfolio theory because the variance of a portfolio is a combination of individual variances and the covariances among all assets in the portfolio. It is also shown that in a portfolio with a large number of securities the variance of the portfolio becomes the average of all the covariances. 3. Similar assets like common stock or stock for companies in the same industry (e.g., auto industry) will have high positive covariances because the sales and profits for the firms are affected by common factors since their customers and suppliers are the same. Because their profits and risk factors move together you should expect the stock returns to also move together and have high covariance. The returns from different assets will not have as much covariance because the returns will not be as correlated. This is even more so for investments in different countries where the returns and risk factors are very unique. 4. The covariance between the returns of assets i and j is affected by the variability of these two returns. Therefore, it is difficult to interpret the covariance figures without taking into account the variability of each return series. In contrast, the correlation coefficient is obtained by standardizing the covariance for the individual variability of the two return series, that is: r ij = cov ij /( σ i σ j ) Thus, the correlation coefficient can only vary in the range of -1 to +1. A value of +1
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This note was uploaded on 05/20/2010 for the course FIN 5DLS taught by Professor Leejohn during the One '10 term at La Trobe University.

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