Compare the results of finding the mean and standard deviation, of the total amount that this investor earns in one year from these four investments, assuming that the returns are independent of each other and are no longer independent of one another
. Explain the differences in your answers.
The mean total returns is what the investor earns in one year from the given four investments, assuming that the returns are independent of each other and that they are not independent of each other. This is essentially the same as the mean annual rates remain unchanged. The standard deviation of the total return when the returns of the four stocks are not independent of each other is less than the standard deviation value computed assuming that the returns of these four stocks are independent of each other. This difference is explained by the fact that the stock returns are no longer independent; in fact, some pairs of stocks have negative correlations. Investing in stocks with negative correlations tends to reduce the overall risk associated with the portfolio.
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