In developing a sampling plan during stock selection, it is imperative that the investor determine the amount of stock in the industry. For instance, the pharmaceutical industry contains a variety of stocks ranging to hundreds. This information is significant as when an industry has more stocks, the sample portfolio's development becomes more predictable. Therefore, it is vital to determine the sample size since it is used in the computation of a sample that contains the provided margin of error using the provided standard deviation.
Thus, to attain the sample size of 93 at a confidence level of 0.95, an acceptable margin of error of $5 and a standard deviation in the price of $24.61 are required for the computation. Therefore, to select the stocks to include in a portfolio, it is relevant the stocks be selected from backgrounds that are differing. Hence, the selection should aim to produce a variety of healthcare products with a volatility that is not significantly higher than the standard deviation across the stocks.
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Evaluation of a Portfolio by Sampling and Estimation
In the evaluation of a portfolio by sampling, the larger the size of the sample corresponds to a smaller confidence interval for the mean. This is demonstrated by Alexion Pharmaceuticals which is the most volatile stock, and with a 95% confidence, the random average stock of 250 individual stock quotes is between 122.71 and 125.07, based on the sample data for the last five years. Additionally, the difference between Alexion’s mean of the stock and the mean of the stocks in the pharmaceutical industry for the same period, using a 95% confidence and the random average of 250 individual stock quotes, falls between the interval of 45.62 and 52.16.
Evaluation of a Portfolio by Testing the Hypothesis
To evaluate the portfolio using hypothesis testing, the null hypothesis predicts the industry average to be the same as the stock average while the alternative hypothesis predicts that the industry average is not equal to the stock average. Thus, the stock average obtained is 81.26, and the critical value for 95% confidence is 1.96. Hence, the null hypothesis is rejected because the critical value is greater than the critical value for the alpha, 1.96>0.95.
