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Pillai 'Variance and Covariance'
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Variances of linear combinations of two random variables are worked out in terms of their respective variances and covariances.
This result is used to demonstrate how to select a linear combination of two random variables so as to minimize the overall variance. This technique is further illustrated with an application to optimizing a portfolio, consisting of two stocks, in terms of minimizing its volatility. It is shown here that when two stocks are negatively correlated there is always an optimum strategy in terms of distributing the capital between the two stocks. (For undergraduate Probability class).
This result is used to demonstrate how to select a linear combination of two random variables so as to minimize the overall variance. This technique is further illustrated with an application to optimizing a portfolio, consisting of two stocks, in terms of minimizing its volatility. It is shown here that when two stocks are negatively correlated there is always an optimum strategy in terms of distributing the capital between the two stocks. (For undergraduate Probability class).
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