Sigman 1 Portfolio mean and variance
نویسنده
چکیده
Here we study the performance of a one-period investment X0 > 0 (dollars) shared among several different assets. Our criterion for measuring performance will be the mean and variance of its rate of return; the variance being viewed as measuring the risk involved. Among other things we will see that the variance of an investment can be reduced simply by diversifying, that is, by sharing the X0 among more than one asset, and this is so even if the assets are uncorrelated. At one extreme, we shall find that it is even possible, under strong enough correlation between assets, to reduce the variance to 0, thus obtaining a risk-free investment from risky assets. We will also study the Markowitz optimization problem and its solution, a problem of minimizing the variance of a portfolio for a given fixed desired expected rate of return.
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