The return and risk of a portfolio are measured by calculating the portfolio mean (or expected return) and the portfolio volatility (or standard deviation). Operationally, these statistics are defined as follows.

if using sample means, the portfolio mean is:

Similarly, the portfolio variance is well defined for both the population variance,

and the sample variance:

Finally, the portfolio's volatility or standard deviation is defined as the square root of the portfolio variance.

and

In topic 2.11 we apply these concepts to two examples.

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