Some basic question

Why is the term expected value used for the Markowitz portfolio theory ?
The reason is "Convinence and Tradition". Since the term is often used people needed a label for it instead of calling it by the conventional name of "weighted average of possible outcomes with probability as the weights".

Why do we use only mean as the measure of return and why not mode or median ?
If we have the nomral distribution, then a portfolio is mean-standard deviation efficient if and only if it is
mode-probability loss efficient
mode-standard deviation efficient
mean-probability of loss efficient
median-probability of loss efficient
median-standard deviation efficient

The questionnaire was phrased in terms of mode "most likely return" for convinece of computation mode was translated into mean, for ease of interpretation mean was translated back into mode.

Median is insensitive to changes
Mode changes far more dramatically for even small changes in returns as long as it does not effect the midpoint of the distribution.

1)A distribution can never more than one mean but it can many modes and medians.
2) The arithmetic relationship between means of securities and means of portfolios are much simpler than the corresponding relationships for modes and medians


Why do we use only standard deviation as the measure of central tendency and not any other?