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The asset rate of returns is the profit on a particular investment; it includes any change in the asset value, interest, commission or dividends and so, all other cash-flows which an investors receive or pays due to the investment.
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Why can we assume that asset return rates are normally (or lognormally) distributed?
There is also academic discussion on this topic:
Kjersti Aas, "To log or not to log: The distribution of asset returns"
Abstract:
"In the context of the measurement of market risk, the random variable … One may define the return in different ways, the two most common are arithmetic and geometric returns. The distinction between these two types of returns is not well understood. …