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Risk and return

Return

Consider an asset that you bought at an initial price of Pi. Suppose also that you received a dividend D thanks to the same asset and that you finally sold it for a price of Pf. Then the return r of the whole process is:
It is important to know that the return of a security is always dependant on many factors. Among these we can find: the overall situation of the economy, political factors, the industry to which the security belongs (a telecom stock for instance)�etc.
To estimate the average return of a security, we always use probabilities.
In order to understand more this concept let�s consider an asset with n different returns for n different situations. The probability for a situation i to actually happen is
and the correspondant return is ri. Then the average return is given by:
for instance we can have three situations summarized in the following array:
The average return for this asset is:

E[r] = 0.3(-5%) + 0.5(6%) + 0.2(8%) = 3.1%

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