Most investing involves the allocation of funds into an assortment of alternatives. This practice predates any formalized study of portfolio construction. People generally attribute the formalization of portfolio analysis to the seminal work of Harry Markowitz as published in 1952. He then noted that conventional economic wisdom of the time would imply that investors should identify the single best investment opportunity available and place all available funds into it. This perceived best opportunity would be the one offering the greatest expected return. This notion largely followed Mark Twain's famous assertion that the best way to invest was to select the best opportunity available, put all your money into it, and watch it very carefully. The alternate consideration introduced by Markowitz was that investors needed to consider risk along with return.


The fundamental motivation for investing is the potential to earn return. Quite simply, return represents more of the same thing that is invested. Specifically, when money is invested, the investor expects to receive more money as a result. Typically some delay is realized before that additional money is realized. Furthermore, the relative amount of money realized in comparison to the amount invested becomes important. A comparison of the earnings to the investment produces a relative value or a rate. The ultimate measure thus becomes the rate of return over a specified interval.
The simplest representation of the relative amount of money earned on an investment is the return relative. This simple notion is the ending value of an investment divided by the beginning value of that same investment.

\begin{align} Return\ relative =\frac{ending\ value}{beginning\ value} \end{align}

The return relative can be converted into the simple return by subtracting one. The alternate calculation for the simple return is:

\begin{align} return=\frac{ending\ value-beginning\ value}{beginning\ value} \end{align}

Note that in each representation above, the underlying reference is always the beginning value. Thus one is finding the gain or potentially loss in comparison to the starting amount invested. In the event that a dividend is paid or interest is earned between the beginning time and the ending time the above equations are respectively changed to:

\begin{align} Return\ relative =\frac{ending\ value+dividend\ or\ interest\ earned}{beginning\ value} \end{align}
\begin{align} return=\frac{ending\ value+dividend\ or\ interest\ earned-beginning\ value}{beginning\ value} \end{align}


Potentially unfavorable outcomes to investment introduce the concept of risk. The greater the likelihood of unfavorable outcomes the greater the risk. The most commonly accepted representation of risk in financial applications is the distribution of possible outcomes. Standard deviation is the statistical tool employed to measure this risk. Sometimes the square of standard deviation or variance is employed.

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