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The difference between Standard deviation vs Beta of a stock can be understood by starting asking few basic questions.Let us say you have 2 choices, one to pick investment A and other B.

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A is positioned such a way that the expected return, which is the probability of different expected returns due to various factors, is calculated as E(A) = p(x) * E(x) p(y) * E(y) p(z) * E(z)Note that sum of the above probabilities is 1. Any average person would pick either A or B, whichever is higher.

An educated investor would like to find the risk he/she is taking.

If an investment's return varies like a roller-coster to provide the return calculated above, it more sounds like a gamble. The investor would pick C(A) or C(B), whichever is lower since the risk to earn an unit of return needs to be lower.

On the other hand, if the investment has a smaller variance, it is a relatively stable investment where one can lay back and not worry too much on the odds. Std dev = sqrt(Variance)where Variance = (p(x) * (E(x) - E(A))^2) (p(y) * (E(y) - E(A))^2) ( p(z) * (E(z) - E(A))^2 Okay, now that we have a better sense of what the risk is and what the corresponding return is, it makes life easy since the investment with higher return and lower risk wins. Let us assume that the return and risk for Investment A than those of B. With the above detailed explanation of the basics, one should recall the standard deviation as the risk of a particular investment. Beta of a stock/investment is the risk of the stock relative to its market risk.

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