Beta measures the performance of portfolio inrespect of the market as whole. Whereas standard deviation measures the dispersion of sample data from its mean.
Beta is a relative measure whereas standard deviation is statistical measure.
Beta does not show securities individual behavior rather standard deviation shows the volatality of all types of financial instruments or bonds or stock that are based on return spread over period of time.
Beta equals to one shows the securities are performing in line with market and the beta less than one shows securities shows that securities are less volatile than market and vise versa if beta greater than one.
If standard deviation shows that stock are more risky and highly volatile.
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