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We would generally find that the beta of a single security is more stable over time...

We would generally find that the beta of a single security is more stable over time than the beta of the market portfolio.

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A stock's beta is the measure of systematic risk or the market risk. In other words, it is the risk associated with a stock or portfolio based on the past prices with respect to changing prices in the market. A well diversified portfolio will always try to mimick the market, so its beta value will always be near 1 and thereabouts. However a single security might show fluctuations with respect to prices and over time the beta can range wide and far.

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