Market Volatility During the Dot-com Boom The volatility...

Market Volatility During the Dot-com Boom The volatility (see the preceding exercise) of the NASDAQ had an average rate of change of 0 points per year during $1992-1995$, and increased at an average rate of $0.2$ points per year during 1995-1998. In 1995 , the volatility of the NASDAQ was $1.1 .^{39}$ Use this information to give a rough sketch of the volatility of the NASDAQ as a function of time.

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Key Concepts

Average Rate of Change

The average rate of change quantifies how a variable changes on average over a given time interval. It is calculated by taking the difference in the value of the function at two points and dividing by the time interval between them, providing a simple measure of increase or decrease over time.

Graphical Representation of Functions

Graphical representation involves plotting a function on a coordinate system to visualize its behavior over time. This process is essential in understanding trends, such as periods of constant behavior and periods of change, making abstract numerical information more intuitive through visual sketches.

Volatility

Volatility is a measure of the extent to which an asset’s value fluctuates over time. In financial contexts, it reflects the risk associated with price swings and is often used to assess the uncertainty or variability in market performance.

Piecewise Functions

Piecewise functions are mathematical functions defined by different expressions over different intervals. They are useful for modeling situations where the behavior of a variable changes distinctly at specific points in time, such as a sudden shift from a constant rate to a linear increase.

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