## Normal Distribution

For many different random events in nature, a particular frequency distribution, the normal distribution (or bell curve), is useful for describing the probability of ending up in a given range. For example, the idea behind "grading on a curve" comes from the fact that exam score distributions often resemble a bell curve.

Figure 12.11 illustrates a normal distribution and its distinctive bell shape. As you can see, this distribution has a much cleaner appearance than the actual return distributions illustrated in Figure 12.10. Even so, like the normal distribution, the actual distributions do appear to be at least roughly mound shaped and symmetric. When this is true, the normal distribution is often a very good approximation.

Also, keep in mind that the distributions in Figure 12.10 are based on only 75 yearly observations, whereas Figure 12.11 is, in principle, based on an infinite number. So, if we had been able to observe returns for, say, 1,000 years, we might have filled in a lot of the irregularities and ended up with a much smoother picture in Figure 12.10. For our purposes, it is enough to observe that the returns are at least roughly normally distributed.

The usefulness of the normal distribution stems from the fact that it is completely described by the average and the standard deviation. If you have these two numbers, then there is nothing else to know. For example, with a normal distribution, the probability

Ross et al.: Fundamentals V. Risk and Return 12. Some Lessons from of Corporate Finance, Sixth Capital Market History

Edition, Alternate Edition normal distribution

A symmetric, bell-shaped frequency distribution that is completely defined by its mean and standard deviation.

Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition

V. Risk and Return

12. Some Lessons from Capital Market History

© The McGraw-Hill Companies, 2002

PART FIVE Risk and Return

Work the Web

Standard deviations are widely reported for mutual funds. For example, the Fidelity Magellan fund was the second largest mutual fund in the United States at the time this was written. How volatile is it? To find out, we went to www.morningstar.com, entered the ticker symbol FMAGX, and hit the "Volatility" link. Here is what we found.

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