Using Past Returns to Predict the Future

We use the Gaussian, defined by the mean and standard deviation.

Assume:

• The distribution of a stock’s return is identical each year.
• The distribution of the returns is independent of prior year’s return.

Historical Average Return (the average realized return) is an estimate of the expected return in the future.

We can then use the standard deviation to determine a reasonable range for the actual return:

$$95\%\text{ confidence interval}=\text{Average}\pm (2\times \text{Standard deviation})$$