Over the past four years, a stock produced returns of 13 percent, −9 percent, 8 percent, and 14 percent, respectively. Based on these four years, what range of returns would you expect to see 99 percent of the time?

The range of returns that would be expected to be seen 99 percent of the time is (-25.5%, 38.5%).

Explanation:

Let the random variable X represent the percentage of returns produced by a stock.

The data for the return produced over the past four year is:

S = {13%, -9%, 8%, 14%}

Compute the average return as follows:

Compute the standard deviation of returns as follows:

The 99% probability range is given by:

Compute the range of returns that would be expected to be seen 99 percent of the time as follows:

Thus, the range of returns that would be expected to be seen 99 percent of the time is (-25.5%, 38.5%).

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