The Risk of an Investment Is Measured by the Variability

The risk of an investment is measured by the variability of the changes in its value over a fixed period, such as a year. More variation from year to year means more risk. The government's Securities and Exchange Commission wants to require mutual funds to tell investors how risky they are. A news article (New York Times, April 2, 1995) says that some people think that "the proposed risk descriptions, especially one that goes by the daunting name standard deviation" are hard to understand. Explain to a friend what the standard deviation means, using the fact that the changes in a mutual fund's value over many years have a roughly Normal distribution.

A) The standard deviation is the distance between the first and third quartiles, so it spans half the yearly changes in the fund's value.
B) The standard deviation is the largest change we ever expect to see in a year.
C) The yearly change in the fund's value will be greater than the standard deviation half the time and less than the standard deviation half the time.
D) Start with the average (mean) change in the fund's value over many years; the actual change will be within one standard deviation of that average in about 68% of all years.
E) Start with the average (mean) change in the fund's value over many years; the actual change will be within one standard deviation of that average in about 95% of all years.