Chapter 4.2, Problem 29E

Morningstar is an investment research from that publishes some online educational materials. The materials for an online course called “Looking at Historical Risk” (news.morningstar.com/classroom2/course.asp?docld=2927&page=2&CN=com,retrieved August 3, 2016) included the following paragraph referring to annual return (in percent) for investment funds:

Using standard deviation as a measure of risk can have its drawbacks. It’s possible to own a fund with a low standard deviation and still lose money. In reality, that’s rare. Funds with modest standard deviations tend to lose less money over short time frames than those with high standard deviations. For example, the one-year average standard deviation among ultrashort-term bond funds, which are among the lowest-risk funds around (other than money market funds), is a mere 0.64%.

1. a. Explain why the standard deviation of percent return is a reasonable measure of unpredictability and why a smaller standard deviation for the percent return of an investment fund means less risk.
2. b. Explain how a fund with a small standard deviation can still lose money. (Hint: Think about the average percent return.)