Which of the following statements about investment risks is FALSE?

Higher capital gains are indeed associated with higher risk, not lower risk. This is based on the fundamental principle of investing that suggests the potential for greater returns usually comes with the acceptance of greater risk. In financial markets, investments that have a potential for substantial capital appreciation, such as stocks, are often more volatile and may experience significant price fluctuations. Conversely, investments perceived as low-risk, like government bonds or treasury bills, typically offer lower potential capital gains.

The other statements accurately reflect investment principles. Diversification is a risk management strategy that involves spreading investments across various financial instruments, industries, and other categories to reduce exposure to any single asset or risk. Average returns and standard deviation are standard measures used in finance to assess the performance of an investment and its volatility. Finally, while it's common to seek risk-free investments, such as government securities, there is always some level of risk involved, so the concept of a truly risk-free investment can be complicated; however, it is accurate in the context of traditional finance discussions.