Stock prices, as measured by the S&P 500 index, have:  declined substantially since they peaked in the mid 1980s.   risen smoothly over time.                     been quite volatile over time.   not changed much over time.

The statement that best describes the behavior of stock prices, as measured by the S&P 500 index, is that they have been quite volatile over time.

Here's why:

1. The S&P 500 index is a market-capitalization-weighted index of the 500 largest U.S. publicly traded companies. The index is widely regarded as the best gauge of large-cap U.S. equities.

2. If you look at the historical chart of the S&P 500 index, you will see that it has not declined substantially since the mid-1980s. In fact, it has generally been on an upward trend, but with significant ups and downs along the way.

3. The statement that the S&P 500 has risen smoothly over time is also not accurate. While the long-term trend has been upward, there have been many periods of significant volatility. For example, the dot-com bubble burst in the early 2000s and the financial crisis in 2008 both led to substantial declines in the index.

4. The claim that the S&P 500 has not changed much over time is also not true. The index has seen substantial growth over the long term, despite periods of volatility.

5. Therefore, the statement that the S&P 500 has been quite volatile over time is the most accurate. The index has seen periods of both significant growth and significant declines, reflecting the inherent volatility in the stock market.