Final answer:
Averaging percentage changes may not accurately reflect the true rate of return, as this method ignores the volatility of investments and the effects of compounding. Using the geometric mean to calculate the compound annual growth rate provides a more accurate depiction of investment performance.
Step-by-step explanation:
Averaging percentage changes can produce an inaccurate measure of the true rate of return because it can mask the volatility and the compound nature of returns over time. Investments like stocks can have significant fluctuations in their value, as seen with the example of the S&P 500 increasing 26% in 2009 after declining 37% in 2008. Such large swings in percentage change can have a non-linear effect on the overall growth of an investment.
Average returns do not illustrate the impact of gains and losses on the principal amount. The true rate of return over time, particularly with compounding, is affected by the sequence of returns, not just the average. For example, if you calculate a simple average return of investments with a +26% return one year followed by a -37% return the next year, you wouldn't capture the actual decrease in the investment's value due to the negative compounding effect.
Therefore, to get an accurate picture, the geometric mean, which takes into account the compounding effect over time, is more appropriate for calculating average annual growth rates (AAGR) and compound annual growth rates (CAGR). When dealing with investment returns, these two methods of calculating averages can provide a more precise understanding of an investment's performance.