The Universal Effects of Compounding and Geared Funds
Compounding is a universal mathematical concept that affects the returns of investments. It is important for all investors to understand how compounding affects returns in different market conditions—upwardtrending, downwardtrending and volatile. For geared (leveraged and inverse) fund investors, it is particularly important to understand that the effects of compounding may be more pronounced in funds with larger or inverse multiples, and in funds with volatile benchmarks. It's possible for significant gains and losses to occur much faster in geared funds.
Compounding with conventional investments:
Let's take a hypothetical look at how compounding affects conventional investment returns in upwardtrending, downwardtrending and volatile markets.
When "10% + 10% = 21%" 

When "10% + 10% = 19%" 

When "10% + 10% = 1%" 
Note: All examples use extreme and simplified hypothetical market movements, and are for illustrative purposes only. Actual market movements can be meaningfully different. Examples do not reflect the impact of expenses or taxes, which would lower the results shown.
The use of leverage and/or aggressive investment techniques, such as through the use of futures or other financial instruments, may expose funds to dramatic gains and losses as well as impact correlation of returns. The funds do not limit the frequency of purchases and exchanges which may increase expenses including taxes which can negatively impact performance. Read the prospectus carefully before you invest.
Glossary
 Compounding – the cumulative effect of applying gains/losses and income to principal over time. Each period's gains or losses enlarge or shrink the base from which the next period's returns are calculated.
 Conventional investment – Any investment that does not use leverage or inverse exposure to provide a multiple or a multiple of the inverse return of a benchmark (e.g., index funds, savings accounts, stocks, bonds, mutual funds).
 2x leveraged fund – A fund designed to provide twice the daily return of an index or other benchmark. (These funds do not attempt to produce the return during any period other than a day. Results for longer than one trading day will likely differ from the return of twice the index over the longer period.)
 Volatile market – A market characterized by substantial up and down price swings over a period of time.
Compounding with geared investments: "The same but more"
Now let's use a 2x leveraged fund as an example to see how compounding affects geared fund returns in upwardtrending, downwardtrending and volatile markets. Compounding in geared funds can result in gains or losses that occur much faster and to a greater degree than with conventional investments.
When "20% + 20% = 44%" 

When "20% + 20% = 36%" 

When "20% + 20% = 4%" 
Does compounding affect the returns of conventional index funds?
If so, why don't I see it?Over time, compounding can make returns of an indexed investment either greater than or less than the simple sum of the individual daily returns. However, this effect is not easy to see by merely comparing the return of the investment versus the return of the index. The reason? Conventional indexes such as the S&P 500 and the Dow Jones Industrial Average have the effect of compounding incorporated into their returns.
Why aren't the longerterm returns of a geared 2x fund normally two times the return of its underlying index?
The impact of compounding on a 2x fund is generally greater than twice the impact of compounding on an equivalent conventional investment. As a result, the longerterm return of a geared fund can be significantly greater than or less than two times the return of its underlying index for the time period. For instance, the leveraged fund return in the volatile market example on this page (third example) results in a 4% loss, a much greater loss than two times the 1% loss in the volatile market for the conventional investment above (third example).
In summary
The effect of compounding can help returns in upward and downwardtrending markets and hurt in volatile markets, assuming all other variables remain the same. Investors should recognize that over time this effect can be magnified significantly in leveraged funds. The use of leverage generally increases the risk of investing in the funds. Leveraged funds are not suitable for all investors. Investors should actively monitor their holdings consistent with their strategies, as frequently as daily.