In order to properly evaluate the performance of leveraged investment products, it is important to understand the effect of mathematical compounding on their respective returns.
Leveraged products are benchmarked daily to published indices. And while an investment may perform in line with its benchmark on a daily basis or even for several periods in a row, it may appear to either trail or outperform its benchmark over longer periods. This is due to the nonlinear effects of leverage.
An Example of Compounding
For example, consider a hypothetical fund that is designed to produce returns that correspond to 200% of an index. On the first day of a period, the index rises from a level of 100 to a level of 106, producing a 6% gain and an expectation that the fund will rise by 12% (6% x 2%). On the same day, the fund’s net asset value (NAV) increases from $10.00 to $11.20 for a gain of 12.00%—in line with its benchmark.
On day two, assume the index falls from 106 to 99 for a loss of about 6.60%.
The fund, as expected, falls 13.20% to a price of $9.72. On each day, the fund performed exactly in line with its benchmark, but for the two-day period, the fund was down 2.80%, while the index was down only 1.00%.
| |
Index
Level |
Index Performance |
Fund Expectation |
Fund NAV |
Fund Performance |
Assessment |
| Start |
100 |
|
|
$10.00 |
|
|
| Day 1 |
106 |
6.00% |
12.00% |
$11.20 |
12.00% |
In line |
| Day 2 |
99 |
-6.60% |
-13.20% |
$9.72 |
-13.20% |
In line |
| Cumulative |
|
-1.00% |
-2.00% |
|
-2.80% |
-2.80 |
Without taking into account the daily compounding of returns, one would expect the fund to lose 2.00%. However, due to compounding, the fund actually lost 2.80%. This example is summarized in the table on the previous page. As illustrated by this simple example, the effect of leverage can make it difficult to form expectations or judgments about fund performance given only the returns of the unleveraged index.
Volatility Impacts Leveraged Performance
While compounding may work against an investor any time there is a change of direction in an index, it would work to an investor’s advantage any time the index moves in the same direction—whether upward or downward—for two or more periods in a row.
As a general rule of thumb, more leverage will magnify the compounding effect, while less leverage will generally produce results that are more in line with expectations. In addition, periods of high volatility in an underlying index will also cause the effects of compounding to be more pronounced, while lower volatility will produce a more muted effect.
 
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