Seventeen years ago we saw the first leveraged mutual fund with daily reset. Now we have dozens of them along with ETFs that work the same way. Yet after all this time, many investors still don’t understand what leveraged funds can and cannot do ^{[1]}. Even professional investors ignorantly called these products “failures” because the long-term performance is not a multiplicative factor ^{[2]} of the unleveraged performance.

Numerous hypothetical examples attempt to “prove” that leveraged funds will lose money over time. To paraphrase a famous line: “Hypos? We don’t need no stinkin’ hypos.” Why use hypothetical examples when we have real-life actual examples right in front of us?

Today we will examine the performance of leveraged performance over more than one day. This is not rocket-science. It is elementary school math. So in our real-life example I will call on some old friends from elementary school: Dick and Jane, and their dog Spot.

Being just a dog, Spot doesn’t know much math so he just follows the prevailing price, which is why it is called the “Spot” price. We will use silver to illustrate. The iShares Silver ETF (SLV) doesn’t buy stocks; it holds actual bars of silver in an attempt to track the spot price. Therefore, SLV will represent our Spot.

Dick is in the second grade. He is learning to multiply by 2, though sometimes he still struggles. Dick is no dummy, though; he knows he can use first grade addition to add a number to itself and get the same answer as multiplying by 2. Dick likes to chase Spot but needs to move twice as fast since he has only two legs to Spot’s four. Therefore, Dick moves twice as much as Spot (SLV) every day, just like ProShares Ultra Silver (AGQ).

Young girls often seem smarter than boys, and Jane is no exception. Not only has she mastered how to multiply by 2, she also knows about negative numbers. At that age, many girls also want to act the opposite of boys. No special reason why – just because. Therefore, instead of chasing Spot every day like Dick does, Jane decides to move twice as much in the *opposite *direction. Therefore, we can think of Jane as ProShares UltraShort Silver (ZSL), which moves twice the opposite of Spot (SLV) every day.

Now we will review Spot’s (SLV) activity over four days last week. We will also keep tabs on Dick (AGQ) and Jane (ZSL) to make sure they are doing their arithmetic correctly. Dick, Jane, and Spot live together on a hill. Every day, Spot decides to run either up the hill or down the hill. Dick chases Spot at 2x (+200%). Jane does the opposite by moving 200% opposite of Spot.

For the past few months, Spot would take off running up the hill nearly every day. On Monday, May 2, Spot surprised Dick by running 8.6% down the hill. Dick used his first grade addition to determine he needed to go 17.2% down the hill. Jane knew she needed to go 17.2% up the hill. Neither was accustomed to Spot moving that much in one day, and due to some rounding errors Dick went 17.4% down while Jane went 16.6% up.

Spot realized that running downhill was easier than going up and decided to do it again Tuesday. Spot ran 5.3% down. Dick doubled that by running 10.6% down. Jane tried to do the opposite but went uphill only 10.1%. Wednesday was a near repeat of Tuesday with Spot down 5.7%, Dick down 11.6%, and Jane up 11.1%.

Spot began to realize just how hard it would be to knock Dick and Jane off their mission. On Thursday, Spot decided it was time to go for a new record and ran down the hill 11.9%. Dick had never been called upon to move that far before, but he managed to go down 23.4% that day. Jane was up to the task, moving 25.1% up the hill.

It was a wild four days and Spot traveled a great distance. However, to find out how far Spot traveled, we cannot simply add the percentage moves together. We need to use daily compounding. By comparing his ending point to his starting point, we determine that Spot went 28% down the hill over those four days.

Lazy Larry, Dick and Jane’s neighbor, is always looking for short cuts and refuses to use more than first grade arithmetic. Lazy Larry tried to determine Spot’s four-day move by simply adding the percentages together. However, that does not work, yielding an incorrect answer of 31.5% down.

Lazy Larry eventually learns that the correct answer is 28%, and then once again uses his lazy approach to determine that Dick must be 56% down and Jane 56% up. Another neighbor, Doubting Thomas, claims this cannot be correct because the leverage used by Dick and Jane will make them both lose ground over time. Therefore, explains Thomas, Dick’s loss must be greater that 56% and Jane’s gain must be less than 56%.

Just like Spot’s 4-day move cannot be solved by adding four percentages together, Dick and Jane’s 4-day moves also cannot be determined so easily. Daily compounding must be considered. For Spot, the detailed math is (1-8.6%) x (1-5.3%) x (1-5.7%) x (1-11.9%) -1= -28.1%.

It turns out that when we apply the correct formula, both Dick and Jane came out better than Lazy Larry and Doubting Thomas had predicted ^{[3]}. Instead of losing 56% or more, Dick (AGX) only lost 50%. Instead of gaining 56% or less, Jane actually gained 78%, even after falling short of her goal on each of the first three days.

The table below shows the life of Dick (AGX) and Jane (ZSL) and Spot (SLV) during four days in May. This is how leveraged funds with daily reset work. Don’t be a Lazy Larry or Doubting Thomas. Take the time to study this real life example. The math is not all that complicated. If Dick and Jane can do it, you can, too.

Dick & Jane & Spot | Spot (SLV) Price | Spot % Change | Dick (AGQ) Price | Dick % Change | Jane (ZSL) Price | Jane % Change |
---|---|---|---|---|---|---|

Friday 4/29/11 | 46.88 | 358.96 | 13.64 | |||

Monday 5/2/11 | 42.83 | -8.6% | 296.50 | -17.4% | 15.90 | 16.6% |

Tuesday 5/3/11 | 40.58 | -5.3% | 264.97 | -10.6% | 17.51 | 10.1% |

Wednesday 5/4/11 | 38.27 | -5.7% | 234.20 | -11.6% | 19.45 | 11.1% |

Thursday 5/5/11 | 33.72 | -11.9% | 179.34 | -23.4% | 24.34 | 25.1% |

4-day Total | 33.72 | -28.1% | 179.34 | -50.0% | 24.34 | 78.4% |

*Disclosure covering writer, editor, and publisher: No positions in any of the securities mentioned. No positions in any of the companies or ETF sponsors mentioned. No income, revenue, or other compensation (either directly or indirectly) received from, or on behalf of, any of the companies or ETF sponsors mentioned.*