Originally written on Feb. 9, 2008.
A week ago I concluded that the UltraShort FTSE/Xinhua China 25 ProShares fund (FXP) was not working as advertised. I decided to follow up with ProShares to get to the bottom of the mystery and ended up discovering that there is much more to these leveraged funds than meets the eye. In short (no pun intended) this fund is working as advertised but it's not what most people expect. And judging from the exchanges on the message boards I can assure you that there are a lot of people out there that don't understand what they are invested in. Apparently ProShares is used to the confusion because they have the subject aptly covered in all kinds of handout materials.
First, let my clarify what the target index is. It is not the Hang Seng and it is not the iShares FTSE/Xinhua China 25 Index as some people have suggested. The former is a Hong Kong index and the latter is an index fund marketed by Barclays which attempts to track the same index that FXP attempts to track. The FTSE/Xinhua China 25 Index consists of "25 of the largest and most liquid Chinese stocks (Red Chips and H shares) listed and trading on the Hong Kong exchange." Unfortunately, it's hard to find historic values of this index but I was able to pull a few key values off of stockcharts.com. Using those values I redid the analysis presented in my last blog post and pretty much got the same result:
So why am I not getting the result I'd expect? Given the 15.3% drop in the FTSE/Xinhua index I should have seen a 30.6% increase in FXP, right? Wrong! Here's why.
As explained in the ProShares Supplement of Additional Information [SAI] the fund's objective is to to match 200% of the performance of the index on a given DAY. The SAI goes on to explain that "for periods greater than one day, the use of leverage tends to cause the performance of a ProFund to be either greater than, or less than, the index performance times the stated multiple in the fund objective." It turns out that mathematically it is virtually impossible to match 200% of the index over longer periods as illustrated in this extreme example that I fabricated, where I assume that the index goes up 20% one day and down 10% the next day and the fund meets its objective each day.
As you can see, while the index ends up 8% the ultrashort fund would end down 28%, not 16%. A bit counterintuitive, isn't it?
As the ProShares folks explain it this phenomenon is caused by the leverage and the volatility of the index they are tracking. This is such an important concept that ProShares even went so far as to produce a table of estimates of how the fund would perform under different combinations of index return and volatility. What it shows is pretty staggering. With 40% volatility the fund can drop by 38% over the course of one year even if the underlying index is unchanged. With no volatility the fund can rise by almost 178% in one year while the index drops by only 40%. Unfortunately, this analysis is in the SAI and not in the prospectus. Even more unfortunate is the fact that it wouldn't have made any difference to me since I didn't read the prospectus anyway because the whole concept of this fund seemed pretty simple to me. Boy was I wrong!
So, the obvious question is why do they have a fund that tries to match the daily return of an index? Why can't you have it match a longer period? If I hold the fund for a year I expect it to match the performance of the index over a one year period. Well, the problem is that every shareholder has a different holding period and you can only get the math to work out for one holding period. So you might as well target a one day holding period.
The way I see it this holding period problem is created by the leverage. In a leveraged fund you end each day with different leverage than you started with. If you start the day with 2:1 inverse leverage and the index moves up 10% you end up with 2.25:1 leverage at the end of the day. If you were targeting the fund's long term performance for someone whose holding period began that morning you would let the leverage roll over each day since they would measure their performance relative to their starting point when the leverage was 2:1. But in that case someone who buys in on day 2 would not be buying a 2:1 leverage fund. They would be buying a 2.25:1 leverage fund. So I suspect that the fund manager rebalances the leverage at the start of each day.
This whole thing sort of reminds me of Einstein's theory of relativity. I think it would be a lot easier to just buy twice as much of an unleveraged short fund. That way you will know exactly what you are getting.