This means that if you are invested in their S&P/TSX 60 ETF and the index goes up by 1% one day, the ETF should go up by 2%. They also offer a bear version of each ETF where a 1% rise in the index gives a 2% drop in the bear ETF. Obviously, the owners of the bear ETFs are hoping for the index to drop.

Let’s focus on the ETF based on the S&P/TSX 60 index, which is based on the biggest companies in Canada. If the TSX 60 goes up by 10% one year, you’d expect the corresponding Horizons BetaPro ETF (ticker symbol HXU) to go up by 20% that year. But, that’s not how it works. For example, in its first year, HXU returned 13.28% and the TSX 60 rose 9.19%. If we double the TSX 60 return, we find that there is a 5.1% gap.

What causes this 5.1% gap? I tried reading the prospectus, but like most such documents, clarity doesn’t seem to have been a priority. Page 36 outlines a number of fees including 1.15% management fees, operating expenses, and various expenses attached to forward contracts.

In addition to fees, the method used to achieve double exposure contributes to the 5.1% gap. This can be interest on borrowed money or built-in bias of stock options (called forward contracts in this case). When you trade in stock options, the expected rise of the underlying stock (the TSX 60 in this case) is built in to the option prices.

If this explanation of the 5.1% gap makes no sense to you, don’t worry. Just accept that it exists for what follows.

It might seem like we just need the TSX 60 to return at least 5.1%, and then HXU will perform better than the TSX 60. This works for one year, but doesn’t take into account the effect of volatility on long-term compounded returns.

Based on historical data, the long-term compounded return will be lower than the expected one-year return by about 2%. However, HXU’s doubled volatility increases this penalty by a factor of 4 to about 8% per year.

Combining all this together with the 5.1% gap we observed earlier, the TSX 60 would have to have a long-term compounded return of 9.1% for HXU to break even with the TSX 60. Suddenly, HXU doesn’t look as appealing as it did before.

(

**Math interlude that can be ignored**: If the expected one-year return of the TSX 60 is x, then its long-term compounded return will be x-2%. HXU’s one-year return will be 2x-5.1%, and its long-term compounded return will be 2x-5.1%-8%. Equating the two compounded return gives x=11.1%, or a long-term compounded return for the TSX 60 of 9.1%.)

The bear versions of the ETFs are much easier to argue against. Investors and pundits cannot reliably predict when the stock market will drop. The bear ETF corresponding to HXU is HXD and it had a one-year return of -19.85%. An investor who chose the bear for this year would be in a very deep hole trying to catch up to investors who just bought the TSX 60.

Hi

ReplyDeleteIs the gap you identified not due (at least in part) by the daily re-baselining?

q

Anonymous:

ReplyDeleteDaily re-baselining causes some volatility losses within a single year, but not that much. Leverage always has costs, but they are spread out over the year and are too small to be visible in the returns of a single day.

Circling back to this post after several years, I now think the Anonymous commenter was right, and I was mostly wrong; much of the 5.1% gap within a single year could easily be explained by the daily re-baselining.

DeleteWell, compared to the inception date of HXU (about 17 months ago), HXU has gained ~42% whereas XIC has gained only ~19%. Your hypothesis simply doesn't bear out! HXU has provided about a 20% (=1.42/1.19) better return over this period than XIC with all fees considered. I think any buy & hold investor would take a 20% improvement, yet that is not the best use of any index fund. Indices are best exploited through wave trading. Buying HXD today, & then about four months from now short selling it or buying HXU, should yield a superior return. Rinse & repeat.

ReplyDeleteAnonymous: According to the Horizons BetaPro web site, the return from 2007 January 8 to 2008 May 31 was 27.27%. The closing price May 30th was $34.50 making the price at inception $27.11. This differs from the TSX chart. Perhaps this ETF sold at a discount initially? Who knows. Using the $27.11 starting figure, the return to date is now 31.9%, far short of the apparent 42% that you report. I'm confident that HXU will continue to underperform double the TSX 60 by significant amounts.

ReplyDeleteAs for wave trading and other market timing methods, there is no evidence that anyone has succeeded at this over the long term. Be careful not to lose all your money.

Michael, can you explain where you get this square relationship between volatility and duration? Also, you seem to have used a square relation here too (double exposure turns 2% under-performance into 8%). I'd like to understand the math behind these. Thanks!

ReplyDeletePatrick: Few things make me happier than being asked a math question. Here is a good explanation on Wikipedia: volatility link.

ReplyDeleteBasically, one measure of volatility, the variance, grows in proportion to time. Standard deviation is the square root of variance, and so the standard deviation of returns grows as the square root of time.

The gap between expected return and expected compound return is equal to half the variance (this falls out of computing the expected value of the lognormal probability distribution). If an investment has double exposure to the index, then its standard deviation is double, which makes the variance 4 times bigger and the gap between expected return and expected compound return 4 times bigger.

You can see why I tried to avoid too many of these details in the post entry. If any of this isn't clear, let me know and I'll try again.

I was thinking of putting some money in the bear hxd and waiting for the market to crash again, resulting in the doubling, or more, of my money. From there I was going to reinvest in the bull hxu, wait for the market to correct itself & voila, another big profit. Think this is a good or bad idea?

ReplyDelete@Anonymous: Your question doesn't seem serious, but in case it is, you should know that even if there is a crash followed by a boom, you aren't guaranteed to make money. I recommend understanding why before making a decision on what to do.

ReplyDelete