Your Complete Guide to Index Investing with Dan Bortolotti

Is Quantitative Arbitrage Right for You?

2012-04-03T00:11:38+00:00April 1st, 2012|Categories: Research|27 Comments

[Note: This post was an April Fool’s joke!]

The volatility we’ve experienced in the last five years has challenged every investor. Yes, diversification can help, but many of the leading minds in finance have been looking for ways to improve on the now discredited Modern Portfolio Theory. I recently met with a quantitative analyst who believes he’s made a breakthrough.

The analyst did not want me to reveal his identity, so I’ll call him Sheldon. His model is based on a concept he calls “quantitative arbitrage,” or QA. The basic idea is combining long and short positions in a portfolio to dampen market volatility. “You remember Newton’s laws of motion from high school physics,” Sheldon says. “The third law says that for every force applied, there is an equal and opposite force. QA is essentially the same idea, but with much more advanced equations.”

At first, I didn’t believe it either. After all, long and short positions should cancel each other out and produce a return of zero. Indeed, after expenses the returns should be negative. But Sheldon has compensated for that by using leverage. “I’ve designed an algorithm that determines the right balance between a leveraged long position and its inverse corollary,” he says. “Now instead of the two positions cancelling each other out, there is a positive return, regardless of whether the markets move up or down. It’s simple when you understand stochastic variables.”

I asked Sheldon if he could apply the QA algorithm to the Global Couch Potato, and here’s what he came up with:

Canadian equity
Horizons BetaPro S&P/TSX 60 Bull+ (HXU) 7.49%
Horizons BetaPro S&P/TSX 60 Inverse ETF (HIX) 12.51%
US equity
ProShares UltraPro S&P 500 (UPRO) 5.12%
Horizons BetaPro S&P 500® Inverse ETF (HIU) 14.88%
International equity
iPath Long Enhanced MSCI EAFE (MFLA) 7.49%
ProShares Short MSCI EAFE (EFZ) 12.51%
Canadian fixed income
iShares DEX Universe Bond Index Fund (XBB) 21.08%
Claymore Inverse 10 Yr Gov’t Bond ETF (CIB) 18.92%

The Canadian and international equity components use double-leveraged ETFs, and Sheldon found the sweet spot to be a 7.49% leveraged long position, paired with a 12.51% inverse position, for a total of 20%. The US holdings use a triple-leveraged ETF, which therefore requires only a 5.12% allocation offset by a 14.88% inverse holding, also adding up to 20%.

To construct the 40% fixed income side, things got more challenging. With no leveraged bond fund available, Sheldon had to balance the iShares DEX Universe Bond Index Fund (XBB) with the Claymore Inverse 10 Yr Government Bond ETF (CIB). In this case, the incremental alpha comes from the fact that XBB’s holdings have an average maturity of 9.5 years, whereas CIB is pegged to the 10-year bond. “It’s not perfect,” he said, “but you have to make do with what you have available. I’m like the MacGyver of portfolio construction.”

The results

When Sheldon compared the backtested performance of the QA portfolio with the regular Global Couch Potato over the last five years, and the results were remarkable. The QA portfolio (red line) produced a total return of 146.63%, or 19.79% annualized, with minimal volatility. The Global Couch Potato, meanwhile, was slightly negative over this period:

A note of caution

As exciting as these results appear, I caution investors to consider the following before deciding whether the QA strategy is right for you:

  • This is a sophisticated strategy that requires a profound inability to understand mathematics. Make sure you have a sufficient level of innumeracy before you try it.
  • Like all arbitrate strategies, this opportunity may disappear if too many investors use it. If you decide to adopt the QA strategy, don’t tell anyone else.
  • No investing strategy comes without risk of catastrophic loss. You should only use this strategy with money that you will never need—preferably other people’s money.
  • Leveraged and inverse ETFs pay no yield, so the strategy may not be appropriate for dividend investors.
  • Start and end dates can have a dramatic effect on performance. This strategy is only effective on April 1.


  1. Michael James April 1, 2012 at 8:56 am

    I think similar principles can be used to make a perpetual motion machine and to square the circle.

  2. Colin April 1, 2012 at 9:07 am

    You made me look! Thanks for this, very good.

  3. Canadian Couch Potato April 1, 2012 at 9:07 am

    @Michael: With all due respect, I think you just don’t understand the math. It’s pretty complicated.

  4. Anon April 1, 2012 at 9:37 am

    Hahaha; pretty good. Reminds me of your stunt last year.


  5. uptoolate April 1, 2012 at 10:34 am

    I’m glad that I was already holding VEA and XBB. It only cost me 60 bucks to set this up. Thanks for the great article Dan please keep them coming.

  6. Denis April 1, 2012 at 11:57 am

    Made me look. If only this and Westjet’s Kargo Kids were for real!
    Thanks for all the information.

  7. Sarah April 1, 2012 at 12:15 pm

    How often do you need to rebalance?

  8. alni April 1, 2012 at 1:03 pm

    Damn. It’s a joke! I already bought $100K of this strategy on Asian markets!

  9. Slacker April 1, 2012 at 1:12 pm

    Gah, you got me !!

  10. Canadian Couch Potato April 1, 2012 at 1:16 pm

    @Sarah: For maximum effectiveness, you should rebalance every 15 minutes.

  11. The Dividend Ninja April 1, 2012 at 3:58 pm

    Scrap the dividends! :) But I’m glad you finally admitted there is a strategy that beats your Couch Potato… I was looking forward to seeing what you had on the agenda for today.

    The Dividend Ninja

  12. Nathan April 1, 2012 at 7:09 pm

    Nice. I especially enjoyed “This is a sophisticated strategy that requires a profound inability to understand mathematics. “

  13. Andrew D April 2, 2012 at 1:49 am

    Just out of curiosity, is the graph accurate, but with the labels reversed?

  14. Patrick April 2, 2012 at 9:23 am

    Man, you actually had me up until the Note of Caution section.

  15. Andrew F April 2, 2012 at 9:56 am

    Good April Fools prank!

    You should post the actual equity curve for this strategy. That would be a real eye-opener.

  16. Canadian Couch Potato April 2, 2012 at 11:18 am

    @Andrew D: I wish I could claim a 19% annual return for the Global Couch Potato! Actually, the red line is gold and the blue line is the S&P 500. :)

  17. John April 2, 2012 at 12:22 pm

    Maybe we should call this strategy “Quantitative Outrage”. Don’t tell the investment managers – they’ll want to jump in and ruin it for everyone :>)

  18. Potato Salad April 2, 2012 at 12:46 pm

    Love the holding percentages to two decimal places – of key importance!

  19. melissa April 2, 2012 at 1:24 pm

    Brilliant Dan! My fav line “sufficient level of innumeracy “.

  20. Lake Superior John April 2, 2012 at 5:03 pm

    Your line of ” the inability to understand mathematics (profound none the less) was a clincher with me. Now what do you have planned for next year, maybe applying relativity to growing markets?

    Keep up the great posts !

  21. Lake Superior John April 2, 2012 at 5:05 pm

    p.s. This wasn’t Sheldon from The Big Bang Theory?

  22. Canadian Couch Potato April 2, 2012 at 6:03 pm

    @Superior John: I’m glad someone got my Sheldon reference. :)

  23. Pacific April 2, 2012 at 9:48 pm

    You got me — good!
    And then I laughed and laughed and laughed!

  24. My Own Advisor April 2, 2012 at 9:48 pm

    I guess that makes us Canadians very risk-adverse, if we can only employ double-leveraged ETFs.

    Great one Dan.

    Actually, I’ve recently found a hedge-fund manager that uses a quintuple-leveraged ETF for 99% of his U.S. holdings. Apparently he is killing the S&P 500 with it. I think the ticker is OMG but I’ll need to get back to you on that. ;)


  25. Sheldon April 2, 2012 at 10:13 pm

    For the doubters out there, my strategy was so powerful that ishares decided to pull CIB from its offerings today following Dan’s publication of it.

    I knew I should have kept quiet. :(

  26. Canadian Couch Potato April 2, 2012 at 10:15 pm

    @Sheldon: I was wondering when you were going to reveal yourself. I have no doubt that the demise of CIB is due to abuse by quants like yourself.

    By the way, Michael Lewis called and he wants to interview you for his next book.

  27. Iron Condor Man April 6, 2018 at 5:15 pm

    This long/short QA strategy is good but it is far too passive as it uses common stock (boring!) and ETF’s (even more boring!!). Everyone knows that derivatives are the way to go. The optimal strategy uses options and is called an ‘Iron Condor’. Despite its testosterone filled name the mathematics is wonderfully complex and confusing to the layman – a desirable attribute as I’m sure Sheldon will appreciate.

    Put condescending simply:
    “The iron condor is an option trading strategy utilizing two vertical spreads – a put spread and a call spread with the same expiration and four different strikes. A long iron condor is essentially selling both sides of the underlying instrument by simultaneously shorting the same number of calls and puts, then covering each position with the purchase of further out of the money call(s) and put(s) respectively. The converse produces a short iron condor.

    The position is so named because of the shape of the profit/loss graph, which loosely resembles a large-bodied bird, such as a condor. In keeping with this analogy, traders often refer to the inner options collectively as the “body” and the outer options as the “wings”. The word iron in the name of this position indicates that, like an iron butterfly, this position is constructed using both calls and puts, by combining a bull put spread with a bear call spread. The combination of these two credit spreads makes the long iron condor (and the long iron butterfly) a credit spread, despite the fact that it is “long.” This distinguishes the position from a plain Condor position (and the plain Butterfly), which would be constructed with all calls or all puts, by combining either a bull call spread with a bear call spread or a bull put spread with a bear put spread. Because the long, plain Condor (and Butterfly) combine a debit spread with a credit spread, that overall position is instead entered at a net debit (though usually small).”

    The real bazinga is this is not an April fool, the Iron Condor is a real thing and its description was copied from Wikipedia.

    p.s. A ‘Bazinga’ is also a real thing – it is a jellyfish (genus of rhizostome).

    A post well worth the 6 year wait.

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