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Combine Two Losses To Make a Profit at Trader’s Narrative

Combine Two Losses To Make a Profit

Wouldn’t you love to take all your losses and combine them to magically create a profit?

Parrondo’s Paradox says this is theoretically possible. According to Parrondo’s paradox, two games guaranteed to make a player lose all his money will generate a winning streak if played alternately.

In other words, alternate between listening to Jim Cramer and listening to Richard Bernstein ;-)

Although it certainly wasn’t invented because the physics professor, Juan Manuel Rodríguez Parrondo, was seeking stock market profits, it has gone on to inspire wide ranging ramifications including the mechanics of evolution and managing investment portfolios. Before you get excited though, bear in mind that the two “games” have to be related to one another before the paradox has any effect. Here’s a visual representation of Parrondo’s Paradox.

From the New York Times article:

Economists are studying Parrondo’s paradox to help find the best strategies for managing investments. Dr. Sergei Maslov, a physicist at Brookhaven National Laboratory in Upton, N.Y., recently showed that if an investor simultaneously shared capital between two losing stock portfolios, capital would increase rather than decrease.

“It’s mind-boggling,” Dr. Maslov said.

“You can turn two minuses into a plus.” But so far, he said, it is too early to apply his model to the real stock market because of its complexity.

I do remember reading somewhere that two trades which by themselves can be unprofitable, can be combined to create a profit. I think it was in the Wizards series by Schwager where a trader was talking about options. I never quite understood how this was possible. Maybe he meant Parrondo’s paradox. Does anyone recall that excerpt? ring any bells?

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9 Responses to “Combine Two Losses To Make a Profit”  

  1. 1 Andrew

    There is this quote from Jeff Yass in the Wizard series.

    “If you invest and don’t diversify , you’re literally throwing out money. People don’t realize that diversification is beneficial even when it reduces your return. Why? Because it reduces your risk even more. Therefore, if you diversify and then use your margin to increase your leverage to a risk level equivalent to that of a non diversified position, your return will probably be greater.”

    I am aware that adding a net losing system to a trading system mix can improve overall profitability, all depends on how they correlate. Haven’t heard the idea that you can make money when all systems are net losing though, amazing.

  2. 2 Eyal

    Very interesting. It reminded me of a somewhat related post by acrary on where he says something along the lines that after many years of trying to tweak and find the best trading systems on a tactical level he realized that all he needed to do was combine several system strategically (trend, counter trend, etc.) and just let them all run.

  3. 3 yo

    Somehow, I’m not surprised that the “evolution” people also believe this theory.

  4. 4 Tyro

    It’s an interesting puzzle, but it requires problem domains that rigid and specified, and the means of combining them is based upon this knowledge. If we had this in trading, then we wouldn’t have to worry about combining two losing strategies, we would win every time.

    As an example, we might have two losing strategies:

    S1: If it is tuesday, buy 100 SPY at open. If it is Thursday, sell 100 SPY at open
    S2: If it is Monday, buy 100 SPY at open. If it is Wednesday, sell 100 SPY at open

    Over a given two month period, the strategies may both be losers, but the strategy:

    SA: If the week is even, trade S1; if the week is odd trade S2

    may be positive. This isn’t because this new strategy is any better, but because of how the market happens to have traded, SA captures the best moves of S1 and S2 while cutting out their worst losses.

    As you said, the key to Parrondos Paradox is that when you join the two strategies, you aren’t trading both simultaneously, you are trading them alternately.

    I don’t think this will be any help to traders any time soon.

  5. 5 Tyro

    I tried to check what Maslov wrote and I found the original citation. It is an article in the International Journal of Theoretical and Applied Finance, 1998, called “Optimal Investment Strategy for Risky Assets.” I wasn’t able to find the original online, but I found other academic papers which summarized his findings.

    In the case of Maslov who was mentioned in the NY Times article, I don’t think the NY Times quote is accurate. What he showed is that the value of a portfolio could increase in a bear market by periodically (even daily) rebalancing a portfolio so that the gains from stocks which have gained in value are distributed to underachieving stocks. The resultant strategy “could outperform ‘Buy-and-Hold’ strategies.” Sounds like a mean-reversion strategy where you sell your winners and buy more losers, which will make money in some cases. Presumably if one ignores slippage, commission, fractional shares, price shocks, or the case that some stocks turn around and start to appreciate, then this frenetic rebalancing will out-perform a buy-and-hope strategy where all of your stocks are losers.

    Pppbbttt… Academics. Sounds interesting in an abstract sense, but I’m not surprised that Hedge funds aren’t scrambling to trade it.

  6. 6 Babak

    thanks for looking it up but the one rattling around in my mind is another one.

    sometimes paradoxes are the only way to go. ‘Logic’ can only take you so far.

    I contacted Maslov to see if he’s come up with anything since then. When/if I hear from him I’ll write about it. I do agree with you though, unless I’m missing something really big, I don’t think this has practical application to trading. Maybe Curtis could shed some light on this.

  7. 7 Tyro

    Babak, thanks for going the extra mile to answer these questions (and for posting it in the first place, I hadn’t heard of it before). I hope something comes up, but I fear it’s like the “Efficient Market Hypothesis” :)

  8. 8 Tom

    I’ve been something similar to that, I call it the George Costanza trading method (ala The Summer of George). You just do the opposite of what you’ve been taught to do I started trading FOREX and got beat up early this month using the 1% risk positioning size rule. I would watch as I get stopped out (and lose 1%) only to see the currency rally a short time later.

    Well I started doing things opposite, I stopped using stops and not using 1% position size and it seems to be working. Weird huh?

  9. 9 GH

    If the Visual Representation linked above is a fairly accurate representation of the Paradox, then the way it applies to trading is obvious. However, the knowledge necessary to apply it is no different than the knowledge necessary to win in the stock market anyway, plus an additional ability - to construct two portfolios that are reliably 180 degrees out of sync with each other.

    Specifically, your capital is invested in a given portfolio only when that portfolio is in the middle of one of its upturns. Then you switch to the other. So the fact that both portfolios are in long-term downtrends doesn’t matter; you only catch the upticks in each.

    The out-of-sync part is trivial; simply have one portfolio short whatever the other portfolio is long.

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