The Myth of Scaling Out

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Photo by Winnifredxoxo. Used under Creative Commons License

A common tactic for some traders is to scale out of successful positions. The logic is this: I’ve already made some money, so I want to hold onto some of that. I’ll cash out a portion of my trade now, and see how the trade continues, but with reduced risk. You see this behavior with day traders, as well as long-term investors.

But it’s a fallacy.

And it’s costing you money.

[important update: this example system I created does not compound returns. Blog reader Adrian pointed out in the comments that the results may be very different for a compounding system. I will cover that in a future post. At this point I can only say confidently that the “myth” applies to non-compounding systems.]

Let’s devise a thought experiment to isolate the scaling out portion of a successful trade.

Imagine you have a trading system where you can invest $100 each time (no commissions or fees), and are guaranteed to double your money the first day. Pretty cool, huh? But the second day’s trade is a toss-up: you have a 50/50 chance of either doubling your money again, or cutting it in half (bringing your position back to your starting point). You have to exit after that second day, regardless. Here’s a diagram to demonstrate that:

scale-out-dia-1

But then you realize you could hold onto some of those winnings by scaling out. So after your guaranteed-win day, where you double your money, you decide to cash out half (your original investment of $100) and let the remaining $100 ride. That remaining $100 has the same 50/50 chance of either doubling or being cut in half. You’d either end up $300 or $150 (i.e. [ $100 + ( $100 * 2) ] or. [ $100 + ($100 / 2) ] ).

scale-out-dia-2Oh sure you don’t make as much profit, but you also don’t suffer as much loss. How would that look over time?

I generated 10 equity curves each for the normal “all in” system and the scaling-out system, with a random 50% chance of winning that second leg of the trade. The red lines are the “all in” system, and the blue lines are the scaling-out system.

Screen Shot 2016-04-06 at 9.37.03 AM
50/50 chance of continued success

 

“Yeah okay Matt, but my system isn’t just due to chance. I’ve got an EDGE! My second leg is going win 55% of the time!”

So what? You’re still leaving money on the table if you scale out. Here’s what a bias toward winning looks like.

Screen Shot 2016-04-06 at 9.36.49 AM
55% chance of continued success

 

“But Mr. Haines, I’m scared. My system makes money, but that second leg…it’s a sketchy thing. It only works 45% of the time. I want to be conservative and hold onto some of my winnings.”

Here’s what those equity curves look like when the win rate is biased to only 45% of the time. The lines are closer together, but the “all in” system is still superior to the scaling-out system.

Screen Shot 2016-04-06 at 9.36.55 AM
45% chance of continued success

 

At this point you might be thinking to yourself: hey, that’s all very tidy to have things double or half, but that’s not realistic. What if the returns are asymmetrical? What if the losses are higher than the gains?

Let’s devise a crushingly risky system. You invest $100. You’re guaranteed to make $100 that first day. But day 2 can give you a smack in the behind. It still has a 50/50 win/loss likelihood. If it wins, you double your position. But if you lose, your position is reduced to 20% (i.e. x 0.2). No longer can you be guaranteed to hold onto your first day’s winnings.

The all-in system:

• invest $100
• day 1: guaranteed doubling to $200
• day 2: your position is either $40 or $400

The scale-out system:

• invest $100
• day 1: guaranteed doubling to $200. You sell half and keep $100.
• day 2: your remaining position becomes either $20 or $200, for a net of $120 or $300.

50/50 chance of winning, with asymmetrical win/loss size.
50/50 chance of winning, with asymmetrical win/loss size.

Was that what you were expecting? I’ll bet not. Yes the lines for each system wander further afield in this system, but the all-in system still beats the scale-out system. Even with the asymmetrical skew toward bigger losses.

If you’re considering the use of scale-ins or scale-outs in your trading system, it’s imperative that you treat each leg as a separate trade (with the corresponding reduced position/commission ratio, different signal quality etc). If you think that a system showing momentum is likely to continue showing momentum, then you’re better off staying all-in than reducing your position size. And conversely, if you think it’s going to fail, then get “all out”!

Perhaps there are instances where scaling in and out are in fact more profitable. If you can cite some examples (preferably not just anecdotal, although those can be fun too), please do so in the comments!

 

5 thoughts on “The Myth of Scaling Out”

  1. Just a quick example, I gotta go, but I’ll revisit your post later. There should be something wrong in the way you formulate the problem.

    I’ll iterate twice through the entire interval day 1 – day 2 – day 3. Because day 2 is a 50/50, I will lose once (cut my money in half), I will win once (double my money). I will start iteration 1 with 100, and iteration 2 with the result of iteration 1.

    Scenario 1 “no scaling out”
    Iteration 1
    Day 1: 100
    Day 2: 200
    Day 3: 400 (on day 2 I was lucky)

    Iteration 2
    Day 1: 400
    Day 2: 800
    Day 3: 400 (on day 2 I was unlucky)

    Scenario 2 “scaling out is used”
    Iteration 1
    Day 1: 100
    Day 2: 200
    Day 3: 300 (on day 2 I was lucky)

    Iteration 2
    Day 1: 300
    Day 2: 600
    Day 3: 450 (on day 2 I was unlucky)

    1. Hi Adrian, and thanks for your comment.

      In the example you give, you’re compounding returns and investing the entire account each time. My example has a position size of $100 each time. Day 1 is always a $100 buy.

  2. You can easily generalize the results and figure out an optimal strategy mathematically.

    Say that on day 0, I invest $100 which double on day 1. I take out $X (X = 0 being then all-in). The next day, I have a probability p of my investment being multiplied by a > 1 and a probability (1-p) to have it divided by b > 1 (Your original scale-out strategy being then X = 100, p = 0.5, a = b = 2).

    You can then estimate the expected return and check in what cases the all-in strategy beats the scale-out. It turns out that X is irrelevant (it will impact of course your expected return – but it is irrelevant regarding which of the two strategy performs best given p, a and b). This first of all confirms that there is no point to scale out. You either want to be all-in or all-out. And the criterion to be all-in is that p >= (b – 1)/(a*b – 1).

    In your original example, you want to be all-in if p >= 1/3, which is the case (p = 50%). In your crushingly risky system, you have a = 2 and b = 5, so you need p >= 4 / 9 ~ 44.4%… which is still true and you should still be all-in.

    In fact with p = 50% and a = 2, scale-out can never beat all-in no matter how bad the downside can be….

      1. (re-posting my comment, because the comment area doesn’t like ‘greater than’ and ‘smaller than’ signs)

        tl;dr
        My conclusions: if you don’t compound – don’t scale out; if you compound – it doesn’t matter (but it’s debatable).

        Just to be clear, because when I first read Oliver’s comment, I understood something else: we have this inequation p >= (b – 1)/(a*b – 1) [A].
        If [A] is true, then ‘no scaling out’ is better.
        If [A] is false, then ‘using scaling out’ is better.
        But note that this logic should be used when your goal is to maximize your profit (or to minimize your loss) _without compounding_.

        If you’re wondering what should you do in order to maximize your profit _using compounding_, then we have this inequation 2 < [(1 + 1/a)**p] * [(1 + b)**(1-p)] [B] (** means exponent, 2**3=2*2*2=8) (my math skills stop me making this inequation look nicer, or drawing more subtle conclusions)
        If [B] is true, then ‘using scaling out’ is better.
        If [B] is false, then ‘no scaling out’ is better.

        Even if it may look somehow counter-intuitive (at least for me, it was), the 2 inequations [A] and [B] are not equivalent (I mean: they don’t always send the same message). For instance, for Matt’s initial example, where p=0.5, a=b=2, if you don’t want to compound, it’s better not to scale out, but if you plan to compound, scaling out is better.

        The bigger the arithmetic average of strategy’s returns, the bigger the not compounded profits.
        The bigger the geometric average of strategy’s returns, the bigger the compounded profits.
        But note: if a set of numbers has the arithmetic average bigger than another set of numbers, it doesn’t imply that the same is true about their geometric averages. For instance, the set [1, 49] has the averages 25 (arit) and 7 (geom), and the set [10, 10] has the averages 10 (arit) and 10 (geom). That’s the reason why having 2 strategies (with scaling out and without scaling out), depending if we want to compound or not, the optimal strategy may be different.

        But Matt, your scenario is a bit too specific and somehow confusing. The fact that you have $100 that always double is irrelevant and should not matter. If we try to find out if scaling out is a myth or not, we only need to know that we have $200, with a 50/50 chance to double or cut in half. How you got that $200 (in our case: by doubling your initial $100) shouldn’t be an input in our problem.

        I would try to answer this question if scaling out is a myth for a more general and more realistic scenario. (There’s no reference to scaling out in the sacred writings, this would be the first clue that this is not a myth.)

        Let’s say we have a strategy and the n returns for each trade are: r1, r2, .., rn (ri will be percentages like 10%, -5% etc)
        The arithmetic average of strategy’s returns is: r_arit_avg = (r1 + r2 + .. + rn)/n
        The geometric average of strategy’s returns is: r_geom_avg = (rg1 * rg2 * .. * rgn)**(1/n) (where rgi = (100+ri)/100; so, if ri=10%, then rgi=1.1)

        Presuming you can know beforehand when you will close a trade, I define ‘scaling out’ as closing half of your position at the temporal middle of your trade (middle time between the open and the close of the trade) and keeping the other half til the trade closes.
        I would argue it is reasonable to assume that this statement decently approximates the reality (or at least, is useful for our current thought experiment): over a very large number of instances, the ‘scaling out’ price, the price at which you will close half of your position, will be the mean of trade opening price and trade closing price. A ‘scaled out’ trade (taking into accounts both halves) will have a return (profit or loss) of 75% of the same, but not ‘scaled out’ trade. For instance, we have a stock that trades at $100 when you buy it, at $200 when you sell it, and (based on our assumption) at $150 at the ‘scale out’ moment. Without scaling out, your profit will be $100 (or 100%), if you scale out, profit is $25 + $50 = $75 (or 75%). The same happens with a losing trade: if the loss for ‘no scaling out’ is -50%, the loss for ‘with scaling out’ is -37.5% (which is 75% of -50%). Leaving aside when exactly during the trade we will scale out and what exact % of the position we’ll close by scaling out, generally, on average, after multiple runs, what ‘scaling out’ does is making our both profits and losses smaller.

        A. If you don’t want to compound (but you should, ask Einstein or Buffet if you don’t believe me)
        A1. if r_arit_avg < 0, no sense to trade, your strategy will lose money
        A2. if r_arit_avg > 0,
        A2a. no scaling out – your profit will be [amount invested] * n * r_arit_avg
        A2b. using scaling out – your profit will be [amount invested] * n * r_arit_avg * 75%
        So, it doesn’t make sense to scale out.

        B. If you want to compound
        B1. if r_geom_avg < 1, no sense to trade, your strategy will lose^ money
        B2. if r_geom_avg > 1
        Should we scale out or not? For a reasoned answer, we need to determine if this inequation is true or false: (100+r1) * (100+r2) * .. * (100+rn) > (100+0.75*r1) * (100+0.75*r2) * .. * (100+0.75*rn)
        Unfortunately, I don’t know how to solve that, and maybe there isn’t one single response, maybe it depends on the actual set of returns r1, .., rn (their exact values, their variance etc).
        Doing some tests, with some randomly chosen returns, I noticed that sometimes you should scale out, sometimes – not. But I didn’t see a pattern. But leaving aside profit maximization, the benefit of scaling out would be that, because of the smaller profits and losses, the portfolio curve will be smoother, the drawdowns will be smaller.
        I defined ‘scaling out’ in certain way. But there are other ways. See Adam Grimes’ 1R profit target scaling out (http://adamhgrimes.com/blog/trade-exits/). Is that useful? I have to think about it. What’s interesting about this scaling out at 1R is that by doing so, you can transform some losing trades into break evens (of course, this could happen when applying my ‘scaling out’ rule, but in Adam’s style, (also depending on the nature of your strategy, how you define 1R etc) this could happen more frequently.)
        B3. if r_geom_avg >> 1, just send me the rules of your strategy, and I will be your devoted friend forever!

        ^ – not necessarily true, Kelly formula may give you a fractional position size that would make the strategy profitable

        (Note that I just ignored things that could complicate this discussion: position sizing, holding multiple positions simultaneously, and other things that I ignored without even being aware that I ignored them.)

        I would really like someone to point out any eventual logic mistakes in my comment.

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