Money Management

It has been almost a year since my last post.  I have been far too busy getting a new trading desk up and running.   I  thought to discuss money management, since am revisiting right now.

Overview

It is easy to think that trading signal is the most important aspect of a trading strategy, but money management (and execution) can be even more important.   Loosely defined, money management is a mechanism for position-level risk management.  The mechanism attempts to regulate, accomplishing a number of things:

  1. ride out a profitable signal as long as there is continued profit potential
    1. close out a profitable position when the p&l is drifting sideways
    2. close out a profitable position, alternatively when there is a drawdown
    3. otherwise, allow the position to continue to profit, even through transient negative noise
  2. close out our losing positions as quickly as possible
    1. close position once we have a view that it is unlikely to be profitable
  3. close out strategy if seems unstable
    1. for example keeps hitting stop-loss
    2. risk measures indicative of unstable market situation for strategy

A desirable feature of a money manager is that when pairing the money manager and signal together, we have a return distribution with positive skew and very limited negative tails.   We can even have a signal with < 50% wins, but because of the generated bias in + returns / – returns, have an overall positive equity curve.   Of course I would advocate for much a much higher win ratio than 50% ;)

Signal → Position

I take the approach of having a trading signal that scales between [-1,1] or [0,1] on a continuous basis.   In my trading systems the money manager not only works as a risk manager, but also decides how to scale the signal into a desired position.

For example, if our maximum position is $5 million, we might scale our desired position from 0 to $5 million (if the signal reaches full power at 1).  The 0 or close to 0 level would indicate being out of market, 0.5 being at 1/2 strength or 2.5 million in.   Here is an example signal from 0 to 1:

Trading signals can be noisy, though we do our best to provide smooth signals.   Without regulation of how we map the signal to position size, the up and down dips in the signal would imply thrashing in and out of position, which would be costly.

Hence, we should try to enforce direction monotonicity, so as to avoid thrashing.

Types of stop-loss

There are a number of stop-loss types we should consider:

  1. stop-loss:
    1. stop when (smoothed) equity curve has reached a negative return threshold
  2. stop-profit:
    1. exit an up-to-current profitable trade, but one that has lost some % from the high
  3. stop-drift
    1. a time and slope based stop that closes out a position whose equity curve is drifting more-or-less sideways for a significant period

Risk Reentry Avoidance

On a stop-loss not only want to close the position, but also have to “back away” from the signal, such that we do not immediately get back into an undesirable situation.   Depending on why we exited the position, we may want to:

  1. disable market entry until the signal has gone to zero
  2. impose a time penalty
  3. impose a market reentry restriction (wait for the market regime to reach a certain stage)

A FSM

Here is a finite state machine that illustrates a possible state system guiding position scaling and money management:

The state system expresses some of the above money management features.   To make it effective, one needs to be clever about deciding on whether a negative movement is a sign to get out or a transient movement.   One can use a combination of signal, smoothed series, and aspects of order book and trade data to have a better read on this.

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12 Comments

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12 responses to “Money Management

  1. Ian Burris

    Glad to see a new post :) I’m extremely interested in computational investing and enjoy reading all your posts. Keep them coming!

  2. Tobias

    Good to see you posting again. I’ve been following your blog for a few years now and got some nice ideas from your musings. Interesting to see you posting on money management – I guess it reflects the overall sentiment in the industry at the moment as opposed to, say, 2009 and early 2010 ;) when the (main) focus was a different one. BTW, I was also wondering if you ever took your ideas on the UKF from your posts last year any further – ie into prod?

    • tr8dr

      Well, money management has always been important. I just never wrote about it previously. That said, there are different money management approaches depending on strategy. This particular approach is most appropriate for medium frequency trading, and not necessarily HFT. With HFT, take a different approach.

      As for the UKF, I use state systems where appropriate. However, I more often than not use machine learning or reinforcement learning approaches than SDEs.

  3. Good to see you back blogging again.

  4. Scott

    any thoughts on combining HFT and MFT? If the HFT signal says profit +1.0 to sell now, but the MF showing a +2.0 profit to sell later..any thoughts on a framework to combine the different signals? even 2 different medium frequency strategies with different time horizons would have the same issue, I’ve looked at having them trade against each other in product but often one strategy cannibalizes profit from another and the PNL of both is inaccurate.

    • tr8dr

      Good question. I often try to build signals that are a combination of short-term and longer term views. We all know the adage of letting your profitable trades ride and dropping non-profitable asap.

      There are multiple problems though:

      – execution for MFT signals is often aggressive
      – execution for HFT is almost always passive
      – HFT signals are more reliable, so have different error / confidence
      – MFT signals can carry more capacity

      One can create a mini optimisation problem that tries to maximize return / risk against some capacity target.

      One can even look at a 2 part SDE that describes the expected drift / MR for the HFT component + error, and the expected drift / MR for the MFT component + error.

      The error of the MFT portion will generally be larger, hence with enough imbalance between the errors, one might prefer to trade the HFT signal and close out, not using the MFT signal in that scenario.

      On the other hand, the return / risk for the MFT signal may be advantageous, so use the HFT to get cheaper entry in the same dir of the MFT signal and play it out.

      Definitely worth some study.

  5. Ken Jarrad

    Could you describe how you allocate capital across positions in a portolio? For example, you might use fixed fractional or mean-variance. For me this is more difficult than entry/exit signals. My goal is to benefit from diversification while being wary of high positive correlation. My goal is also to avoid ruin, of course. Smoothness of the equity curve is ‘nice to have’ goal.

    • tr8dr

      Ken, yes, portfolio allocation or allocation across strategies is a much harder problem than money management. The mean-variance approach often fails as it makes some unreasonable assumptions:

      1. prior mean return is a predictor of next period return
      2. covariance structure is stable

      There are other approaches, both statistical and ML based that I favor. I’ll try to do a post on this early next year or sooner.

  6. S

    There might be a way to extract some useful info from the equity curve itself.

    • tr8dr

      Yes, I agree. Indeed money management falls into:

      – measures on equity curve
      – signal
      – orderbook & price information

      • S

        So you are taking the second approach? I’ve seen your comments on using ML (supervised learning) on position sizing. What’s the conceptual framework there. Thanks,

  7. Riccardo

    Hi,

    I think this is very much of interest.
    A hint on combining signals would be using bayesian model averaging (or similar) to combine multi step ahead forecasts.

    I personally did not have much luck looking at the equity curve trend, but smoothing the portfolio position saves you a lot of transaction costs.
    I managed to make a portfolio of medium freq (CTA type) strategies very resilient to slippage.
    Your are right it works.

    I also favour vol targeting but it does not work for everything.

    Cheers

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