The Art of Expectancy: Defining Money Management & Risk Management

Discussion in 'Risk Management' started by tireg, Mar 20, 2006.

  1. tireg


    We all understand the idea of expectancy:

    Expectancy = (Probability of Win * Avg. Win Size) - (Probability of Loss * Avg. Loss Size)

    Namely, over the long run, with positive expectancy, your average winners will be greater than your average losers. Now... how does this relate to money management and risk management?

    1. Money management deals with optimizing or maximizing profit. IE the (Probability of Win * Avg. Win Size) part. In this sense, you can either increase your probability of wins or increase the average size of your wins, both while holding risk constant (in order to isolate this part of the equation).

    To increase win rate (and thus reduce loss rate), one can (a) create better entries, or (b) lower price targets to more probable hit rates; both increase probability of win. Option (b) has the added problem of reducing average win sizes.

    To increase average win size, one can (c) increase position size, thus increasing avg. win size but at the risk of increasing avg loss size, or (d) increase the price target of trades, therefore increasing average win size. But as the price target grows greater, the probability of it being hit before you are stopped out is smaller, which would serve to decrease win probability. As such, the fine line or 'art' part of this is finding the optimum win rate and avg win size targets. Again, this is all done while attempting to hold risk constant.

    2. Risk management deals with reducing or minimizing loss. IE the (Probability of Loss * Avg. Loss Size) part.

    In this sense, you can either (c) decrease your probability of loss or (d) decrease avg. loss size. As mentioned above, the only way to decrease your probability of loss is to increase your win rate or probability of wins. As such, the main part of risk management deals with part (d), decreasing your average loss size. In this aspect of it, one can set smaller (tighter) stops, but at the risk that they get triggered more often and actually increase probability for loss. Another aspect would be setting smaller position sizes, but this again comes at the cost of reducing average wins if the trade goes in your favor.

    Putting it together:
    Now that we've got the general idea of expectancy, we have to do three things:
    1. Find better entry points - usually dealt with by effective technical analysis and whatever entry criteria you use, timing is critical.
    2. Find the fine balance between setting price targets for profitable exit and stops to exit bad trades -- this will be different for everyone, depending on trading time frame as well as risk tolerance. This is the risk/reward aspect of it. (For me, this means ideally 2:1 or greater R/R)
    3. Find the optimum position size to take on when entering a trade or adding on to a trade. Again, different for everyone, as some like to scale into positions and some like to enter whole and scale out. Too great of a position size, and the risk will be high if you get stopped out -- this will increase your average loss size. Too small of a position size and the reward will be too small -- you're not maximizing your average win size. For me, maximum position size is found by my 2% risk per trade rule. I divide 2% of the entire portfolio by the risk per share/contract to get maximum position.

    Again, achieving these 3 things will be different for everyone, and that is why there is not a one-fits-all system. For most, once you decide what type of risk you're willing to take, then most things fall into place.

    Perhaps the hardest part of all of this is that these factors often change as the trade develops. The good part is, usually the downside doesn't change unless you start averaging down or *gasp* move your stop lower if you're long or higher if you're short... both generally very bad moves.
  2. Good summary.

    One correction:

    Not necessarily. Your cumulative wins need to be greater than your cumulative losses (i.e., profit factor over 1), for positive expectancy. Average win vs. average loss may be >, = or <, as you know.
  3. jordanf


    I think you are leaving off one important factor.

    You have considered things that effect expectancy, but one other factor affects profit.

    Profit = N*Expectancy, where N is number of trades. If you can increase the frequency of trading while keeping expectancy the same, you will generate greater profits.
  4. Or, a fact that is missed by many traders trying to develop the "Holy Grail", you can "loosen" your entry criteria to a degree and give up some expectancy if it results in enough additional trades to total more profits. That's the difference between "being right" and "making money".
    Most new or unprofitable traders focus too much on "being right", or looking for the "infallible indicator" because they can't handle being told by the market that they were "wrong" on a trade.
  5. tireg


    Thanks for the input, guys. I whipped this up last night around 3-4am.

    But totally agree with what's been said, namely that it's actually *cumulative* wins I meant.

    And indeed true that the way to maximize profit is to have maximize frequency of trading if you have positive expectancy. However, this then goes into the risk of overtrading and being overexposed to the market, a key aspect of risk management which wasn't mentioned.

    Also just found a fascinating article that goes in depth... touches on almost everything mentioned in the other articles floating around the internet, which are also of some value...

    Discusses expectancy, risk, effective risk management, Edward Thorp's advantage, Van Tharp's stories, and more money management, even asymmetric leverage, drawdowns, martingale and antimartingale systems, fixed lot sizing vs fixed fractional, etc.

    From the article:
    <i>"Van Tharp made an even more striking example. In an Asian Tour for Dow Jones Telerate TAG (Technical Analysis Group) he gave lectures in 8 cities before 50-100 listeners each time, most of them professional traders for large companies or banks that traded shares, bonds or exchange rates on Forex. In an analogous game over a half of highly professional traders lost!"</i>

    But my favorite:
    <i>"The most popular method of money management is no money management. There are three variants of it..."</i>
  6. BENG


    I believe only the expected profit factor and number of trades matter at the end.