Position Sizing and Expectancy

So where does system development start?

Investors will be prepared to trade in situations when the odds are in their favor by properly understanding position sizing techniques and calculated system expectancies. A system that has been tested will have an approximate expectancy that will tell the trader how much will be gained or lost during each trade over a period of time. Using this knowledge, the investor will determine how much risk to undertake by calculating a position sizing algorithm which tells you how much to place on a specific trade. The word ‘algorithm’ sounds scary but I have developed very simple position sizing and expectancy spreadsheets that can be found through the links below. They can be downloaded, studied and tweaked without any advanced spreadsheet or mathematical experience.

Most traders look for three major factors when developing a system:

  • How much to trade on each position
  • The right odds or positive expectancy
  • Number of trades or how much opportunity the system presents

How do we Calculate Position Size?
We can determine how much to place on each trade by assuming a $100,000 account with 1% risk on each position. Using a basic trading approach, I will place my stops approximately 8% below the ideal entry area or pivot point. Please use more advanced methods for locating the ideal stop rather than a general 8% (I am doing this for example purposes only). Look for the ideal risk-to-reward setup based on recent support and resistance levels and set your stop and potential target accordingly.

$100,000 Account
1% Risk = $1,000
8% Stop Loss
Position Size will be $12,500

We calculate the position size by dividing the 1% risk by the 8% stop loss or $1000 / 8% = $12,500.

If the stock we are watching has an ideal entry of $50, we now know that we can buy 250 shares or $12,500 worth of stock. Our stop loss is $46 or 8% of $50 and our maximum loss is $1,000 of the original $100,000 portfolio.

What exactly is expectancy?
Expectancy tells you what you can expect to make (win or lose) for every dollar risked. Casinos make money because the expectancy of every one of their games is in their favor. Play long enough and you are expected to lose and they are expected to win because the “odds” are in their favor. Most games at a casino are completed in a short period of time so they can increase their odds of winning.

The same holds true for trading. If your expectancy is positive; you can make money with a certain number of trades within specified periods of time.

Expectancy is your profit percentage per win multiplied by your win rate minus your loss percentage per loss multiplied by your loss rate. I will use an example of Expectancy from Dr. Van K. Tharp’s Book: Trade your way to Financial Freedom:

Expectancy = (Probability of Win * Average Win) – (Probability of Loss * Average Loss) Expectancy = (PW*AW) less (PL*AL)

PW is the probability of winning and PL is the probability of losing.
AW is the average gain (win) and AL is the average loss

So let’s do an example using another basic approach (assume $12,500 per position, a $100,000 portfolio using 1% equity risk):

If my trades are successful 40% of the time and I realize an average profit of 20% but I lose an average of 5%, my expectancy is $625 per trade.

(0.4 * $2,500) – (0.6 * $625) = $1,000-$375 = $625

I lose 60% of the time yet I show a profit of $625 per trade. If I have a system that produces 65 trades per year, I would realize an annual gain of $40,625 (hypothetical scenario). A 40% gain on the original $100,000 (minus all commissions, fees, taxes and compounding).

Let’s look at the calculation one more time using only percentages:
PW: 40%
AW: 20%
PL: 60%
AL: 5%
(40% * 20%) – (60% * 5%) = 5.00%

What this tells me is that I have a positive expectancy of 5% or $625 per trade from the original $12,500. It doesn’t mean that I will make $625 on every single trade but my system will average a profit of $625 per trade over the course of a year with a combination of winners and losers. I can always make more trades or fewer trades in a year so my total profit will be adjusted accordingly.

Final Note:
I didn’t cover how to develop a trading system in this post but that was not the point. I will assume that you are already trading or possibly developing a system that can be applied to the techniques above. The techniques above are used by professional traders everyday; the same people that treat their trading as a business. To last in this game, you must think and act as a professional or they will eventually suck you dry like the rest of the amateurs on Wall Street.

Comments

  1. Thx for the spreadsheets. Have you used google spreadsheets before? You could post these up there as public spreadsheets and we could import. (for some non-office users ;) Anyways, just a thought. On a side note, should we also include commissions and estimated slippage for risk/position sizing?

  2. JM,
    I haven’t used Google spreadsheets but I will take a look for all non-office users! Yes, commissions and slippage is very important when making your true calculations! These two items can take a profitable system and turn it into a break-even or losing system.

  3. Chris,

    Thank you so much for generously offering the spreadsheets! They are very helpful to generate ideas and get us thinking more about how our trades fit in the larger structure of our trading system.

    Corey

  4. Great info and awesome spreadsheets. I have one question about the interactive portfolio spreadsheet. I noticed that it calculates total porfolio gain/loss but that won’t be accurate if I deposit funds into my trading account regularly (which I do). How do I work around this? Can I simply add and subtract % gains/losses throughout the year and that’s my figures? Thanks in advance for any help.

  5. Clark,
    You could modify the spreadsheet to include the additional funds and then calculate your returns based on a rolling balance. I am sure examples of this exist – if I see one, I will post it here in the comments.

  6. As Chris alludes, no one should use these spreadsheets to calculate position sizing. It is folly not to include commission.

    A 40% profit after several hundred trades can be a loss if 0.2% entry comm, and same for exit, is excluded.

    Leverage has to be considered.

    Chris, maybe you can increase the value of the education by including these considerations.

  7. Chris,
    In the portfolio spreadsheet, portfolio gain is calculated as average of %gain of individual positions,

    if i have 2 positions
    $1000 with 10%gain and
    another position $10000 with (10%) loss,

    is it correct to say portfolio gain is 0%, but in reality loss is $1000 and gain is only $100, the portfolio is in negative $900.

    thanks
    Srinivas

  8. Chuck Krug says:

    How do you do this for futures?

  9. some of our worl is eerily similar – I have developed and advanced Excel based risk management, position sizing and probability spreadsheet that may be of interst to you

    clikc on my blog link and there are a number of current tutorials
    I definitely take it to the next level so I hope you enjoy – hope to hear back from you and if not – best of luck trading !

    Brian

  10. Guruprasad V says:

    Thanks for this wonderful stuff. Really helpful for me. I’ve been working with it for more than couple of hours to formulate strategy for consistent profits for very long term period that could span for couple of decades. This is really helpful for me.

Trackbacks

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