Position Size to Determine How Many Shares to Buy

Let’s say (hypothetical): The market is trending higher. You find a stock to buy. You setup the proper risk-to-reward scenario.

So, how do you determine how many shares to buy?

Let’s setup a few hypothetical scenarios with three investors trading different size accounts.

  • Trader A has an account with $100,000
  • Trader B has an account with $50,000
  • Trader C has an account with $10,000

This exercise will teach novice investors how to properly position size their trades, preventing you from blowing-up your account or risking too much on one position.

These examples will buy the same stock (XYZ in this case) but we will do so with different stops based on different trade setups: 5%, 10% and 15% sell stop. The positions will also be placed in three different accounts. My free excel position sizing spreadsheet is the only tool I am using to determine the size of each position based on the entry price, sell stop (risk) and size of the account.

The number of shares change but the risk stays the same! Let me say that again, the number of shares change but the risk stays the same for all three traders.

Please note that these examples don’t consider other variables such as commissions, slippage, etc. Please read the book by Van K. Tharp to study the detailed models of position sizing. I will also like to note that it is very difficult to employ position sizing strategies with accounts smaller than $10,000 (even this is a small amount and can blow-out if not traded carefully).

Total risk of the accounts will be 2% in each scenario!

Trader A ($100,000 account)
Example #1:
Stock XYZ is trading at $60 per share
Portfolio size of $100,000
The stop loss is 5%
Risk will be $2,000 = ($100,000*2%)
Amount to Trade at 5% stop: $40,000 = ($2,000 / 5%)
Shares to be bought: 667

Example #2:
Stock XYZ is trading at $60 per share
Portfolio size of $100,000
The stop loss is 10%
Risk will be $2,000 = ($100,000*2%)
Amount to Trade at 10% stop: $20,000 = ($2,000 / 10%)
Shares to be bought: 333

Example #3:
Stock XYZ is trading at $60 per share
Portfolio size of $100,000
The stop loss is 15%
Risk will be $2,000 = ($100,000*2%)
Amount to Trade at 15% stop: $13,334 = ($2,000 / 15%)
Shares to be bought: 222

Trader B ($50,000 account)
Example #1:
Stock XYZ is trading at $60 per share
Portfolio size of $50,000
The stop loss is 5%
Risk will be $1,000 = ($50,000*2%)
Amount to Trade at 5% stop: $20,000 = ($1,000 / 5%)
Shares to be bought: 333

Example #2:
Stock XYZ is trading at $60 per share
Portfolio size of $50,000
The stop loss is 10%
Risk will be $1,000 = ($50,000*2%)
Amount to Trade at 10% stop: $10,000 = ($1,000 / 10%)
Shares to be bought: 167

Example #3:
Stock XYZ is trading at $60 per share
Portfolio size of $50,000
The stop loss is 15%
Risk will be $1,000 = ($50,000*2%)
Amount to Trade at 15% stop: $6,667 = ($1,000 / 15%)
Shares to be bought: 111

Trader C ($10,000 account)
Example #1:
Stock XYZ is trading at $60 per share
Portfolio size of $10,000
The stop loss is 5%
Risk will be $200 = ($200*2%)
Amount to Trade at 5% stop: $4,000 = ($200 / 5%)
Shares to be bought: 67

Example #2:
Stock XYZ is trading at $60 per share
Portfolio size of $10,000
The stop loss is 10%
Risk will be $200 = ($10,000*2%)
Amount to Trade at 10% stop: $2,000 = ($200 / 10%)
Shares to be bought: 33

Example #3:
Stock XYZ is trading at $60 per share
Portfolio size of $10,000
The stop loss is 15%
Risk will be $200 = ($10,000*2%)
Amount to Trade at 15% stop: $1,334 = ($200 / 15%)
Shares to be bought: 22

Please understand that the number of shares changed in each scenario based on the size of the portfolio as the risk remained constant at 2%. Now watch what happens when the risk is cut in half to 1% of the total account. We will use “Trader A” with the $100,000 account using 1% risk, a 7% sell stop and a buy of XYZ at $60 per share.

Trader A ($100,000 account)
Example #1a:
Stock XYZ is trading at $60 per share
Portfolio size of $100,000
The stop loss is 7%
Risk will be $1,000 = ($100,000*1%)
Amount to Trade at 7% stop: $20,000 = ($1,000 / 7%)
Shares to be bought: 238

Please feel free to ask questions!

Comments

  1. Hi, thanks for the examples, I am in the middle of this book and it’s a great read. My account started at only $5000 (that’s what I had), but I still emply this with options trading which usually lets me purchase one contract of between $100-$200. My recent post on VIP goes through that process for a current position.

  2. Excellent examples. A clearer way (I believe) of calculating the number of shares is:

    1. 5% stop loss on XYZ share of $60 is $3

    2. Max risk on $100,000 account is 2% or $2000

    3. No of shares is $2000 / $3 = 667 shares

  3. Hello, Chris. Thanks for the article. Something similar is also available in your portfolio spreadsheet, which is also very cool. I was only wondering why is the Exit Share Price included? Oh, and I also wanted to ask you, if you delete your positions from the Portfolio Spreadsheet after you sell them or do you leave them in? Thanks.

  4. Hey Chris, nice post and great blog!

    You mentioned that position sizing is tricky under 10k. Is it possible/advisable to use position sizing for a non-margin account that is under 5k?

    Thanks.

  5. When I sell maybe I’m wrong? If stock costs £3 buy £9000 = 3000 shares. Say up to £4 sell about 700 taking the profit. left with 2300 shares. Profit taken = £2800. That’s if stay the same. If they go up sell difference on price. Moves to 4.5 sell .5. You keep shares in case of large rise or if they drop you still have taken cash out. Clear? as mud. neil UK

  6. Terry Sandbek says:

    In the above example how an why did you pick 5%, 10% and 15% sell stops?

  7. Terry,
    For educational/ example purposes – that’s the only reason.

  8. Hi,

    Tharp has come out with a new book called Definitive Guide to Position Sizing. He uses a trade simulator to optimize position size based on the desired objective (e.g. 100% profit) and the trader’s personal definition of ruin (e.g. 33% loss of initial equity).

    You can use an equivalent position size simulator at http://www.afltools.com/positionsize.html to plug in your own objective/ruin for many of the examples in the book.

    It can be a real eye opener!

  9. Work out how much you want to risk in your trade (as low as possible) then divide that figure by the price of the stock.

  10. Stock Position Size Lite for iPhone helps traders trade at the optimal size, maximizing your gains and limiting your loss. And it is free!

    http://itunes.apple.com/sg/app/stock-position-size-lite/id436732505?mt=8

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