Money Management ... and the Size of Trades

motivated by email from Dan M.
Suppose you have some scheme for buying and selling and you get a Buy signal, what do you do?
>What scheme?
It doesn't matter. Some BuySell strategy says: "Buy now." What do you ...?
>I buy, of course. That's a pretty silly question. I mean ...
You buy how much? $10K worth? 100 shares? How much?
>Uh ... if I really believed in the buy signal I'd buy lots.
Would you risk all the money you have?
>Are you kidding? What if the stock tanked?
Yes, exactly.
We usually talk a lot about buysell strategies and very little about "How much?"
See Figure 1?
You're interested in a stock that currently sells for $30.
You already have 1000 shares plus $20K in cash.
You also have a strategy which gives the Buy and Sell signals shown.
>What strategy?
It doesn't matter. The point is, in Figure 1, the number of shares we buy or sell is 5% of what we currently hold.
That is, if we have 2000 shares and our scheme says Buy, we buy just 5% of 2000 or 100 shares.
If our scheme says Sell, we sell 100 shares.
We never risk more than that. We ...
>So if the stock drops drastically, you don't have that much to lose, eh?
Something like that. You'll notice that our Portfolio had a lesser volatility and didn't suffer the same drops as the stock.
 Figure 1 
>And if the stock really took off? What then?
Okay, here's a few more examples. In each case we start with 1000 shares of $30 stock
(that's $30K in stock equity) and $20K in cash for a portfolio worth $50K.
We multiply the portfolio dollars by $30/$50,000 so we can plot this scaled Portfolio and compare to the closing price of the stock.
>I can't get too excited about that last chart. You shoulda put all your money into ...
Then, as soon as I did that, the stock would look like Figure 2
... and my portfolio would follow the stock chart.
>Yeah, that always happens, don't it? Okay, but what's that BuySell strategy?
You may ask "Why 5%?"
Why not trade 2% or 10% of your holdings?
>No, I'm asking what's the BuySell strategy you're using!
If you're aggressive, you might pick 10%. If you're conservative you might pick 1%.
Note that we're calling this “money management”, defined as "how much of available capital is to be allocated in a specific market position", also called position size.
 Figure 2 
A common form of fixed fractional trading goes like this:
 If you expect a worstcase "possible" loss per share of $L and you trade N shares, you might expect a possible loss of $L*N (for an Nshare trade).
 If you insist that this be no greater than a fraction f of your equity (worth $E), then you'd have: $L*N = $f*E.
 That means you should trade: N = f*E / L shares per trade.
For example, if we are prepared to lose no more than L = $5 per trade and we have E = $30,000 in stock, then we should trade N = f*E / L = f*30,000/5.
Using a 5% fraction, so f = 0.05, we'd get: N = 300 shares per trade.
>Hey! For a $30 stock, that's 300*$30 = $9,000 for a single trade. Isn't that a bit much?
It's agressive, especially designed for them that don't mind risk.
I understand that the most common figure is f = 0.02, or 2% of your Equity, so N = 0.02*30,000/5 = 120 shares, worth $3600.
I should also point out that you can consider a fraction f of your total portfolio
(including cash) or a fraction f of your equity dollars
or a fraction f of the number of shares or ...
>Yeah, I understand ... it's up to me. If I use N = f*E / L, I'd be increasing the number of shares traded as my Equity increased, right?
Yes.
If the stock is trading at $60 per share, and you put in a stop loss at $58 (so you'd automatically sell if the stock drops from $60 to $58),
then you can lose no more than L = $2.00 per share.
If you're Equity is $25,000 and you're using f = 0.02, or 2%, then your trade size should be no more than 0.02*25,000/2.00 = 250 shares.
If the stock price doubled (and you kept L = $2.00 loss per share) then the trade size would double.
>So how do I know whether to do the 2% or 5% or ...
Well, for one thing, you can play with this spreadsheet:
Here's what you can do:
 Pick some Mean Annual Return and Standard Deviation (or Volatility) in cells E1 and E2.
 Pick some starting stock holdings (in cell O3) and cash (cell R3).
 Pick your favourite trade percentage (cell O4).
 Monies held in Cash grow at an annual rate. You stick that in cell R4.
 Click the button which says: Click Here ... and get a few dozen randomly generated daily returns (using the Mean and Standard Deviation you specified).
 Keep pressing that button and gaze in awe and wonder at the chart.
>That's always a $30 stock, right?
Well, it starts at $30, but ...
>And you Buy and Sell according to what scheme!
Buy low, Sell high.
>Very funny. Are you going to patent that scheme? What if I wanted to look at a real live stock, not a fictitious one where you randomly ...
You can play with this spreadsheet:
It's as before, except you type in a stock symbol (in cell B4) then click the Button to download a few dozen daily prices.
>Okay, but what if I want more than a few dozen prices and what if I want to change the BuySell scheme and what if ...?
That's your problem
... you gotta change the stuff in columns M and N.
>What if I wanted a different prescription for the size of trades or maybe consider a percentage of the TOTAL portfolio rather than just the stock component or maybe ...?
Just google.
>But what if ...?
zzzZZZ
>But what if you randomly choose daily returns a jillion times, sorta like Monte carlo and ...?
zzZ huh? Good idea! I've added a piece like so:
When you click the Monte Carlo button, you repeat the procedure noted above (selecting a bunch of random returns) a bunch of times
(100 times, in the example shown).
The percentage of times that your Portfolio beat the Stock is calculated.
>So I can change the Mean Return and Volatility and percentage and other stuff, then do another Monte, eh?
Why not? It's great fun!
to continue
