motivated by email from Dan M.
Money Management ... and the Size of Trades
Suppose you have some scheme for buying and selling and you get a Buy signal, what do you do?
It doesn't matter. Some Buy-Sell 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?
>And if the stock really took off? What then?
We usually talk a lot about buy-sell 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.
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.
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.
A common form of fixed fractional trading goes like this:
>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 Buy-Sell strategy?
You may ask "Why 5%?"
Why not trade 2% or 10% of your holdings?
>No, I'm asking what's the Buy-Sell 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.
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.
- If you expect a worst-case "possible" loss per share of $L and you trade N shares, you might expect a possible loss of $L*N (for an N-share 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.
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?
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:
>That's always a $30 stock, right?
- 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.
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 Buy-Sell 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 ...?
>But what if ...?
>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!