|
PureBytes Links
Trading Reference Links
|
Betting your minimum amount (2.5%) of total equity on each given trade seems fine
if you are only trading 15 or less Model/Market combinations (a unique model or
trading system applied to a given market). With 15 Model/Market combinations at
2.5% risk, you would never have more than 37.% of your total equity at risk at
any given time. What happens if you are trading 2 models on 25 markets (50
Model/Market combinations)? In this scenario, you could have more than your
account value (125% of equity) at risk at any given time. The numbers only get
worse as you add markets or add models (and these number only reflect your most
conservative 2.5% risk as opposed to your more aggressive 5.0% risk). How do you
address this potential problem?
Best regards,
Andrew Peskin
Mark Johnson wrote:
> I posted this to a local futures trading discussion group
> last weekend, and it got a positive response. So I thought
> it might also be useful to at least a few omega-list readers.
> Special note: for those packrats who zealously snarf and
> hoard trading-related computer programs, IT CONTAINS CODE.
> Woo hoo!
>
> >Date: Sat, 28 Oct 2000 06:32:04 -0700
> >From: Mark Johnson <janitor@xxxxxxxxxxxx>
> >Subject: Betsize Selection: how I trade my real-money account
> >
> >Roger has badgered and cajoled me into posting
> >this article. I originally wrote it for a newsletter named
> >_Club_3000_News_, and it was published in April 1999.
> >
> >The Figures referred to in the article, and a lovely Microsoft
> >Word formatted copy of the article, are available on the world
> >wide web. You can download them from the address
> >
> > http://www.mjohnson.com/omega-list/betsizMJ.zip
> >
> >Besides the articles and the figure, you get a PERL program
> >that implements all of the math calculations in the betsizing
> >algorithm. This program is exactly what I use, every single
> >day, in trading my real-life, real-money account. It's
> >a relatively simple little thing: 42 lines long, and 15 of
> >those are blank lines or comments.
> >
> >Hope you enjoy it. -- Mark Johnson
> >-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_
> >
> >
> >Reprinted from _Club_3000_News_ #99.04 April 24, 1999
> >
> >A formula for betsize selection -- Mark Johnson
> >
> >I trade futures using a 100% mechanical approach that has two
> >separate components: (1) a system of entries and exits; and
> >(2) a betsize selection formula. The first component generates
> >my trading signals: buy tomorrow at 127-19 stop, exitshort
> >tomorrow at market, etc. The second component tells me how
> >many contracts to buy or sell, each time a trade entry is
> >signalled. Entry and exit signals are thoroughly covered in
> >books, magazine articles, and commercial software packages, but
> >discussions of betsize selection are relatively scarce,
> >particularly when a diversified portfolio of markets is traded
> >out of a single account. I thought readers might enjoy seeing
> >an example of a betsize selection method for trading multiple
> >markets simultaneously.
> >
> >Whenever my system generates an entry signal in any of the
> >markets I trade, I use the following equation for betsize
> >selection:
> >
> > N = 0.025 * (E / R1) * A
> >
> >The formula has one output value (N), and it has three input
> >values: (E, R1, A). The output value N is the number of
> >contracts to buy or sell for this entry signal in this market.
> >N is the betsize, expressed as a number of contracts.
> >
> >The number E is the total account equity in dollars. It is the
> >sum of cash in the account, plus T-Bills, plus open trade
> >equity of all positions in all markets.
> >
> >The number R1 is the Single Contract Risk of this trade, in
> >dollars. R1 is the amount of money I could lose on a one-lot,
> >if the market immediately went against my position and smoothly
> >ran all the way to my stoploss price, where I then exited with
> >a loss. For a long trade,
> >
> > R1 = (EntryPrice - StopLossExitPrice) * BigPointValue
> >
> >BigPointValue is the dollar value of a price move of 1.000 in
> >the market; in Coffee it is $375, in Crude Oil it is $1000,
> >etc. For a short trade,
>
> >
> > R1 = (StopLossExitPrice - EntryPrice) * BigPointValue
> >
> >Notice that I have to calculate R1, the Single Contract Risk,
> >the night before I enter the market. Therefore "Entry Price"
> >and "StopLossExitPrice" are ITALICS{estimates} - I may or may
> >
> >not get filled at exactly the prices the system expects, due to
> >gaps, slippage, locked-limit days, etc., and so R1 is an
> >ITALICS{estimate} of the dollar risk of a single contract
> >position. ITALICS{Reality could be worse.}
> >
> >If my total account equity were exactly R1 dollars, and I traded
> >one contract, then I would be risking 100% of my account on this
> >trade. Alternatively, if I put on one contract when my account
> >contained exactly (5 times R1) dollars, then I would be risking
> >only 20% of my account {Math: R1/(5*R1) = 0.20}. So the next
> >problem to attack is "What percentage of my account should I
> >risk on any one trade?"
> >
> >Several traders interviewed for the Market Wizards books suggest
> >risking a constant 2% of equity on each trade. Similarly, Ralph
> >Vince's books advocate risking a UNDERLINE{fixed fraction} of
> >equity on every trade. And, mostly, that's what my approach
> >does. Look at my betsize selection equation above, and for
> >moment, neglect the last term (i.e. temporarily assume A=1).
> >Then my betsize election reduces to "Bet 2.5 percent of equity
> >on every trade." Pretty simple.
> >
> >But what is this mysterious number "A" in the betsize formula,
> >anyway? It's something I have added to introduce aggressiveness
> >into betting. I got the idea from Randy McKay's interview in
> >New Market Wizards, and from Ryan Jones's Kamikaze Trading
> >Newsletter: What if we ITALICS{don't} bet a constant, fixed
> >fraction of equity on every trade? What it we make the betsize
> >percentage ITALICS{vary} with equity? Hmmm, that sounded
> >intriguing.
> >
> >McKay offered this idea as a defensive strategy; Jones proposes
> >it for offense too. As Mr. Jones explains the idea, it is based
> >on a simple underlying premise: when your account is small, you
> >intentionally take bigger risks. Later, if and when your
> >account grows, you throttle back on risk and bet more
> >conservatively as you become wealthy.
> >
> >There's no free lunch here; a more aggressive betsize percentage
> >inevitably produces a greater Probability of Ruin and a larger
> >Volatility of Returns. It also produces a faster appreciation
> >of capital (if the underlying entry/exit system has positive
> >expectation!), taking you from a little guy to a fat cat more
> >quickly. After I studied a lot of computer backtests of "what
> >if" scenarios, I concluded that I could tailor this idea
> >ITALICS{to fit my own personal risk-tolerance profile} and my
> >own pain threshold. So I developed the aggressiveness factor
> >"A" that is graphed in Figure 1.
> >
> >Normally, A is equal to 1.0, and so I bet 2.5 percent of equity
> >on every trade. {Math: (0.025 * A) = 0.025 when A=1}. But in
> >some cases, depending on equity, A can become as large as 2.0,
> >causing me to aggressively bet 5.0% of equity on each trade.
> >{Math: (0.025 * A) = 0.050 when A=2}. Notice that my
> >aggressiveness peaks when the account equity is below $200,000,
>
> >and it gradually returns to 1.0, where I revert to betting a
> >fixed 2.5% of equity on every trade.
> >
> >The aggressiveness curve A in Figure 1 is defined by the
> >following equation:
> >
> > A = max(1.0, B)
> > where B = (J/E) + [ (K/E) - ((L/E)^2) ]^M
> >
> >Parameter values are: (J = $46,400) , (K = $1,370,000) ,
> >(L = $369,000) , (M = 0.47) . As before, E is the total account
> >equity. I am using the symbol " ^ " to denote raising a number
> >to a power, thus " x^y " means "x raised to the y power".
> >
> >For those who wish to experiment with the aggressiveness formula
> >in spreadsheets, charting packages, etc., here are a few test
> >cases to help verify that your setup is correct:
> >
> > (E = $102,420 A = 1.1000)
> > (E = $119,487 A = 1.7500)
> > (E = $270,506 A = 1.9000)
> > (E = $581,114 A = 1.4500)
> >
> >If you implement the complete betsize selection formula, these
> >test cases might be helpful:
> >
> > (E = $103,671 R1 = $1,555 N = 2.0000)
> > (E = $131,077 R1 = $1,245 N = 5.0009)
> > (E = $384,137 R1 = $1,484 N = 11.001)
> >
> >To illustrate the operation of the betsize selection formula,
> >suppose that on a certain day my system gave entry signals
> >(and stoploss exit prices) for three markets: Crude Oil,
> >Japanese Yen, and Orange Juice. First, I'd use the stoploss
> >exit prices to calculate a single contract risk value (R1) for
> >each of these three trades. In general, R1 for a trade in one
> >market (e.g. Crude) will be different than R1 for a trade in
> >another market (e.g. Juice), even if the entry signals are
> >received on the same day. Next, I'd take these three different
> >R1 values and use them to calculate three different N values
> >(N = number of contracts to trade). In general, the numbers of
> >contracts (N) will be different for each different market.
> >
> >Finally, I'd like to stress that the aggressiveness curve A in
> >Figure 1 was derived from ITALICS{my} backtest simulations that
> >started with ITALICS{my} tolerance for risk, drawdown,
> >probability of ruin, etc. But ITALICS{your} threshold of pain
> >is probably different than mine, and so you would probably
> >prefer a completely different aggressiveness curve.
> >
>
> --
> Mark Johnson Silicon Valley, California mark@xxxxxxxxxxxx
>
> "... The world will little note, nor long remember, what we
> say here..." -Abraham Lincoln, "The Gettysburg Address"
|