|
PureBytes Links
Trading Reference Links
|
Over the Labor Day weekend, I decided to try out the
Fixed Ratio approach for choosing position sizes when
trading commodity futures. This scheme appears in Ryan
Jones's book "The Trading Game":
http://www.amazon.com/exec/obidos/ASIN/0471316989/
The book is pretty forceful in asserting that its
Fixed Ratio concept is powerful, profitable, and
conservative. So I decided to take a look and
see for myself.
I compared Fixed Ratio against a betsizing algorithm
by Bob Spear (author of "Trading Recipes" software),
which was included free when I purchased the software
in 1995. Both betsizing algorithms (the Jones "Fixed
Ratio" algorithm , and the Spear algorithm) were applied
to the exact same underlying system-of-entries-and-exits,
namely Channel Breakout.
Channel Breakout is neither secret nor exotic; in fact
it is well-known and more than 40 years old. I am using
it with the parameters (89 and 13), both of which are
Fibonacci numbers, giving the following rules:
Enter Long 1 tick beyond the Highest_High of 89 days
Exit Long 1 tick beyond the Lowest_Low of 13 days
Enter Short 1 tick beyond the Lowest_Low of 89 days
Exit Short 1 tick beyond the Highest_High of 13 days
This is NOT a reversal system. It goes flat (has no
position) between trades.
The Fixed Ratio betsizing algorithm seems to have been
invented in the summer of 1995, and it seems to have
first appeared in Ryan Jones's "Kamikaze Trading Newsletter"
dated September 1995. I don't feel like typing up a
description of Fixed Ratio; if you are curious, read the
book or the newsletter or look at the code below.
The flavor I tested is what Jones calls "100% Rate of
Decrease".
Bob Spear's betsizing algorithm is in a software file
whose creation date is 12 August 1994. It's a combination
of 3 very simple position sizing ideas:
1: Don't risk more than 4% of total equity on one trade.
Of course this is nothng but dear old Ralph
Vince's FIXED FRACTIONAL idea, dressed up a bit.
2: When you get an entry signal, don't put on so many
contracts that the dollar volatility of the
position will exceed 1% of total equity
3: Never trade a position size more than 200 contracts,
regardless of total equity
You calculate how many contracts are allowed by rule 1,
and how many are allowed by rule 2, and how many are allowed
by rule 3. Then you pick the smallest. Simple. Code
is provided below. By the way, these ideas are also
discussed in Van Tharp's new book "TYWT Financial Freedom",
pages 292 and 296.
Please observe, this is a COMPARISON BETWEEN TWO BETSIZE
ALGORITHMS. It is not a "study" of a "trading system".
Description of Test Procedure
------------------------------
I decided to investigate what happens when you trade
the Channel Breakout system on a portfolio of fifteen
commodity futures markets, simultaneously, out of a
single account. I ran a test the first time, using
betsize selection according to Fixed Ratio, and I
ran it again the second time using betsize selection
according pto Bob Spear's betsize algorithm. The
fifteen markets I used in the tests were:
CD DM FV LB TU
CL DX JY MB TY
CT ED KC SF US
Commission+Slippage was set to $75.00 per contract
per round trip trade. Interest on T-bills (held as
margin) was ignored. The tests ran from 01 Jan 1987
to 10 Aug 1999, a total of 12.7 years.
Tests were performed using the Trading Recipes software
package, a marvelous backtesting product which (alas!)
has been killed by the Omega juggernaut. TR code for
both of the tests is presented in the Appendices below.
Both tests started with $80,000 in the account on
the first day of trading. The Fixed Ratio algorithm
parameters were S=$80,000 and Delta=$12,000. The
Spear algorithm parameters were risk=4%, volatility=1%,
and nmax=200.
These parameter sets were chosen to give approximately
equal drawdowns in the two tests. If you consider
"drawdown" to be equivalent to "pain" and if you
consider "net profits" to be equivalent to "gain",
then these two betsize algorithms had approximately
equal "pain". The only difference was the "gain"
that they produced.
TEST RESULTS
TEST RESULTS
FixedRatio SpearAlgorithm
------------------------------------------------------------------------
Starting equity........................... 80000.00 80000.00
Final equity.............................. 5319261.50 13159391.00
Net profit................................ 5239261.50 13079391.00
Compound Annual Growth Rate (percent)..... 39.06 49.32
Max Drawdown (percent).................... 40.61 39.12
(CAGR / MAXDD) Ratio...................... 0.962 1.261
# trading days in longest drawdown........ 572 302
Annual Standard Deviation (percent)....... 38.36 36.89
Average max annual drawdown (percent)..... 24.29 26.46
Percent of days making new equity highs... 6.393 7.739
Sharpe Ratio.............................. 0.888 1.201
Semideviation Ratio....................... 1.282 1.748
Return Retracement Ratio.................. 3.567 4.270
Sterling Ratio............................ 0.556 1.503
Number of Trades.......................... 715 715
Winning Trades............................ 321 321
% Winners................................. 44.9 44.9
First day of test......................... 870128 870128
Last day of test.......................... 990810 990810
# days.................................... 3269 3269
Comm+slippage per contract................ 75.00 75.00
DISCUSSION OF RESULTS
DISCUSSION OF RESULTS
It appears that the parameter sets did indeed give roughly
equal drawdowns, as desired. The FixedRatio equity curve had
a worst-case drawdown of 40.6% while the SpearAlgorithm equity
curve's worst case was a 39.1% drawdown.
If we take the worst drawdown seen in calendar year 1987,
and then the worst drawdown seen in calendar year 1988, and
then the worst drawdown in 1989, and ..., and the worst
drawdown seen in calendar year 1999, and we AVERAGE THESE
SINGLE YEAR WORST DRAWDOWNS, then we get a number called
"Average max annual drawdown". Again, FixedRatio and
SpearAlgorithm are pretty close: (24% vs 26%).
However, look at the _duration_ of the longest drawdown.
It is 572 trading days for Fixed Ratio, but only 302
trading days for the SpearAlgorithm. Spear is clearly
superior here.
In the "reward" category, Spear's algorithm is also
clearly superior. It achieves a compounded annual
growth rate of 49 percent per year, while Fixed Ratio
only gives 39 percent per year, AT THE SAME LEVEL OF
DRAWDOWN.
Of course, Spear's algorithm is also better in the
various reward-to-risk ratio measurements. Spear's
Sharpe ratio is superior, and so it its semideviation
ratio (Schwager's modified sharperatio), and all
the others.
I would conclude that in these tests, the Spear
algorithm is clearly superior to Fixed Ratio.
It gave greater profits at the same drawdown,
thereby achieving a superior reward-to-risk ratio.
*Why* is it superior? I suppose that calls for
_opinion_, whereas this message is mostly filled
with DATA. But nevertheless, I will offer my
_opinion_, that the Achilles heel of the Fixed
Ratio method is found in Chapter 9 of Jones's
book. It dictates that if you are trading
a portfolio having two components: (1) Coffee
and (2) Corn, then you should put on equal numbers
of Coffee contracts as you put on Corn contracts.
Even though the average 1-week range of a single
contract position in Coffee, swings more than 6.8
times as many dollars as the average 1-week range
of a single contract position in Corn, Jones
tells you to trade the same number of Corn that
you trade Coffee. Similarly he wants you to
trade equal numbers of Oats and S&P maxi's.
Oh Really. But of course this is my _opinion_.
APPENDIX A. TRADING RECIPES SOFTWARE CODE FOR CBO + FIXED RATIO
APPENDIX A. TRADING RECIPES SOFTWARE CODE FOR CBO + FIXED RATIO
************begin************
COL1 = ATR[15]
COL2 = MAX[H,89,1] + TICK[1]
COL3 = MIN[L,13,1] - TICK[1]
COL4 = MIN[L,89,1] - TICK[1]
COL5 = MAX[H,13,1] + TICK[1]
BUYSTOP = COL2
SELLSTOP = COL4
' Using S=80000 and Delta=12000
' Ryan Jones Fixed Ratio algorithm is next 6 lines
STARTUPCASH = 80000
MEMORY[1] = EQUITY - 80000
IF MEMORY[1] < 0.01 THEN MEMORY[1] = 0.01 'avoid sqrt(negative)
MEMORY[2] = 0.5 + ((2 * MEMORY[1] / 12000) + 0.25) ^ 0.5
IF MEMORY[2] < 1 THEN MEMORY[2] = 1
NEWCONTRACTS = MEMORY[2]
SELLSTOP = COL3
BUYSTOP = COL5
************end************
APPENDIX B. TRADING RECIPES SOFTWARE CODE FOR CBO + SPEAR ALGO
APPENDIX B. TRADING RECIPES SOFTWARE CODE FOR CBO + SPEAR ALGO
************begin************
COL1 = ATR[15]
COL2 = MAX[H,89,1] + TICK[1]
COL3 = MIN[L,13,1] - TICK[1]
COL4 = MIN[L,89,1] - TICK[1]
COL5 = MAX[H,13,1] + TICK[1]
SYSTEM = COL1[1] * POINTVALUE
BUYSTOP = COL2
SELLSTOP = COL4
' Bob Spear's betsizing algorithm is the next 6 lines
STARTUPCASH = 80000
MEMORY[1] = (0.04 * EQUITY) / NEWRISK
MEMORY[2] = (0.01 * EQUITY) / SYSTEM
IF MEMORY[2] > 200 THEN MEMORY[2] = 200
IF MEMORY[2] < MEMORY[1] THEN MEMORY[2] = MEMORY[1]
NEWCONTRACTS = MEMORY[2]
SELLSTOP = COL3
BUYSTOP = COL5
************end************
I hope you enjoyed reading this.
-- Mark Johnson mark@xxxxxxxxxxxx
--
Mark Johnson Silicon Valley, California mark@xxxxxxxxxxxx
"... The world will little note, nor long remember, what we
say here..." -Abraham Lincoln, "The Gettysburg Address"
|