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At 7/27/2002 08:17 PM, Gary Fritz wrote:
> > Jones says you should always require the same gain *per contract*
> > when going from X to X+1 contracts, whether X is 1, 2, 5, 10, or
> > 100. That means you require increasingly large profits per
> > contract to increase your position size by 1.
>
>First I say Jones requires the SAME gain PER CONTRACT, then I say you
>need increasingly LARGER profits PER CONTRACT. Ooops. :-) The
>first comment was correct, the second was not. The second sentence
>should have read "That means you require increasingly large profits
>to increase your position size by 1."
Yes, this is part of what I have been trying to communicate, and what you
say above is now correct. Now, to continue what you started above, the
increasing large profits are based upon the trading of increasing large
position sizes. In particular, your original post pointed to the need for
$1 million profit to increase from 100 to 101 contracts. Actually, the $1
million profit to increase from 100 to 101 contracts is not unreasonable
because it is only $10K per contract.
But rather than continue with this back and forth, I came up with a
completely new approach to explaining this which I think is going to clear
up all of this confusion and misconception about Fixed Ratio.
I have constructed a simple spreadsheet showing the account thresholds
where Fixed Ratio position size increases occur with a given delta and
given starting account size. Note that this spreadsheet is not a historical
test. Rather, it is only showing the account equity thresholds at which
position size increases occur. It is saying that if there was a historical
test, these are the account equity thresholds where the position size
increases occur if and when the account size grows to the shown threshold
levels.
As an aside, I want to mention that this spreadsheet is only showing the
basic Fixed Ratio position size increase calculations. That is only part of
what the Jones book discusses. He also discusses more advanced topics,
including various strategies for position sizing in a drawdown and
weighting market systems individually.
With this spreadsheet we can finally start looking at some actual numbers
instead of the speculating as we have been doing. I think it is a much
better approach to this discussion.
I placed the spreadsheet on my web site, at
http://www.powertesting.com/FixedRatioExample.html. This web page will show
the spreadsheet numbers. There is also a link within the web page to the
original .xls (Excel) spreadsheet file which can be downloaded. The
advantage of downloading the .xls file is you can view the formulas used to
construct the numbers.
The following is a paragraph from your original post. I am repeating this
paragraph because one of the reasons for the spreadsheet is to study what
you are saying in this paragraph in more detail:
<<<<
But ignoring that, I think his Fixed Ratio approach is bogus. IMO
his entire premise is flawed: he looks at the per-contract profit it
takes to move from 1 to 2 contracts, and he says that it should take
the same per-contract profit to move from X to X+1 contracts. I.e.
if you need $10k profit to move from 1 to 2 contracts, you should
need $10k profit **per contract** to move from 100 to 101. You'd
need $1M total profit to increase by 1 contract.
>>>>
The spreadsheet extends some of the tables in the Jones book, starting at 1
contract and going until 101 contracts, to match your original example
above. Also, a delta of $10K is used, again to match what you say in the
above paragraph. Since you do not specify a starting account size, I used a
$30K starting account because that is a size I pulled out of the air in an
example earlier in this exchange.
The spreadsheet shows the account equity thresholds when Fixed Ratio
specified position size increases, starting at 1 contract, and going until
101 contracts. I already explained the formula used to calculate these
account thresholds in my previous post. The formula is that to increase
from N contract to N+1 contracts requires an N * delta increase in account
equity.
Finally we have some real numbers to look at. Yes, we can see that the
spreadsheet shows $1M profit is necessary to increase from 100 to 101
contracts, as you said in your original post. However, the spreadsheet also
shows that account equity at that point is $50 million. It is only 2% of
account equity to add that 101st contract. To emphasize this, I added a
column showing the percent of account equity needed to add additional
contracts. You can see that this progressively goes down as contacts are
added (as it should). I think it is now obvious from the spreadsheet that a
required increase of $1 million to move from 100 to 101 contracts is not in
outer space. It is only a 2% growth in account equity.
On the other hand, I think that the more interesting discussion is the next
column I added to the spreadsheet. I think this next column is going to
finally make this whole Fixed Ratio discussion much clearer. The next
column shows the percent of account equity risked at the various position
size thresholds for a $1500 risk per contract trade. In other words, assume
the trading system this Fixed Ratio is being applied to risks $1500 per
contract per trade. This spreadsheet shows the risk per trade percent at
progressive account thresholds.
I was very happy with the results of this very first test using this
somewhat randomly picked delta and starting account size. Some highlights:
+) The peak risk per trade is 7.50% when account equity is between $40K and
$60K.
+) Risk per trade drops to 5% when account equity hits $180K.
+) Risk per trade drops to around 3% when account equity crossed $500K.
+) Risk per trade is 2.08% when account equity reaches $1 million.
To me this sounds like a very reasonable approach for someone starting with
a $30K account.
Beyond $1 million, risk per trade percent continues to drop. For example,
at $10 million risk per trade is only .66%. So, I can see why Jones says to
switch to Fixed Fractional at higher account levels. I placed a suggestion
as a comment in the spreadsheet that when the account reaches $1 million,
it might be good to start trading a flat 2% Fixed Fractional.
However, let's put this into perspective. It was a starting account of only
$30K which has grown to $1 million before risk per trade starts to fall to
2% and below. If I was starting to trade with $30K, I don't think I would
get too wrapped up in worrying about what my position sizes will be when I
reach $1 million. I would be much more concerned in getting to the $1
million mark. So, it looks like the need to switch to Fixed Fractional
really isn't much of an issue until way down the equity curve.
I don't see these number above as being "reductio ad absurdum" as you said
in an earlier post. The numbers seem very reasonable to me. I think it
would fit my psychological makeup if I was trading a $30K account with a
goal of growing the $30K to $1 million.
Let's contrast my Fixed Ratio spreadsheet with the same scenario trading
Fixed Fractional. Again let's use the example of a $30K account and a
system that risks $1500 per contract per trade. We are forced to be willing
to risk 5% on the first trade because 5% * 30K = $1500. So we are forced to
risk at least 5% in order to be able to trade a single contract. Then we
have to wait until the account reaches $60K to add the second contract (5%
* 60K = the $3000 risk for 2 contracts). Then we have to wait until the
account reaches $90K to add the third contract (5% * 90K = the $4500 risk
for 3 contracts).
Contrast this to the Fixed Ratio spreadsheet where we increase to 2
contracts at $40K and 3 contracts at $60K. I think I personally would be
willing to increase my risk in early trades from 5% to 7.5% to be able to
hit these difficult initial thresholds this much faster.
At $180K, Fixed Ratio and Fixed Fractional match each other with both
risking 5% per trade. Above $180K the Fixed Ratio risk percent starts to
slowly reduce to 2% where Fixed Fractional stays at 5%. I think that at a
$180K threshold I myself would be more comfortable starting to reduce from
5% because I would start getting concerned about risking my nice $150K in
profits.
Overall, it strikes me that the Fixed Ratio numbers would better fit my
psychological makeup than the Fixed Fractional numbers. But more to the
point, certainly I think that these Fixed Ratio numbers are reasonable, and
don't see why anyone would be adamantly negative about these numbers and
say that they reflect a bogus or flawed strategy.
>As someone on the traderclub discussion said, Fixed Ratio is in some
>ways a form of curve-fitting, just like Optimal F. Opt F is the risk
>level that will produce the highest gains **in the test period**.
>But trading it forward is a near-guaranteed recipe for disaster.
>Similarly, fixed ratio works great if you carefully select when the
>drawdowns happen, but you don't get to do that in real life.
I cannot resist commenting on this one statement from your last post.
I absolutely agree that Optimal F is curve fitting. It is calculating the
maximum possible (i.e. optimal) position sizes based upon historical
performance. If forward performance is not as good, you're dead meat. Yes,
it is curve fitting.
Fixed Ratio would be curve fitting if it calculated the "Optimal Delta"
that generates maximum profit without going bust based upon historical
performance. Then, it would be curve fitted, the same as with Optimal F.
However, that is not the way it is done. The way it is done is that the
user of Fixed Ratio makes a judgement about what they consider to be
reasonable risk they want to expose themselves to (likely based upon
historical drawdown), and that becomes the Delta parameter.
I suspect you were actually expressing an opinion about the examples in
Jones book being curve fitted to the test data in the examples. But that is
a different subject. It is essentially saying you think that Jones choose
too aggressive a Delta (and/or too small an initial account), so that if
the worst drawdown occurred earlier in the test it would have been
disaster. The solution to that is to choose a less aggressive delta (and/or
start with a larger account). In other words, the examples in the book
being "cooked" (your term) does not necessarily imply that the Fixed Ratio
strategy would not work with uncooked examples.
I wouldn't call the maximum 7.5% risk per trade in my sample spreadsheet a
recipe for disaster. Besides, if someone feels that 7.5% is to high to
risk, increase the delta. So, to experiment with this I played with the
original spreadsheet a little with the goal of finding numbers which peak
at a maximum 5% risk per trade instead 7.5%.
This is my analysis of what I found. Limiting risk to 5% max with the $30K
account requires a $30K Delta, which slows down the initial account
thresholds to the same levels as 5% Fixed Fractional. This makes sense
based upon the observation above that 5% is the minimum risk per trade to
trade a single contact at $30K. Later, when position sizes increase, the
Fixed Ratio progressively lowers risk compared to Fixed Fractional, which
could be considered by some to be an advantage. But in general, the number
with the $30K account with $30K Delta don't look very attractive to me.
So, I decided to see what happens if initial account size is increased.
Experimentation yielded a $45K initial account with a $15K delta that maxes
risk at 5% risk per trade with pretty nice looking numbers overall. A
conclusion that could be reached from this is that if you want to limit
risk per trade to max 5% you should consider that a $30K initial account
may not be adequate.
These variations are shown as additional worksheets in the .xls file which
can be downloaded from my web site (see the link above). Also, anyone can
use the .xls file spreadsheet to experiment themselves with different
combinations. With the spreadsheet it is very easy to experiment with
different deltas and account sizes, and view the resulting risk per trade
percentages.
In conclusion, it is unfortunate that the explanation in the Jones book is
lacking, etc., etc., because I do think Fixed Ratio is a money management
strategy worthy of consideration for some traders. However, the book causes
a lot of confusion. I hope my posts and the spreadsheet has helped to clear
up some confusion and misinterpretation about this Fixed Ratio money
management strategy.
I believe my descriptions above and the spreadsheet are accurate. If not, I
hope someone will correct me. Of course, this is not investment advice. Do
you own research and reach your own conclusions.
To repeat something I said in an earlier post, it strikes me that Fixed
Ratio is for the individual trader starting with a smaller account, willing
to take higher initial risks to reach the early account thresholds faster.
On the other hand, a money manager or an individual who has already grown
to a larger account would more likely be interested in the risk control of
Fixed Fractional. I would like to someday extend this discussion into more
comparison of Fixed Ratio and Fixed Fractional, as well as some thoughts
about potential extensions to Fixed Ratio, but for now I have already spent
quite a bit of time on this and need to get back to other tasks.
I want to acknowledge list member Paul Zislis for contributing to these
posts about Fixed Ratio and reviewing drafts before I posted them. It was
Paul who really helped me figure out Fixed Ratio. What understanding I have
of Fixed Ratio is to a large extent because I have asked him a lot of
questions in the past.
Bob Bolotin
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