Re: Re: Re: RE: RE: [amibroker] Re: more positionsize results I don't

[advenosa <advenosa@xxxxxxxxxxxx>]

Thank you, Tomasz, for clarifying the point on max dd%. It was very
understandable. I'm not sure your compromise is the solution, however. I
think what most traders are interested in is the maximum peak to trough
drawdown in the equity curve, which I believe you are doing right now using
total equity. I don't even know if there is a solution when considering
variable trade sizes. In my example, I was not exactly risking 1% of equity
on a trade. Rather, I was investing 1% of equity multiplied by the
buyprice/volatility. So, for example, if initial equity were $100 K and the
buyprice were 30 and the ATR were 1, then my investment in that trade would
be 1000*30/2*1 = $15 K, which is 15% of equity allocated to the trade.
Suppose I also set a max stoploss at 2*ATR below the buyprice, which in this
example would be $28. If the stock declined to 28, I'd be out of the trade
with a $1000 loss. This is the fixed 1% risk model. My actual loss might be
more than that, depending on whether the price gapped thru my stop. The
$1000 loss is 1% of equity but 6.7% of invested capital. It would still
represent a 1% dd, despite the $15 K invested. 

If I may ask one final question: what about on the profit side of the
equation? How do you calculate compound annual growth rate (CAGR) when using
position sizing as I have described? Again, the way you are doing it is
based on total equity. If, in the example, the price of the $30 stock rose
to $35 in 3 weeks ($2500 profit), that would be a 16.7% profit in 3 weeks on
the basis of the amount invested ($15 K). However, on the basis of my $100 K
equity, my new equity would be $102.5 K, which is a profit of 2.5% in 3
weeks (not annualized). So, the CAGR Amibroker calculates when using
position sizing will necessarily be substantially lower than when no
position sizing were being used. I suppose there is no easy solution to this
problem, either, is there? 

Regards, AV


>On Wed, 17 Sep 2003 17:48:57  0200 Tomasz Janeczko <amibroker@xxxxxx>
wrote.
>Al,
>
>It depends what you would like to calculate.
>I guess your would like to have igures related to actual trade size.
>igures calculated based on total initial equity are simply are simply
>different - they measure completely different thing therefore can not
>be used the way you like it.
>
>Dollar figures on the other hand are always the same - dollar / point
>calculations do not involve 'starting amount'.
>
>I have choosen initial equity as base of percentage
>profit/loss calculations because it is more straightforward and easy
>to understand for the user.
>
>Calculations based on actual (variable) trade size would cause new
troubles:
>lets suppose that in one trade you enter set position size to 1f your
equity
>and the trade is bad enough so drawdown for this trade (measured
>for actual trade size) is 50
>Now you have second trade with position size of 10nd now you have drawdown
>of 10nly.
>
>So you have 2 drawdown figures 50first trade) and 10second trade).
>
>When you are using TOTAL equity as a base of your calculations
>the maximum drawdown would be
>max(  1size) * 50drawdown), 10size) * 10drawdown) )
>= max( 0.51 = 1>
>This is 1f TOTAL equity (very small amount because you kept 90f equity
>in cash and cash did not experience drawdown)
>
>Now consider using actual trade size, drawdown would be
>max( 5010= 50>
>It will report 50rawdown. Is it correct figure - I guess not. After all
first
>trade was very small and you would have lost only 0.5f your capital in
worst point
>of equity in first trade.
>
>For me the best solution would be to use maximum trade size for that
calculation,
>so the formula would look like this:
>max(  1size) * 50drawdown), 10size) * 10drawdown) ) / max( 1ize, 10ize)
>
>= 1 0.1 = 10>
>In that case the system would tell that the biggest drawdown was 10the
drawdown
>that occured in second larger trade)
>
>
>Best regards,
>Tomasz Janeczko
>amibroker.com
>----- Original Message ----- 
>From: "advenosa" <advenosa@xxxxxxxxxxxx>
>To: <amibroker@xxxxxxxxxxxxxxx>
>Sent: Wednesday, September 17, 2003 4:51 PM
>Subject: Re: Re: RE: RE: [amibroker] Re: more positionsize results I don't
>
>
>> Thank you, Tomasz. I knew you'd set me straight. This leads me to ask the
>> following question: often, I use a position size statement as follows:
>>
>> PositionSize = -1 * BuyPrice/(2*ATR(10));
>>
>> In this case, I'm investing 1f my current equity in the trade, but the
>> position size amount is variable because I'm mulitplying that dollar
amount
>> by the buyprice divided by the volatility. So, each trade will have a
>> different amount invested due to differences in the buyprice and
volatility.
>> Perhaps that is what I meant when I said the percentage figures will be
>> inaccurate and that one should use the actual dollar amounts to judge the
>> performance of a system. Is this right, or am I still misstating the
>> situation? Maybe the word "inaccurate" is incorrect. If so, what word
would
>> better represent what I'm describing? TIA.
>>
>> Al V.
>>
>>
>> >On Wed, 17 Sep 2003 16:35:42  0200 Tomasz Janeczko <amibroker@xxxxxx>
>> wrote.
>> >Indeed esults are accurate but always related to total initial equity,
>> >regardless of position size you set with each trade. If you have
>> >90f equity in cash your percentage risk/drawdown/etc is of course 1/10
>> >of values that you would expect trading 100f your funds.
>> >
>> >Best regards,
>> >Tomasz Janeczko
>> >amibroker.com
>> >----- Original Message ----- 
>> >From: "advenosa" <advenosa@xxxxxxxxxxxx>
>> >To: <amibroker@xxxxxxxxxxxxxxx>
>> >Sent: Wednesday, September 17, 2003 3:55 PM
>> >Subject: Re: RE: RE: [amibroker] Re: more positionsize results I don't
>> understand
>> >
>> >
>> >Dave,
>> >
>> >On several occasions on this board, long ago, TJ said that, when using
>> >positionsize statements (other than -100), any number reported in the
html
>> >report (like max ddnnual return, etc.) in terms of percent will not be
>> >accurate since the program calculates these percentages on the basis of
>> >total equity rather than amount invested per trade. The actual dollar
>> >amounts are accurate, but not the percentage amounts. Since, in the -100
>> >case, everything is being reinvested, the igures are accurate. But in
the
>> >-10 case, 90f your equity is idle and not participating in the trading,
>> >so the annual returns and max dd  are much different from what they
would
>> >be otherwise. Perhaps one workaround might be for you to use 1/10th of
your
>> >equity and still use -100 as your position size to compare against the
full
>> >equity at -100 position size. In that case, you should get exactly the
same
>> >output in terms of percentages. If I said something wrong, I'm sure TJ
will
>> >interject here.
>> >
>> >AV
>> >
>> >>On Wed, 17 Sep 2003 09:13:32 -0400 Dave Merrill <dmerrill@xxxxxxx>
wrote.
>> >><html><body>
>> >>
>> >>
>> >><tt>
>> >>hi AV, thanks for stepping in.<BR>
>> >><BR>
>> >>the following result columns were the same at 100nd 10osition
sizes;<BR>
>> >>the rest were different:<BR>
>> >> Trades, # of winners, # of losers, Exposure<BR>
>> >><BR>
>> >>looking at individual trades for the first stock, the trade dates,
>> >prices<BR>
>> >>and hange are the same, so the issue appears to be something about
the<BR>
>> >>way results are reported, not actual investment performance.<BR>
>> >><BR>
>> >>here's the 100ase (hope this is readable):<BR>
>> >><BR>
>> >>-------------------------------------------------------------<BR>
>> >>Profit rofit Shares Position Cum. Profit<BR>
>> >>-------------------------------------------------------------<BR>
>> >>948.62 9.50bsp; 632.41 10,000.00 948.62<BR>
>> >>276.68 2.50bsp; 632.41 10,948.60 1,225.30<BR>
>> >>-1,122.53 -10.00bsp; 665.20 11,225.30 102.77<BR>
>> >>-1,122.53 -11.10bsp; 665.20 10,102.80 -1,019.76<BR>
>> >>1,526.64 17.00bsp; 604.98 8,980.24 506.88<BR>
>> >>-53.07 -0.50bsp; 849.04 10,506.90 453.81<BR>
>> >>420.25 4.00bsp; 840.51 10,453.80 874.07<BR>
>> >>-1,087.41 -10.00bsp; 840.51 10,874.10 -213.34<BR>
>> >>43.89 0.40bsp; 702.18 9,786.66 -169.46<BR>
>> >>1,671.19 17.00bsp; 702.18 9,830.54 1,501.74<BR>
>> >>1,955.29 17.00bsp; 1,088.92 11,501.70 3,457.03<BR>
>> >>3,194.83 23.70bsp; 1,549.01 13,457.00 6,651.87<BR>
>> >>1,195.99 7.20bsp; 1,471.99 16,651.90 7,847.86<BR>
>> >>1,593.56 8.90bsp; 1,699.80 17,847.90 9,441.42<BR>
>> >>-106.24 -0.50bsp; 1,699.80 19,441.40 9,335.18<BR>
>> >>-1,933.52 -10.00bsp; 1,681.32 19,335.20 7,401.66<BR>
>> >>3,518.37 20.20bsp; 1,521.46 17,401.70 10,920.00<BR>
>> >>-429.13 -2.10bsp; 1,716.52 20,920.00 10,490.90<BR>
>> >>0.00 0.00bsp; 1,647.51 20,490.90
>> >10,490.90<BR>
>> >>2,059.39 10.10bsp; 1,647.51 20,490.90 12,550.30<BR>
>> >>881.85 3.90bsp; 2,015.67 22,550.30 13,432.10<BR>
>> >>1,889.69 8.10bsp; 2,015.67 23,432.10 15,321.80<BR>
>> >>-------------------------------------------------------------<BR>
>> >><BR>
>> >>here's the 10ase:<BR>
>> >><BR>
>> >>-------------------------------------------------------------<BR>
>> >>Profit rofit Shares Position Cum. Profit<BR>
>> >>-------------------------------------------------------------<BR>
>> >>94.86 0.90bsp; 63.24 1,000.00
>> >94.86<BR>
>> >>25.51 0.30bsp; 58.31 1,009.49
>> >120.37<BR>
>> >>-101.20 -1.00bsp; 59.97 1,012.04 19.17<BR>
>> >>-111.32 -1.10bsp; 65.97 1,001.92 -92.16<BR>
>> >>168.43 1.70bsp; 66.75 990.78 76.28<BR>
>> >>-5.09 -0.10bsp; 81.42 1,007.63 71.19<BR>
>> >>40.49 0.40bsp; 80.97 1,007.12
>> >111.68<BR>
>> >>-101.12 -1.00bsp; 78.16 1,011.17 10.56<BR>
>> >>4.49 0.00bsp; 71.82 1,001.06 15.05<BR>
>> >>170.26 1.70bsp; 71.54 1,001.50 185.30<BR>
>> >>173.15 1.70bsp; 96.43 1,018.53 358.45<BR>
>> >>245.92 2.40bsp; 119.23 1,035.85 604.37<BR>
>> >>76.16 0.70bsp; 93.74 1,060.44
>> >680.54<BR>
>> >>95.36 0.90bsp; 101.72 1,068.05 775.90<BR>
>> >>-5.89 -0.10bsp; 94.22 1,077.59 770.01<BR>
>> >>-107.70 -1.00bsp; 93.65 1,077.00 662.31<BR>
>> >>215.58 2.00bsp; 93.22 1,066.23 877.89<BR>
>> >>-22.31 -0.20bsp; 89.25 1,087.79 855.58<BR>
>> >>0.00 0.00bsp; 87.28 1,085.56
>> >855.58<BR>
>> >>109.10 1.00bsp; 87.28 1,085.56 964.68<BR>
>> >>42.88 0.40bsp; 98.01 1,096.47
>> >1,007.55<BR>
>> >>88.77 0.80bsp; 94.69 1,100.76
>> >1,096.32<BR>
>> >>-------------------------------------------------------------<BR>
>> >><BR>
>> >>first off, it looks like eturns are rounded to tenths of a percent.
>> >this<BR>
>> >>and other rounding may make a difference, but if that's the only issue,
>> >it's<BR>
>> >>surprising to me how significant it is. outside of that and the x10
>> >scaling,<BR>
>> >>rofit is the same for each trade. I tried rasing the initial
account<BR>
>> >>equity to $1M, and percentages stayed the same.<BR>
>> >><BR>
>> >>by the end, the 100ersion has made a profit of $15,321.80 or 143.2f<BR>
>> >>its original $10k investment. the 10ersion has made $1,096.32, only<BR>
>> >>99.63f its original $1k.<BR>
>> >><BR>
>> >>things diverge immediately. the first trade is reported as making
$948.62,
>> >a<BR>
>> >>9.50rofit in the 100ase, and making $94.86, a 0.90rofit in the 10R>
>> >>case. odd, especially seeing as the reported profit s higher in the
100R>
>> >>case, but the dollar amount is a smaller fraction.<BR>
>> >><BR>
>> >>simple version: I have 10 stocks, the worst performing of which
>> >returned<BR>
>> >>more than 150rofit that year when traded this way, if you believe
the<BR>
>> >>100esults. investing the entire account equally in all of them
should<BR>
>> >>give at least a 150rofit overall, by any intuitive logic I can see.<BR>
>> >>returns should actually be considerably better than that minimum, since
>> >all<BR>
>> >>but 2 give over 200eturn, and 3 are over 500but when I do that
equal<BR>
>> >>split in AB, the individual stock returns are way lower, and the
>> >overall<BR>
>> >>return is about 17BR>
>> >><BR>
>> >>big difference. one's not too shabby, the other's well below the
21.95R>
>> >>return of !COMP that year.<BR>
>> >><BR>
>> >>???<BR>
>> >><BR>
>> >>dave<BR>
>> >><BR>
>>
>>==========================================================================<BR>
>> >>AV wrote:<BR>
>> >><BR>
>> >>When comparing 100s. 10osition sizes without changing anything
else,<BR>
>> >>even though you got different profits, was everything else the same
(i.e.,
>> >R>
>> >>profitable trades, W/L ratio, profit factor, no. of trades, etc.,
>> >etc.)?<BR>
>> >>When you set positionsize = -10, you are committing 10f your
current<BR>
>> >>equity to each trade and reinvesting the profits from that trade into
>> >the<BR>
>> >>next one, etc. The other 90s sitting idle. It's as if you set your<BR>
>> >>position size at -100 but your equity at 1/10 the equity of the
-100<BR>
>> >>scenario. Also, do you have positionsize shrinking checked or
unchecked?
>> >If<BR>
>> >>it was unchecked, you might not have had enough equity to have made a
>> >trade<BR>
>> >>using the -10 setting as in the -100 setting, although with stocks,
>> >since<BR>
>> >>you can buy 1 share at a time, this shouldn't be a problem. I can't
think
>> >of<BR>
>> >>anything else that could be giving you these differences. Fred
>> >suggested<BR>
>> >>that the -100 situation should give 10 times the profits as the -10<BR>
>> >>situation. However, since the compound interest equation is involved in
>> >the<BR>
>> >>computations, I suspect that the differences may not be linear as
Fred<BR>
>> >>suggested.<BR>
>> >><BR>
>> >>AV<BR>
>> >><BR>
>> >></tt>
>> >>
>> >><br>
>> >>
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