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Have you actually tried backtesting with 1,000,000 initial equity vs. 100,000? I think that you will see that there is no difference at all in the metrics.
As described on the same page from which you found the formula, AmiBroker uses *exposure* as the initial_value, where exposure is summed bar by bar from position sizes.
http://www.amibroker.com/guide/w_report.html
Mike
--- In amibroker@xxxxxxxxxxxxxxx, Ted Byers <r.ted.byers@xxx> wrote:
>
> Thanks. That helped a lot.
>
> However, I am not especially happy with the following:
>
> System test report window
>
> correctly_annualized_perc_return = 100% * ( (final_value/initial_value) ^ (
> 365 / days_in_test ) - 1 )
>
> where x^y means rising x to the power of y
>
>
> The problem I find lays in knowing precisely what initial_value is supposed
> to be. Yes, the formula is correct, and makes sense, if the initial value
> is fully utilized in the investment (such as the initial and final value of
> a house one has purchased). However, in the system I am working on, at no
> point does the total value of all open positions exceed $100,000, and yet I
> have been instructed to set, as a default for backtesting purposes, initial
> cash at 1,000,000 (the trader we're working with doesn't want to deal with
> any limits posed by the available cash). But that means I can arbitrarily
> improve the rate of return by a factor of ten if I use an initial value of
> 100,000 or arbitrarily make it worse by using an initial value of
> 2,000,000. Obviously, I can't use an initial value less than 100,000 or the
> trades the system recommends would not be possible, but apart from that
> constraint, that I can arbitrarily alter initial value without affecting
> total return seems to make this figure just so much meaningless BS. At no
> time, when using this code, is position size computed from the available
> cash.
>
> How, then, can I define things in such a way that ensures that the rate of
> return actually has a meaningful value? So far, it seems I can only compute
> a meaningful value for the rate of return for a specific trade (where the
> initial value is obviously the cost of buying the shares, for a long
> position, or the value received from the sale of shares, for a short
> position), but not for a collection of trades distributed over a period of
> several years. Is there a standard way for handling this? One that is
> demonstrably valid?
>
>
> Thanks
>
>
> Ted
>
>
> On Mon, Feb 8, 2010 at 4:11 PM, reefbreak_sd <reefbreak_sd@xxx> wrote:
>
> >
> >
> > In AB, click on HELP -> SEARCH
> > type in "BackTester Report" in the search window
> > Under the "Select Topic" that comes back, click on "System Test Report
> > Window" and you will see a definition of each term. Many of these are
> > industry standard metrics of performance.
> >
> > You can go to www.investopedia.com and type in for example "risk adjusted
> > return" and get a more detailed explaination of most of the report items.
> >
> > Reef
> >
> >
> > --- In amibroker@xxxxxxxxxxxxxxx <amibroker%40yahoogroups.com>, Ted Byers
> > <r.ted.byers@> wrote:
> > >
> > > Hi All,
> > >
> > >
> > > I am digging into how AmiBroker computes the various statistics it
> > reports
> > > on a given back test.
> > >
> > > For example, I see the following reported:
> > >
> > > Exposure %
> > > Net Risk Adjusted Return %
> > > Annual Return %
> > > Risk Adjusted Return %
> > >
> > > Where will I find the details of exactly how AmiBroker computes these
> > from a
> > > given suite of trades? Now, I know what a risk adjusted return is, but in
> > > my previous work, it is based on 100% of the cash being invested, and it
> > > carries a specific definition of "risk". In the system I am working with
> > > now, it is rare for 100% of the available cash to be invested, and a
> > really
> > > really long lived trade lasts only a couple weeks (though 9 out of 10
> > trades
> > > were profitable in my last back test using my own C++ code - which in my
> > > view was quite bad - average position size of about 50,000 and total
> > profit
> > > over 2 years being about 10,000). It seems rather meaningless to report
> > an
> > > annual rate of return if one is in the market for less than a month.
> > >
> > > In this "system", the position size is not a function of the total amount
> > of
> > > cash available; so if these rates are defined relative to the total
> > amount
> > > of cash available, I can arbitrarily change these rates by increasing or
> > > decreasing the amount of cash available, within limits. I am afraid my
> > > understanding of these ideas is derived from the perspective of an
> > investor
> > > (where one buys a stock, and looks at returns based on the combination of
> > > dividends and long term change in share value, adjusted for splits, &c.).
> > > If I can see how AmiBroker computes these stats for a given backtest, I
> > hope
> > > to understand these from the perspective of a trader.
> > >
> > > So where will I find the documentation of how AmiBroker computes these
> > back
> > > test statistics?
> > >
> > > Thanks
> > >
> > > Ted
> > >
> >
> >
> >
>
>
>
> --
> R.E.(Ted) Byers, Ph.D.,Ed.D.
> TED@xxx
> CTO
> Merchant Services Corp.
> 350 Harry Walker Parkway North, Suite 8
> Newmarket, Ontario
> L3Y 8L3
>
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