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Thanks Thomas, but no, I don't believe that post does not answer my
question. The post below explains the the difference between K-Ratio
(1996) and K-Ratio(2003). However, it does not explain the
Backtester results.
K-Ratio(1996) = LinRegSlope / (StdErr * sqrt(n))
K-Ratio(2003) = LinRegSlope / (StdErr * n)
K-Ratio(Ami) = LinRegSlope / StdErr * sqrt(n) / sqrt(12)
The sqrt(12) function is typically used to convert a monthly StdDev
(or StdErr) to an annualized one. I do not understand its purpose
here.
Alternatively, there could be additional errors in mys undertanding
of these functions:
LinRegSlope returns the slope for 1 period. Since the slope is
linear, it can be annualized by multiplying a daily slope by 252
market days in a year. Multiplying by n will provide total increase
over the entire backtest.
StdErr returns the standard error function (the 1-period average of
the entire range). Since it is essentially a 1-period standard
deviation, to annualize this value you should multiply by sqrt(252).
It seems to me that LRS / StdErr = K-Ratio for one day.
To annualize this, it should be multiplied by 252/ sqrt(252).
Of course, any number multiplied by its sqrt = its sqrt, to the
annualized version can be simplified to
LRS/ StdErr * sqrt(252).
If for some reason, you do not want an annualized version that can be
compared for various time frames, you can create the cumulative
version by replacing 252 with n (the number of observations). This
suggests that sqrt(252) should be in numerator instead of n being in
the denominator.
My thinking and/or assumptions must be off somewhere, but I cannot
determine where.
--- In amibroker@xxxxxxxxxxxxxxx, Thomas Ludwig <Thomas.Ludwig@xxx>
wrote:
>
> TJ once explained that in a posting in this list:
>
> > Hello,
>
> > By the way it is NOT surprising that you are getting lower values
> >than before.
>
> > In his book Mr. Lars Kestner writes:
>
> > ' The K-ratio is a unitless measure of performance that can be
> >compared across markets and time periods. [ - - - ] Traders should
> > search for strategies yielding K-ratios greater than +0.50.
> >Together, the Sharpe ratio and K-ratio are the most important
> > measures when evaluating trading strategy performance. Note: When
> >I created the K-ratio in 1996, I thought I had created a
> > robust measure to evaluate performance. In mid-2000, trader Bob
> >Fuchs brought a small error to my attention regarding the
> > scaling of the K-ratio. He was correct in his critique and I have
> >corrected the error in this text. Publications prior to 2002 will
> > show a different formula for the K-ratio. The updated formula in
> >this book is correct.'
>
> > Previous AB versions contained old K-ratio formulation [of 1996]
> >and newest one contains
> > new formulation [from Kestners book of 2003].
>
> > The difference between those two formulations [i.e. 'trader Bob
> >Fuchs brought a small error to my attention regarding the
> > scaling of the K-ratio. ' ]
> > is just the factor denominator that is now [NumberOfObservations]
> >instead of SQRT[ NumberOfObservation]
>
> > Since [NumberOfObservations]/SQRT[NumberOfObservations] = SQRT
> >[NumberOfObservations]
> > it makes it obvious that new K-ratio figures will be SQRT
> >[NumberOfObservations] times smaller than previous.
>
> > The relationship between new and old version can be written as:
> >
> > KRatio[ NEW2003 ] = KRatio[ OLD1996 ]/SQRT[NumberOfObservations]
>
> > You can correspond with Mr. Kestner why 'new' is better than 'old'
> >but do not discuss this with me, because I did not invent it.
>
> I guess that answers your question.
>
> Greetings, Thomas
>
> > I made two posts on this subject a couple of weeks ago, but it
seems
> > those posts have disappeared.
> >
> > Anyway. I am now able to duplicate the AmiBroker 4.96 beta CBT
results
> > for K-Ratio. My implmentation follows and appears to match the
> > AmiBroker results for backtest periods lasting from 2 months to
17+
> > years.
> >
> > Eq = Foreign("~~~EQUITY", "C"); // Assign Close of Backtest
Equity = Eq
> > n = Barcount -1; // Number of periods
> >
> > // K-Ratio - only valid for non-compounding systems
> > EqLRS = LinRegSlope(Eq, n+1); // Linear Reg Slope of entire (n+1)
range
> > EqSE = StdErr(Eq, n+1);// Std Err of entire (n+1) range
> > EqKR = EqLRS/EqSE; // K-Ratio (unitless measure)
> > EqKRAmi = EqKR*sqrt(n+1)/sqrt(12);// AmiBroker 4.96
implementation
> >
> > My question is: Why does it require a divide by sqrt(12) to work?
> >
> >
> >
> >
> > Please note that this group is for discussion between users only.
> >
> > To get support from AmiBroker please send an e-mail directly to
> > SUPPORT {at} amibroker.com
> >
> > For NEW RELEASE ANNOUNCEMENTS and other news always check DEVLOG:
> > http://www.amibroker.com/devlog/
> >
> > For other support material please check also:
> > http://www.amibroker.com/support.html
> >
> > Yahoo! Groups Links
> >
> >
> >
>
Please note that this group is for discussion between users only.
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SUPPORT {at} amibroker.com
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