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On Wed, 22 Oct 2003 19:14:13 +0200, in Amibroker you wrote:
[...]
>
> HELP ON NEW FEATURES
> New backtest report
> New report is hugely enhanced compared to old one. It includes separate statistics for all, long and short sides as well as large number of new metrics. You can get short help on given figure by hovering your mouse over given field name. You will see the description in the tooltip. Short explanations are provided also below:
>
[...]
>
> Sharpe Ratio of trades - Measure of risk adjusted return of investment. Above 1.0 is good, more than 2.0 is very good. More information http://www.stanford.edu/~wfsharpe/art/sr/sr.htm . Calculation: first average percentage return and standard deviation of returns is calculated. Then these two figures are annualized by multipling them by ratio (NumberOfBarsPerYear)/(AvgNumberOfBarsPerTrade). Then the risk free rate of return is subtracted (currently hard-coded 5) from annualized average return and then divided by annualized standard deviation of returns.
>
> K-Ratio - Detects inconsistency in returns. Should be 1.0 or more. The higher K ratio is the more consistent return you may expect from the system. Linear regression slope of equity line multiplied by square root of sum of squared deviations of bar number divided by standard error of equity line multiplied by square root of number of bars. More information: Stocks & Commodities V14:3 (115-118): Measuring System Performance by Lars N. Kestner
Tomasz,
Thanks a lot for all these improvements. But as helpful as these new
figures might be they do not tell us if the backtesting results are
statistically significant.
Therefore I suggest to add a new figure proposed by Arthur Merrill in
Stocks & Commodities some years ago (Bonus Issue 1993). It's called
the "chi squared with one degree of freedom, with the Yates
correction". It's calculated using the following simple formula:
X^2 = ( |R-W| -1)^2 / (R+W)
where: R = number of times right
W = number of times wrong
Interpetation:
Below 3.84: Significance doubtful.
Above 3.84: Probably significant. Probability of one in 20 that the
result was by chance.
Above 6.64: Significant. Probability of one in 100 that the result was
by chance.
Above 10.83: Highly significant. Probability of one in 1,000 that the
result was by chance.
Let`s apply this formula to a simple example. Let's assume that the
backtest gives 10 signals with 7 of them profitable; let's also assume
that the other figures in the backtest report are okay. So the results
look good at the first glance. However, the chi squared figure is just
0.9 - very insignificant!
On the other hand, if the backtest gives 100 signals with 70 of them
profitable the chi squared figure is a whopping 15.21 - highly
significant!
I agree that these a very simple examples and that the difference
between them sholud be rather obvious. But I'm afraid that even
obvious things are often overlooked, especially if the other figures
in the backtest report seem to be good. Therefore the chi squared
figure would be a valuable addition for the correct interpretation of
the backtest results.
Tomasz - what do you think about this?
Regards, Thomas
--
Thomas Ludwig
PGP key (RSA) available on request.
Fingerprint: 4356 55FF 3412 277A 9741 1CFA B9A6 7B90
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