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Please forgive me if someone has already followed-up to Mark Johnson's
reply to Paul Lasky's T-Test results. As Mark pointed out the statistics
were calculated on the incorrect time series, i.e. raw-equity curve. To
apply the t-test to the equity curve it is better to look at the monthly
rate-of-return of the two betting strategies. I did this using the data
provided by MarkJ and as suspected in Spear vs. Fixed Ratio - that Spear
is better with a T-stat value of ~1.5, which is pretty good although
some statisticians would probably like to see a P-value of 0.05 for
which this test does not pass. As for Spear vs. UnequalFR the T-stat is
~0.01, which shows there is no difference between the two strategies.
Now of course the above results make sense since looking at the return
figures, drawdown-stats, etc.Spear is much better then Fixed-ratio and
not too different then the Unequal-FixedRatio scheme. This can also be
seen with the Sharpe ratio values reported by Mark. Remember as Bill
Sharpe has pointed out in his many papers on the use and abuse of the
Sharpe ratio is it closely tied to the T-stat.
So is the case closed? Maybe... the only main problem with the above
analysis is that the T-Test assumes a normal distribution (or near
normal). So we need to see if the return distribution follows a normal
distribution. If it does we are done - if not then the t-test might be
suspect. Using the KS-GOF test or by just looking at Q-Q plots one can
see the distributions are no where near normal. To get around this you
would just need to Bootstrap the betting strategy results using say a
1000 samples and see how many times Spear beat FixedRatio. Just an FYI,
even for distributions that are not normal most bootstrap test results
do follow the t-test results in the trading strategy studies I have seen
and performed.
Well enjoy trading which ever betting scheme (aka money management
scheme) you like.
Marc
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