Discussions about Money Management and Risk Control.
kianti
Roundtable Knight Posts: 335
Joined: Fri May 02, 2003 6:10 am
Location: Florence - Italy

Positive Trade Ratio   sluggo
Roundtable Knight Posts: 2987
Joined: Fri Jun 11, 2004 2:50 pm
It's ironic that Gardner says PTR is similar to the Sortino Ratio except that "there is no need for Downside Deviation" - - - and immediately afterwards, he calculates his own slightly-modified Downside Deviation (in the denominator).

The only difference between his denominator and Sortino's, is the fraction in front of the summation.

Gardner uses (1 / (#returns - 1))

Sortino uses (1 / (#negativeReturns - 1))

Whoop de do

Eventhorizon
Roundtable Knight Posts: 229
Joined: Thu Jul 08, 2010 2:36 pm
Location: Boulder, CO
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I may be wrong here but ...

Sortino uses a different numerator AND a different denominator. The denominator is different in two ways from Gardner's statistic:

Sortino numerator: cumulative average return (geometric return) less target return

Gardner Numerator: average (arithmetic) trade return.

Sortino denominator: root mean (i.e. 1/n) square deviation from the target of period returns that were below the target return. i.e. SQRT(SUM(Ri - T)^2/n) for all (Ri < T) where Ri is the ith period return, T is the Target, n is number of periods for which Ri < T.

Gardner Numerator: population estimate (i.e. 1 / (n+1)) of the deviation from the mean trade return of trades that were below the mean trade. i.e. SQRT((Ti - Tbar)^2 / (n+1)) for all (Ti < Tbar) where Ti is the ith trade, Tbar is the average trade and n is total number of trades.

Essentially, Gardner's Positive Trade Ratio uses the average trade as the target return - that's why he claims there's no need to select a minimum acceptable return (the target).

But, still, whoop de do!