No. of Recommendations: 18

In his encyclopedic book, *Trading Systems and Methods*, Perry Kaufman introduces his efficiency ratio, ER, also called fractal efficiency. It is the absolute value of the price change over n periods divided by the sum of the absolute price change for each period. It has value of 1 when prices have moved in the same direction for each period. When prices move in opposite swings during the n periods the ER approaches zero. Kaufman uses the ER to calculate an adaptive moving average based on the trendiness of the market.

Having a collection of monthly SIPro data disks I looked at a monthly ER based on monthly price moves over the last nine months. Thus my ER is

ABS(Price-Price M010)/[ABS(Price-Price M002)+ABS(Price M002-Price M003)+ .... +ABS(Price M009-Price M010)]

In general, a final sort by 4wk return is unstable, sometimes mean-reverting and other times not. I looked at a 4wk sort for stocks with high ERs and low ERs to see if there was a predictive ability. In general, a low ER with a high 4-week sort made a good short screen, and a high ER with a 4-week sort made a decent long screen, albeit volatile.

We thus have the makings of an ER hedge. The long screen is

Price > 5

Price * Volume--Average Daily 10d > 500

ADR/ADS Stock = False

Exchange <> Over the Counter

Industry <> 0721-Misc.FinancialServices

Price M010 > 0

Create [EffRatio]: ABS([SI Price]-[SI Price M010]) / (ABS([SI Price]-[SI Price M002]) + ABS([SI Price M002]-[SI Price M003]) + ABS([SI Price M003]-[SI Price M004]) + ABS([SI Price M004]-[SI Price M005]) + ABS([SI Price M005]-[SI Price M006]) + ABS([SI Price M006]-[SI Price M007]) + ABS([SI Price M007]-[SI Price M008]) + ABS([SI Price M008]-[SI Price M009]) + ABS([SI Price M009]-[SI Price M010]))

EffRatio < 0.9

EffRatio >= 0.7

Sort Descending Price Change 4 week

And the short screen is the same except that

EffRatio < 0.2

EffRatio >= 0

The results for the long and short screens up to 2003 can be found in Keelix jobs 312341 and 312342. Early in 2003 the Keelix backtester switched to weekly data and a 4-week hold rather than monthly. Thus the dates began to drift and introduce a lag. The results from 2003 on are based on monthly data disks.

So, how has the hedge performed over the last 14 years? Not bad, considering most hedges are lucky to yield a CAGR of 10%. (Well, actually any method that yields 10% a year has beaten the S&P500 by 6 percentage points and done quite well.)

The results for a monthly hold of five long stocks and five short; the only disappointing year was 2006.

Hedge S&P500

CAGR 26% 4%

GSD 27 20

Ratio 0.96 0.20

.

1997 38% (4 months)

1998 72

1999 18

2000 82

2001 38

2002 41

2003 27

2004 27

2005 70

2006 -24

2007 8

2008 - 3

2009 50

2010 - 2

2011 3

For someone with facility with Robbie's GTR1 backtester, it would be very interesting to see this approach tested with daily data and different look-back periods.

DB2