Maximum profitability,
a new measure of returns.

 J. Ignacio Ulacia F. (12.3.2002)


The study was performed assuming that during a specified time period, it would be possible to time the market. Enter at the open (O), obtain the high(H), hit the low (L) and liquidate the trade at the Close(C). With two complete cycles per time-period. A complete cycle will be the buy and sell process to return to cash; is not relevant the position long or short. Even though during the timeframe specified, the market may have several highs and lows and more cycles could be completed, this study only considers the O,H,L,C values.

From these assumption it is possible to determine the maximum return in a specified time-period is

Long : I1= Io * (H/O)*(H/L)*(C/L) = Io * (H*H*C)/(O*L*L)

Short: I1 = Io * (L/O)*(L/H)*(C/H) = Io * (L*L*C)/(O*H*H)

where I1 and Io are Investment at the end of the period and Initial Investment respectively


Since we are looking for the maximum return then

Z1 = Max(I1 (Long) , I1 (Short))


The compounded annualized investment can be deduced as


I2 = I1 * Z1 = Io * Zo *Z1

I3 = I2 * Z2 = Io * Zo * Z1* Z2


In/Io = (1 + R )m = Prod(Zn)[n=1,m]

where "R" is the annualized interest rate and "m" will be the necessary periods to make one year.


Using the Nasdaq as a testing vehicle from inception until 07.2004 and considering several time periods we obtain an annualized rate form Graph 1


Graph 1: Annualized maximum return rates for Nasdaq assuming the new metric. y axis is In/Io. The process was computed daily for the previous year. The time periods are for the first line daily data, then weekly data, monthly data and Yearly data.


It can be seen that for daily data the possible returns could be extremely more profitable because the frequency is higher. Most important is the amount of returns possible. In 2001 it would have been possible to obtain retunes in excess of 1e10.


If the data is normalized to compute interest Rate "R" and exclude frequency of trading related by "m" periods, then it transforms to.


R = 10^((1/m) log(In/Io))-1



Graph 2. Interest rate computed form annualized returns on a period basis. We see that day trading has the lowest average return but frequency of trading is the variable that makes huge returns. The number of days used for each calculation is Daily - 251 periods, Weekly &endash; 52 periods, Monthly &endash; 12 periods, Yearly 1 period).


Taking into consideration that scalpers perform close to 40-60 trades per day (@251 days/year = , day traders form 2-10, Position traders 2-5 per month and Investors 2-10 per year. It can be seen that the largest potential for scalpers and day traders. However it has been noticed that returns for these trading schemes is very poor compared to position traders.


From the literature, we can see that exceptional traders have annual compounded returns as follows



Yearly Return

Stuart Walton

10 years

Dana Galante

5 years

Ahmet Okumus

8 years

Mark Menervini

6 years

Steve Lascarbeau

Mutual Funds
5 years

David Shaw

11 years

Steve Cohen

7 years

Michael Marcus

10 Years

Bruce Kovner

10 Years

Paul Tudor Jones

5 Years

Ed Seykota

16 Years

Larry Hite

7 Years

Michael Steinhardt

21 Years

William O'Neil

10 Years

David Rayan

3 Years

Jorge Soros

Quantum Fund
30 Years

Peter Lynch

Magelan Fund


Warren Buffet

Chales Munger

[1] New Market Wizards, [2] Market Wizards, [3] Pirate Investor ad.


Compared with the possible returns that could be obtained form the maximum return, the returns obtained form these master traders seems ridiculous. Therefore the market should be VERY DIFFICULT to trade.



1) The potential for returns in the stock market are HUGE on a daily basis.

2) It is possible to relate the true returns to the maximum to obtain an efficiency factor for every trader according to market conditions.



[1] Jack D. Schwager, "The New Market Wizards", HarperBusiness, New York (1992).
[2] Jack D. Schwager, "Market Wizards", HarperBusiness, New York (1990).

Copyright 2005© J. Ignacio Ulacia F., All rights reserved