Maximum profitability,
a new measure of returns.

J. Ignacio Ulacia F. (12.3.2002)

Using the market metric is relative.
with trades going long and short the old metric is irrelevant
Having a exceptional goals forces the trader to general exceptional returns

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= I_o * (H/O)*(H/L)*(C/L) = I_o * (H*H*C)/(O*L*L)

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

where I₁ and I_o 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 = I_o * Z_o *Z₁

I₃ = I₂ * Z₂ = I_o * Z_o * Z₁* Z₂

...

I_n/I_o = (1 + R )^m = Prod(Z_n)[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 I_n/I_o. 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

Trader	Vehicle	Yearly Return	Period	Ref
Stuart Walton	Stocks	115%	10 years	[1]
Dana Galante	Stocks	15%	5 years	[1]
Ahmet Okumus	Stocks	107%	8 years	[1]
Mark Menervini		220%	6 years	[1]
Steve Lascarbeau	Mutual Funds	70%	5 years	[1]
David Shaw	Stocks	22%	11 years	[1]
Steve Cohen	Stocks	45%	7 years	[1]
Michael Marcus	Commodities	118%	10 Years	[1]
Bruce Kovner	Currencies	87%	10 Years	[2]
Paul Tudor Jones	Commodities	>100%	5 Years	[2]
Ed Seykota		117%	16 Years	[2]
Larry Hite		30%	7 Years	[2]
Michael Steinhardt	Stocks	30%	21 Years	[2]
William O'Neil	Stocks	40%	10 Years	[2]
David Rayan		1013%	3 Years	[2]
Jorge Soros	Quantum Fund	32%	30 Years	[3]
Peter Lynch	Magelan Fund	29%		[3]
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.

Observations:

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.

Reference

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

Maximum profitability, a new measure of returns.

Maximum profitability,
a new measure of returns.