F-Forex, Diary of a quant forex trader

Kelly formula to calculate optimal f

To calculate optimal f using kelly formula the market system  haves to drop the outcomes in a Bernoulli Distribution. This is a distribution where only 2  possible outcomes are possible. Example:

+2      -1      -1      +2      +2      -1      -1      +2

optimal f = ((B + 1)*P-1)/B

where P = the probability of a winning trade
B = The ratio of amount won on a winning bet to amount lost on a losing bet.

f = ((2+1).5-1)/2
= (3*.5-1)/2
= (1.5 -1)/2
= .5/2
= .25

We will try to find a market system with Bernoulli distribution outcomes to facilitate calculus of optimal f and others.

An optimal f of 0.25 means that i will trade $1 for every $4 in stake to maximize geometrical growth of account equity.

http://en.wikipedia.org/wiki/Kelly_criterion

Tags: bernoulli, bernoulli distribution, geometrical growth, kelly, kelly formula, optimal f

Money mgmt intro

In this new section i will introduce some notes from the book “The mathematics of money management” by Ralph Vince, other money management definitions and techniques will be also presented and personal experiences, tests of using money management techniques.

A first axiom of money management will be:

Hope for the best but prepare for the worst.

profits and loss will be now defined as holding periods returns(HPR).

a HPR is defined as 1 + % of profit or loss, example: 0.1% of profit, hpr = 1.01. loss of 0.8%, hpr = 0.92.

A market system is each stage of a trade. In our statistical arbitrage strategy we open trades in opposite sides when the pairs are correlated(correlation coefficient in the big window(1440 bars) is greater than 0.80).

if differential is between 1 and 2 std deviations we open 0.1 lots, this will be one market system.

if differential is between 2 and 3 std deviations we open 0.2 lots, this will be another market system.

if we continue up to 1.6 we have 5 market systems in total for this strategy.

We will call a unit in forex to 1 mini lot of 10.000 usd.

At any market there is an optimal amount of money to trade related to the level of account equity to maximize geometric growth, this is called optimal f.

Mathematical expectation refers to the concept that it d0sent matter how profitable a market system is, the only thing that matters is that the system is profitable or have positive mathematical expectation. The account growth is done with money management but if a system don’t haves positive mathematical expectation money mgmt can’t help.

In a game where you have 50% chance of winning $2 and a 50% of losing $1 haves a mathematical expectation of 0.5. On average you can win 50 cents per toss on average.

So going to practice, it will be nice to get a system witch can have a positive mathematical expectation as a first step to develop mathematical money management into an account.

Tags: holding period returns, market system, mathematical expectation, money management, money mgmt, optimal f