# Fixed-proportion money management

Written by Tim T.

According to the method of a fixed proportion, as the number of contracts grows, the sum which is required to buy the next number of contracts increases proportionally. As a result, the ratio of profit and risk is significantly lower than those that are characteristic for a fixed fractional method.

The formula for calculating of the possible levels of the  increase in the number of contracts is the following:

Capital of the previous level + (number of contracts * delta) = Next level

For example:

Initial capital = \$ 10,000

Number of contracts = 1

Delta = \$ 5000

\$ 10,000 + (1 * \$ 5000) = \$ 15,000 to increase the number of contracts up to 2

When the account balance exceeds \$ 15,000, then \$ 15,000 will be the starting sum in the equation:

\$ 15,000 + (2 * \$ 5000) = \$ 25,000

\$ 25,000 + (3 * \$ 5000) = \$ 40,000

\$ 40,000 + (4 * \$ 5000) = \$ 60,000

\$ 60,000 + (5 * \$ 5000) = \$ 85,000

Delta is the basis of changes. It is the only varied constant in the equation, which can be freely changed by trader according to his method or style of trading. Delta may also change the dynamics of the outcome. The general rule is: the smaller the delta, the more aggressive the money management is, and the bigger the delta, the more conservative the method becomes.

There is a proportional relationship between delta and a loss, between delta and the average profit, which allows us to calculate the level at which a trader will be in case he loses money. For example, if delta is \$ 5,000 and an expected fall in the price of a contract is \$ 10,000, the ratio of a loss to delta will be 2:1 and this ratio will always be the same regardless of how many contracts will be needed to estimate the loss. The amount of losses will be two deltas (or two contracts). For example, if a trader reaches the 10-contractual level, using  delta of \$ 5,000, and then loses \$ 10,000 per contract, then the size of the account will not fall more than two contract levels.

10000 \$ / 5000 \$ = 2

10-2 = 8

The following formula determines the change in the level of contracts:

[((Number of contracts)^2 - number of contracts) / 2] * delta = minimum profit level.

For example:

If the number of contracts is 10 and the delta is 5000 dollars, the lowest level of profit will be \$ 225,000.

10 * 10 = 100

100 - 10 = 90

90 / 2 = 45

45 * \$ 5000 = \$ 225,000

At the level of 225 000 of profit a trader (depending on increases or decreases in the size of his account) can either go from 9 to 10 or from 11 to 10 contracts.

To obtain the upper level of profit you should change "- the number of contracts" into "+ the number of contracts". Only this sum may let you increase the number of contracts from 10 to 11, or, conversely, to reduce them from 11 to 10, depending on  the direction of changes of the account.

The upper (275 000 dollars) income levels for the 10-contract trade:

10 * 10 = 100

100 + 10 = 110

110 / 2 = 55

55 * \$ 5000 = \$ 275000

A trader is interested to reduce the risk faster than the growth of profit. In order to protect the received profits it is recommended to use "rate reduction".

The "rate reduction" strategy has two basic functions: profits protection and expansion of capabilities of geometric growth. You'll hardly implement them both, so you need to choose priorities. When you protect your profit the basic idea is that when a trader loses he should quickly switch to working with a smaller number of contracts, so he will limit the amount of damages. So as you increase the effect of geometric growth, the number of contracts will be increasing faster now. Thus, the larger the potential losses, the smaller the amount of capital will be exposed to risk. This method has one drawback: the possibility for compensation of losses is reduced in direct proportion with the rate of risk reduction.

To calculate the new rate of reduction you can use the following layouts of reduction:

If

CL = current level of decrease

PL = previous level

X% = variable rate

CL - [(CL - PL) * X%] = next level of reduction

For example:

If CL = 275 000 dollars and PL = 225 000:

\$ 275000 - [(\$ 275000 - \$ 225,000) * 50%]

\$ 275000 - \$ 25,000 = \$ 250,000 (a new level of reduction)

Similarly, this formula works under a fixed-fraction method. If the number of contracts increases by one, each time the account increases at \$ 10,000, then the same formula is used:

If CL = \$ 100,000, and PL = 90000, then:

\$ 100,000 - [(\$ 100,000 - \$ 90,000) * 50%] = \$ 100,000 - \$ 5,000 = \$ 95,000 (a new level of reduction) 