Things to Consider in Setting Money Management Rules – Part 3: HOW LONG YOUR CAPITAL CAN LAST

In setting money management/position sizing rules, you should also consider:

1) How long your capital can last, or

2) How long your account balance will drop to the risk tolerance you’re willing to take after going through a series of successive losing steaks.

The answers to these questions will depend on:

* The initial capital/account balance

* How much to risk per trade

* The percentage risk tolerance (for Qtn 2)

Suppose your initial capital is $10,000.

If you money management rule is that you would risk maximum 5% of the initial capital (i.e. 5% x $10,000 = $500) in each trade, your capital will be all wiped out after 20 successive losing trades.

Suppose your risk tolerance is 25% (i.e. 25% x $10,000 = $2,500), your balance will reach this level after 5 losing trades in a row.

Notice that the above rule is different from what has been discussed as Option 2 in the previous article.

In the Option 2, the maximum risk in each trade is 5% of the remaining account balance.

Hence, with the initial capital of $10,000, after losing 5% (i.e. 5% x $10,000 = $500) in the 1^st trade, the balance will be $9,500. Then, the 2^nd trade will risk 5% of the remaining balance (i.e. 5% x $9,500 = $475), the balance will be $9,025, and so on.

Using this rule, to answer the above questions is not that straightforward. However, this rule is more common to be used by traders.

Hence, let’s try to formulate it.

Trade 1: $10,000 x (1 – 5%) = $9,500

Trade 2: $10,000 x (1 – 5%) x (1 – 5%) = $10,000 x (1 – 5%)^2 = $9,025

Trade 3: $10,000 x (1 – 5%) x (1 – 5%) x (1 – 5%) = $10,000 x (1 – 5%)^3 = $8,573.75

Trade n: $10,000 x (1 – 5%) x (1 – 5%) x (1 – 5%) x …… = $10,000 x (1 – 5%)^n

Putting in a formula form:

Where:

C = Initial capital (Initial account balance)

R = % Risk for each trade

n = Number of trades

B = Remaining capital/account balance

To answer the above two questions, we need to solve n, which can be done through the basic principles of logarithm, as follows:

Please note that, to answer Qtn 1, we CANNOT set the remaining account balance as zero, as logarithm function will never touch zero line. Hence, we should assume a certain amount, which is small enough and can be deemed as “no more money for trading”.

For example:

Assume we deem $100 as small enough to approach a situation of “no more money for trading”.

Continue with the above case, the values of each variable are:

C = $10,000

R = 5%

B = $100

To find how long the capital can last, we solve n:

Note: Always round down the result.

Likewise, to answer Qtn 2 where the risk tolerance is 25% (i.e. 25% x $10,000 = $2,500), the values of each variable will be:

C = $10,000

R = 5%

B = $10,000 - $2,500 = $7,500

Solving n:

Alternatively, we can also use another method to answer the questions, which is using Tabulation, as what has been done in the previous article:

Using this way, after inputting the formula in MS Excel accordingly, we just need to “drag the row” to copy the formula until we reach the desired account balance.

From the above table, the answer for Qtn 1 is highlighted in yellow, whereas the answer for Qtn 2 is in green.

For reference, the following are the formula used for both methods: