# Risk Management

When we talk about Risk Management we refer to a correct and appropriate use of our capital at hand, in relation to leverage (and not only that).

Let's make an example with a demo strategy (Strategy A) analyzing the number of underlying stock of 158 securities. In the (theoretical) hypothesis of allocate \$10,000 for every signal, we should get ready for an all-front exposition on all securities, 158x10.000 = \$ 1.580.000.

Now the problem of the optimal use of the capital comes into play. It can not ignore some statistic data we can obtain thinking in a portfolio perspective, so to speak.

We will particularly extrapolate the fluctuation of the daily exposition for the different securities in the previous years. In this example, we will control the daily exposition on the securities.

This datum is provided by the following chart:

From here, we can easily infer the daily peaks (118 securities opened on 08/17/11 out of 158) as well as a normal average of the daily average opened positions (an average 24.8 securities per portfolio every day).

If we want to deepen this analysis and see how much capital can be used at best, we need another statistic value that leads us to the following chart.

What we see is an important piece of information: at 90% confidence, the system can be opened up to a maximum value of 28% of all the potentially tradable securities (158). 28% of 158 equals 44.2 securities.

If we want to 'have shelter' from the fact the system may result open up to 44 securities on the same day (that is, not running the risk to have enough money in our account) knowing this scenario covers up to 90% of cases, we will only need to use a proportioned capital of 44 securities, not 158.

In the above mentioned theoretical example of a \$10,000 investment for every signal, we will need only \$440,000, not \$1,580,000.

If we want to make this example more complicated and introduce leverage, we can reach the target for this section: understand how to optimize our used capital and efficiently follow our strategy. Let's put the leverage level at 2, indeed a very cautious one.

This implies that (always use caution) we should achieve an actual leverage of 2 if the system reaches exposition levels that are close to the observed higher levels (44 securities, as in the example). We will then be sure every less exposed value (knowing it will be lower in 90% of cases), our actual leverage will be proportionally lower. Starting from this, taking 2 as the maximum actual leverage, allocated capital will be \$440,000 / 2 = \$220,000.

As a proof, in case of exposition on 44 securities (the maximum example at odds 90%,) the exposed amount will be 44* \$10,000 = \$440,000 ; such amount is exactly twice as much as the allocated capital, that is, our leverage in the worst prediction. In the case of an average exposition of 25 daily securities in position, the total amount will be 25 * \$10,000 = \$250,000.

Such amount has a 1,13 ratio with the allocated capital, the actual leverage with regard to the average exposition of the strategy.

We demonstrated our actual leverage will always be under control and never exceeding the maximum fixed value.

Such counting is meant to be only a suggestion for every savvy investor to reflect upon the maximum risk he/she is willing to undertake. Same thing for the capital a trader is actually willing to allocate and be able to follow the system in every phase of the market, with no need to stumble on the so called margin call.

Let's make another example using the same statistic counting with reference to another strategy, Strategy B.

What we can see at first is that this strategy developed maximum daily peaks of 137 securities out of 158 on 11/25/11 (86% of the maximum available) and an average of the opened position amounting to 37.7 securities (23.8% of the maximum available).

What it clearly stands out is that a 90% level of confidence is reached in this strategy with a 49% exposition.

This says that at odds of 90% the system may stay open on 49% of the maximum number of total securities (158), i.e. 77.4 securities. Implementing the same algorithms on that value, we will be able to easily determine the capital to be allocated for its efficient use, either using physiological levels of leverage or in lack of it.