## Financial Risk Modeling

Financial Risk Modeling can be considered to be a kind of financial models which primarily help in predicting the possibility and magnitude of the impact of unfavorable events on the financial outcomes for any entity, portfolio, business or individual.

As stated by economist Frank Knight,

If you don’t know for sure what will happen, but you know the odds, that is a risk. If you don’t even know the odds, that is uncertainty.

In the context of investments, risks can be typically classified into two major categories:

• Systematic
• Unsystematic.

Systematic risks are those risks which can’t be diversified away and which are highly likely to impact all the investments adversely. Unsystematic risks are also known as ‘specific risks’ which are specific to individual asset classes or investments e.g. interest rate risk, foreign currency risk, country risk, political risk, credit risk etc.

There would always be some events which are completely unknown. These kinds of scenarios are also categorized as “ risk risks” i.e. risk of not knowing some of the risks.

Note: A somewhat relevant term that’s commonly used is ‘black swan’ event which is an extremely improbable but extremely adverse (in terms of magnitude) event.

There are many statistical techniques and software tools such as R, MATLAB, which can be used for modeling and predicting risk. Some of the organizations also develop their own risk models as well as risk modeling programs (software). While the risk parameters measured and monitored by different organizations may vary, the fundamentals of the process remain same.

Financial Risk Modeling is somewhat similar but a lot more detailed as compared to ‘ sensitivity analysis’. The purpose of Sensitivity Analysis is to identify the parameters/ inputs on which an outcome is dependent and to assess the extent of dependency (also called sensitivity). Risk model takes sensitivity analysis to the next level by assessing the probability distributions of the inputs and helps in defining the probability distributions of the outcomes.

Let’s try to understand this concept with a simple example. Let’s assume an output O which depends on 2 parameters say A and B as per the relationship is shown below.

O = A + 3 B

Prima-facie, sensitivity analysis for this output would tell you that ‘O’ is more sensitive to B than A. How? Based on the fact that change in O per unit change in B is greater than the change in O per unit change in A.
Change in O per unit change in B = 3
Change in O per unit change in A = 1

Risk analysis would take the sensitivity analysis to the next level by plotting the probability distributions of inputs A and B. Let’s assume that A and B can be integers between 0 and 3. Also, A and B are independent of each other. Based on these distributions, it would be interesting to plot the probability distribution for the output O. Numbers in brackets along with possible values of A and B are the probabilities of the variables being equal to corresponding values. Based on the assumed relationship between O, A and B (O = A + 3 B), the values of O can be calculated as follows: Probabilities of obtaining the outcomes from the above table would be dependent on the respective probabilities of corresponding values of A and B. Since A and B are assumed to be independent, the probability P(O) can be calculated as:

P(O) = P(A) x P(B). The tables are not very intuitive so plotting the probability distributions below:

P(A) P(B) Based on the assumed probability distributions of A and B (above), the following probability distribution for the outcome (below) can be drawn. It indicates that O can possibly take any integer values between 0 and 12 and the most likely outcome is 6. If the minimum desirable outcome in this case is 8, then the probably of obtaining the undesirable outcome (0 – 7) would be:

` P (O, undesirable)       = 1 – P (O=8) – P (O=9) – P(O=10) – P(O=11) – P(O=12) = 1 – 0.1 – 0.125 – 0. 025 – 0.025 – 0.025 = 1 – 0.3 = 0.7`

In real life, the outcome can possibly be annual return on a stock of a company owned by an investor who is looking for a minimum target of say 8% with A and B being inputs such as, say, growth in profitability in domestic market (%) and growth in profitability in exports (%).

Financial Risk Modeling enables a similar analysis of outcomes and helps various stakeholders in decision making. Some of the key points with respect to financial risk modeling are:

• In real life scenarios, neither the distributions of inputs nor the relationships between the inputs and outcomes are as simple as we assumed in the example above, which makes it extremely challenging to simulate risks through models
• At times, establishing the relationships between the inputs and outcomes is a challenge in itself
• In many business scenarios, a strong knowledge of statistics, probability, advanced mathematics and various modeling tools/ simulators and programming languages is a pre-requisite
• Risk modeling plays a critical role in portfolio optimization based on investor’s ability and willingness to take risk

## Quick Summary:

Financial risk modeling takes sensitivity analysis to the next level and helps in assessing the probability and potential impact of unfavorable outcomes. Based on the assessments, various decisions with respect to managing, hedging or transferring risks are taken.

Happy Financial Risk Modeling!