Risk calculation

How Analys determines risk.

Introduction

Similar to the expected yield calculation, the risk calculation determines how risky each TAF is by aggregating and analysing previously-collected data.

Definition

Risk is the general term referring to the potential and probability of financial realized or unrealized loss. It not also defines the potential drawdown or complete liquidation but also the probability of it. Hence, a project having a 10% chance of seeing a 50% unrealized loss has the same risk score as a project having a 20% chance of seeing a 25% unrealized loss. All losses are calculated in USD and denominated as percentage points.

Machine learning

Similarly to the expected yield calculation. Analys AI uses machine learning to assess which factors are the most important for determining the risk of a TAF. Temporality, as well as the other data collected previously shall be used to infer the determinants for an optimal risk analysis.

Analys AI uses many mathematical models to infer the most optimal way to calculate TAF risk, combining native mathematical models as well as AI-determined ones.

The goal of the machine learning analysis is first to determine the downside probability $P$ and the financial loss $L$ to later put the two values together as determinants for the risk.

Here is a non-exhaustive list of the most important native mathematical models used to determine risk:

• Downside probability model: Statistical models, such as logic regression are used to estimate the probability of downside for each TAF. The formula for the downside probability $P_i$ ​ is given by the logistic function, which ensures that the probability remains within the range of 0 to 1. This function is expressed mathematically as:

  $$P_i = \frac{1}{1 + e^{-\left(\beta_0 + \beta_1 X_1^{\gamma_1} + \beta_2 X_2^{\gamma_2} + \dots + \beta_n X_n^{\gamma_n} \right)}}$$

  where $P_i$ represents the probability of loss, $X_1, X_2, ... , X_n$ the independent variables, $\beta_1, \beta_2, ... \beta_n$ the coefficients and $\gamma_1, \gamma_2, ... , \gamma_n$ the independent coefficients.

• Relative loss expectation model: Expected financial loss percentage $L_1$ is modeled using non-linear regression to capture potential losses based on each criterion. For example, a polynomial regression model is used to determine the relationship between a criterion and potential loss:

  $$L_i = \alpha_0 + \alpha_1 X_1^{\gamma_1} + \alpha_2 X_2^{\gamma_2} + \dots + \alpha_n X_n^{\gamma_n}$$

  where $\alpha_1, \alpha_2, ... , \alpha_n$ represent the loss coefficients, $X_1, X_2, ..., X_n$ the independent variables and $\gamma_1, \gamma_2, ... , \gamma_n$ the exponents for non-linear risk factors.

• Dynamic weighting system: In order to assess the relative weights, which evolve with time, each criterion’s weight is adjusted using a machine learning model that identifies patterns in past performance. Here is an example of the formula used for the determination of $w_i$ of P (note: This is the simplified version of the mathematical model used by Analys AI):

  $$w_i = \frac{P_i}{\sum_{j=1}^{n} P_j}$$

  Where $P_i$ is the historical risk score associated with the $i^{th}$ criterion, allowing Analys AI to dynamically prioritize the most critical risk factors.

Note: These are the basic models used by Analys AI to run the machine learning system in order to infer mathematical formulas. However this is a non-exhaustive list of all the models used, most of them being directly created by Analys AI. The models mentioned should help the reader understand the basis of the machine learning but in no way represent the full method (which would be too heavy to describe in such a short documentation and isn't fully developed as of right now (10.24).

Determination of Risk Influence Score

Risk Influence Score (RIS) refers to the results obtained from the machine learning to infer the most important criteria for the determination of risk. It is therefore an evolutive weighted average of downside probability and relative financial loss in that scenario. Here is the formula used

$$RIS = \frac{1}{n} \sum_{i=1}^{n} \left( w_{P_i} \cdot P_i^{\alpha} + w_{L_i} \cdot L_i^{\beta} \right)$$

Where $Pi$ is the downside probability of the $i^{th}$ criterion, $Li$ the relative financial loss of the $i^{th}$ criterion, $w_{P_i}$ and $w_{L_i}$ the respective weights, $\alpha$ and $\beta$ the respective non-linear factors for $P$ and $L$.

Determination of risk

Combining the present data for each TAF with the newly-determined RIS function, Analys AI is able to assess the RIS for each TAF for all possible timelines.