Expected yield calculation

How Analys predicts real yield.

Introduction

This page covers the important Artificial intelligence part of the project. It is about putting together price of the tokens and the fundamentals of the TAFs to give a realistic approximation of future real yield.

Definition

Real yield is here defined as the yield, adjusted for change in price of the respective token. It is therefore a complete evaluation of a TAFs earning potential, including all factors. Therefore, it is mainly the intersection of apy and token price change. Other minor factors, such as protocol fees are taken into account.

Real yield is calculated on the United States Dollar (USD) value of the different investments. This is because in a highly volatile environment, it is important to have an anchor value that is as stable as possible. In that case, Alchemis chose the USD.

Use of AI

Since the different data collected often are of a subjective nature in relation to the final expected returns, a strict program of a grading system isn't optimal, since it would only take value as they are. That is why the development of an artificial intelligence is mandatory for a protocol such as Alchemis. Once the machine learning has been validated, the AI model will hardly change, only weightings will have the possibility to change over time, under specific circumstances.

However, the factors used will be fixed, these mainly include apy, protocol TVL, token market cap and liquidity. While other factors are used, about 80% of the findings rely on these four elements.

Machine learning

Analys AI is an advanced machine learning system designed to conduct complete analyses of each TAF. By leveraging a robust database built from historical data, Analys AI can evaluate the actual yields generated by different TAFs in the past. The goal at this point is only to determining which factors are the most important for the determination of real yield.

Previous dataset of token and TAF will be the basis for the criteria described in this section. Temporality is also an important criterion used for the determination of real yield. Results will have different values for each temporality.

Analys AI possesses native analysis techniques as well as the ability to create further mathematical models to assess the most important criteria. Here are some of the most important and understandable native mathematical functions embedded in Analys AI's code:

• Linear Regression Models: These models are used to infer yield outcomes based on multiple independent variables (criteria). The general formula can be represented as:

  $$Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + ... + \beta_n X_n + \epsilon*i$$

  where $Y$ is the yield, $X_1, X_2, ... , X_n$ the independent variables (criteria), $\gamma_1, \gamma_2, ... , \gamma_n$ the coefficients and $\epsilon*i$ the incertitude (the deviation of the results from the mathematical model).

• Polynomial regression: Similar to the previous model, this model is used when the relationship between a criterion and yield is non-linear. This model uses polynomial terms to better infer the most important criteria. It can be represented as:

  $$Y = \beta_0 + \beta_1 X_1^{\gamma_1} + \beta_2 X_2^{\gamma_2} + \beta_3 X_3^{\gamma_3} + \dots + \beta_n X_n^{\gamma_n} + \epsilon*i$$

  where $Y$ is the yield, $X_1, X_2, ... , X_n$ the independent variables (criteria), $\gamma_1, \gamma_2, ... , \gamma_n$ the coefficients, $\gamma_1, \gamma_2, ... , \gamma_n$ the exponents and $\epsilon*i$ the incertitude (the deviation of the results from the mathematical model).

• Logarithmic Transformations: Both of the previous models can be modified with the use of logarithms to normalize distribution.

• Multicollinearity Assessment: Analys AI assesses multicollinearity among independent variables to ensure that the criteria used do not excessively correlate, ensuring multiple highly-related criteria don't have an excessive weight.

• Principal Component Analysis (PCA): If a large number of criteria are analyzed, PCA can be employed to reduce dimensionality while retaining essential information. This is to reduce the amount of criteria used to only use the most relevant ones for the determination of real yield.

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 do not represent the full method. The goal of this short introduction was simply to help the reader grasp the main idea of Alchemis' use of machine learning.

Determination of Impact Factor Score (IFS)

The Impact Factor Score (IFS) is the native weighted scoring system used by Analys AI to quantify the influence of each criterion on real yield. It is a parallel process to the linear regression models to determine the impact of each criterion.

Calculation

Each criterion is assigned a weight based on its previously calculated significance in the determination of yield. The formula runs as following:

$$IFS = \frac{1}{n} \sum_{i=1}^{n} w_i^{\gamma_i} C_i$$

where $n$ is the number of criteria used, $i$ each individual criterion, $w_i$ the weight of the $i^{th}$ criterion and $C_i$ the value of the $i^{th}$ criterion and $\gamma_i$ the exponent of the weight. $1/n$ ensures the float value represents the average and not the total.

Determination of real yield expectation

Finally, by combining the present data for each TAF with the newly-determined IFS function, Analys AI is able to assess the IFS for each TAF for all possible timelines.