Forecasting Startup Return using Artificial Intelligence Methods and Econometric Models and Portfolio Optimization Using VaR and C-VaR

In this paper, we have tried to study the main role of startups in economy, their characteristics, main goals and etc. The main goal of article is prediction of startup's return using artificial intelligence methods such as genetic algorithm (GA) and artificial neural network (ANN). Some global indices such as S&P500, DJAI, and economic indicators such as 10 years Treasury yield, Wilshire 5000 Total Market Full Cap Index along with some other special indicators in startups like team, idea, timing and etc. are used as input variables. GA is used as feature selection and finding the most important variables. ANN is used as an optimization model and prediction of startup's returns. We used econometric models such as regression analysis. We have estimated Value at risk (VaR) and Conditional Value at risk (C-VAR) for considered portfolios including three startups (public company) such as Dropbox, Inc. (DBX), Scout24 SE (G24.DE) and TIE.AS and optimal portfolio formation. The results show that AI based methods are more powerful in prediction of startup's return. On the other hand, VaR and C-VaR models are very beneficial approach in minimizing risk and maximizing return.


Introduction
Startups are mainly young companies or teams that have new ideas (Salamzadeh, A., & Kawamorita Kesim, H. 2015). Their main characteristic is innovation. They seek to provide products or services that make the life easier for applicants and customers. So, they try to make a fundamental change in production and services. This is one of the main reasons which startups called "disruptive" (Hyrkäs, A. 2016). Most of the time, they create products or services which do not have any damage to the environment. At first, because they are not known, they may have a small income stream or lack of cash flow generation. So, they need cash. They can raise capital by parents and family or they can refer to rich investors which called angel investors or they can visit venture capitalists (Schückes, M., & Gutmann, T. 2021). Venture capital is a type of private equity financing for startups. Venture capitalists analyze startups based on different parameters such as the rate of growth, income stream or cost structure, future perspective or etc. In addition to financial analysis, other criteria such as idea, team, timing, etc. are important. From financial point of view means financial analysis, a startup may not be acceptable but they may have a good team, idea and etc. that convince investors.

Fig. 1. The main characteristics of Startups
Team is very important in startups. Each one has a special skill and they have a deep commitment to the company. They may face a lot of problems which are risky such as financing, decreased sale and profitability. So, they should be flexible. They use technology to communicate with customers and promote products and services. Due to innovation and creativity and new idea, they have a high growth rate.
Startups play a significant role in the economy for different reasons. They maybe small but they can create jobs, increase productivity and boost the economy (Bjørnskov, C., & Foss, N. J. 2016). In startups, Growth rate is much more than other firms. There is a type of competition between startups that benefits both the companies and the customers, and the economy as a whole. Companies are always trying to decrease their prices and increase their quality in order to sell more. As a result, they can create the conditions to increase the level of quality. On the other hand, they can do different functions and take steps to create value such as building a brand, delivering excellent service or produce goods and services with special features which can lead to higher prices.
Sometimes startups may run out of cash to continue operating or develop their businesses. So, they need to be valued by investors. There are different methods for startups valuation. The main startup valuation models are Berkus model, Scorecard Valuation Method, Risk Factor Summation Method and etc. (Akkaya, M. 2020). Each model has its own limitations and deficits. Each valuation model should be compatible with the company's business models because as we mentioned earlier because each one has different assumptions.
One of the most common and notable prediction methods are artificial intelligence based methods. AI based methods include different sub-branches such as soft-computing, machine learning (ML), deep learning (DL), and etc. These methods have some characteristics that differentiate them from others. They have some features which are considerable: I. High calculation capacity II. Speed up calculations III. Compatible with complex data structure IV. Automation of repetitive tasks V. More efficient process VI. Error reduction and etc. (Wang, M. H. 2017).
Unlike other models such as mathematical, statistical and econometric models, they do not need any preassumption or hypothesis. For example, in econometric models and regression analysis, you need to take a few steps such as examine stationarity, checking linearity and so on. But AI based methods just require and need data and are compatible with any type of data structure.
The rest of the paper is as follows: section2 is dedicated to literature review about different startup valuation models and their results. 3rd Section is about methodology. Section4 is findings and results and the final section is about conclusions and remarks.

Literature review
There are many articles about the definition of startups. Among different definitions, one of the most validated and common definitions which is adapted from Investopedia is that "A startup is a company that is in the initial stages of business". In 2019, Magalhães, R. P. C. surveyed a widespread literature about startup's definitions and research papers in his doctoral dissertation. He studies different papers with/without a startup definition per year from 2008 to 2018.  When startups having lack of cash or liquidity, they may face to different problems such as Inability to establish a company, develop a product, marketing development and etc. One of the main ways to raise capital is to refer to an angel or venture capitalist (Hsu, D. K., et al. 2014). They analyze your financial position and financial statements, potential growth rate, team. Then, as an investment choice, decide whether to approve you or not. They may use different methods to evaluate startups. Different methods have been developed to evaluate different types of startups based on different stages of their life cycle. In the following, recent articles on various startup valuation methods along with the results have been studied.
In a research paper, Jedlickova, M., & Kutnar, P. (2017) tried to create a fuzzy model which shows the promising results for the success prediction of hi-tech companies with a short history. They attempted to

Methodology
In this paper, AI based methods and econometric models are used as prediction models. At first, as mentioned earlier, we need to normalize data using the following equation: In equation 1, numerator is the number of data. is each observation, and is the maximum and minimum observation in each indicator.
Some economic indicators and global stock indices are used as input variables as

Genetic Algorithm
GA is an evolutionary algorithm and it is based on the survival of superior members and Darwin's theory of evolution (Boudieb, D., et al. 2011). It is a process with different parameters such as initial population, crossover and mutation. Crossover which is called recombination, is used to generate new offspring by combining the genetic information of two parents. Mutation is an operator which used to keep genetic diversity of one generation and make it ready for next generation. Each one has an approximate value or size. For example, DeJong, K. (1975) suggested that an approximate value for crossover and mutation rate can be around the rate of 0.6 and 0.001 respectively. changing these two parameters can lead to different search space means a kind of exploration and exploitation. As you know, each algorithm begins with an initial population. Table (3) shows the GA parameters: We used 70% of data as training and the remaining as validation and testing. We considered 0.01 as training rate which will decrease during time and repeating. chromosomes with 24 bits are used which 19 bits represents the selection or rejection of the variables and 5 other bits shows the number of neurons in hidden layer. To obtain better results, simulated annealing is used as an optimization method which can affect mutation operator. In GA, new solutions are called offspring which are the results of crossover of two parents. Figure4 shows the GA process as feature section.

Fig 4. GA process as feature selection
New generations will be 20 best individuals and until the achievement of desired requirement, this loop and process will continue.

Initial Population Parent selection Crossover
Mutation Survivor selection Terminate and return best

Artificial Neural Network
Artificial neural network is a computing system that tries to simulate the human thinking style or method (Agatonovic-Kustrin, S., & Beresford, R. 2000). The neural network can learn through data and be improved or reinforced through training. It including three layers: I. Input layer II. Hidden layer and III. Output layer. Firstly, considered variables or indicators insert in input variables. Each layer consists of two main parameters. I. weight II. Bias. In each layer, these two parameters add up together. Then they pass through an activation function which is used to recognize non-linear features. This process is done again in hidden layer but this time, weights and biases passing through a linear activation function.
There are different types of ANN such as Feedforward Neural Network (FNN), Convolutional Neural Network (CNN) and etc. In this paper, we used multi-layer perceptron (MLP). One of the most important parameters in ANN is training algorithm. In this paper, Levenberg-Marquardt (LM) is used as an optimization network. Initial training rate and the number of iteration is 0.01 and 1000 respectively. ANN parameters are as Table (4):

Econometric Models
Economic has its own special scientific language. Econometric models are statistical models used in econometrics (Baltagi, B. H. 2011). When you want to explain the relationships between different economic indicators or variables, econometric models can be used. One of the most important concepts in econometric is regression analysis. Regression analysis is a statistical process which used for estimation (Chatterjee, S., & Hadi, A. S. 2013). In regression analysis, there are two types of variable: I. dependent variable (s) II. Independent variable (s). There are two types of regression analysis: I. multivariate regression analysis II. Univariate regression analysis.
As we mentioned earlier, every model has assumptions and limitations. So, econometric models are not exception. When you want to do regression analysis, it is necessary to take a few steps:  Linearity: checking linearity is the first step in regression analysis and it is significance because they define the range of the method within which the results are obtained accurately and precisely. You can use Kolmogorov-Smirnov test (K-S) or Jarque-bera test for checking linearity.  stationarity: before doing regression analysis, you should be assured that series is stationary or not.
Unit root test like Augmented Dicky Fuller (ADF) test or differencing can be used to flat the trend, constant variance because The trend and seasonality will affect the value of time series at different times (Ryabko, D. 2019).
After checking these two assumption, you can do regression. A simple linear regression with one independent variable and two dependent variables is presented below: : dependent variable 0 : intercept 1 : coefficient : independent variable Finally, we predicted return for the next day using ARIMA model. ARIMA is a statistical analysis model that uses time series data to either better understand the data set or to predict future trends.
Figure (6) shows the regression analysis process:

Portfolio Optimization
After predicting the return of companies, we will create an optimal portfolio including maximum profit and minimum risk. So, we used Value at Risk (VaR) and Conditional Value at Risk (C-VaR) to estimate the highest possibility of risk or maximum loss.

Value at Risk (VaR)
Because the focus of this article is about optimization of portfolio, we assume that returns follow normal distribution and correlation between risky assets are constant. In this condition, VaR is calculated as below: Where and are conditional mean and variance of portfolio respectively and Ǿ −1 is an inverse cumulative density function at probability level. For portfolio optimization problem, VaR is defined as a minimum real number ( ) that does not exceed ′ with probability. This definition is expressed as: Where and are returns and weights vectors of n risky assets and Ṝ = ′ is portfolio mean. Also, P indicates probability distribution of asset returns. Thus the portfolio optimization problem based on VaR definition can be written as: (5) Where is a vector of ones and budget constraint indicates that sum of assets weights equals (1).
In finance, it is assumed that distribution and return is normal with mean vector of and variance-covariance matrix of . By using and assuming parametric approach, the optimized portfolio is as below: Where г is target gain and second constraint shows that expected mean of portfolio should be equal to г. and . and are achieved simply regarding equations 7 and 8 respectively.

Conditional Value at Risk
Another measure of risk is C-VaR which have introduced by Uryasev and Rockafellar (1999). This indicator has some merits and advantages than VaR. One of them is that C-VaR can estimate risk under unfavorable economic condition. In other words, VaR measures expected loss under specified confidence or probability level in normal market state while C-VaR give helpful information about market and expected loss during unexpected economic condition. On the other hand, C-VaR provide information about left hand sie of distribution curve when expected loss exceeds VaR. C-VaR can be shown in mathematical way like as below: Due to definition of VaR and assuming ( ) as density function, C-VaR can represented as below: If ( ) considered as normal density function, C-VaR configured as follow: Where is normal standard density and Ǿ is its cumulative distribution function. It is obvious that C-VaR is larger than VaR.
Problems can be solved and optimized by C-VaR risk measure as below: At first, we calculated the return. After that, we have made a portfolio by a specified amount about 1milion dollar. Then this portfolio optimized with VaR and C-VaR models. Then the efficient frontier calculated.

Findings and results
As we mentioned earlier, we want to predict startup's return for three startups like DBX, G24.DE and TIE using daily historical data from the last three years. GA is used as feature selection and ANN used to find optimal solution. For comparability, we used econometric models like regression analysis. VaR and CVaR are two methods which are used to portfolio optimization. Finally, these two methods mean AI based methods and econometric models are compared using predictive performance metrics like precision, recall and sensitivity.

Genetic algorithm results
After getting data, we need to prepare and process them. Table (5) shows the normalized prepared data:  (6) shows the list of variables as input and target:

Fig 7. instances pie charts
One of the main indicators that can be useful to better understand the importance of variables is correlation. Table (7) shows the coefficient correlation between inputs and target. In DBX and G24.DE startups, the highest correlations are between returns and US dollar index while in TIE startup, TNX indicator has the highest correlation. Model selection is applied to find a neural network with a topology that optimize the error on new data. There are two kind of model selection: I. order selection which used to find the best architecture II. Input selection which used to find the most important variables.
The order selection algorithm chosen for this application is simulated annealing. This is a stochastic method inspired by the metallurgical industry. The parameters of order selection algorithm are as Table (8): Error history for the different subsets during the SA order selection can be seen in the next charts. The blue line represents the training error and the orange line symbolizes the selection error.

Fig 8. Simulated Annealing error plots
Table (9) shows the order selection results using SA optimization algorithm. They include some final states from the neural network, the error functional and the order selection algorithm.  (9) shows that appropriate and optimal neurons in hidden layer for DBX, G.24 and TIE.AS are 2, 3 and 6 respectively. Genetic algorithm is used as feature selection. Table (10) shows the GA parameters as input selection model:   Table (11) presents the input selection results by the GA. It is including some optimal parameters like the number of optimal input variables, generations number and etc.  (10) represents graphical results such as the number of input variables and hidden layers. the yellow circles represent scaling neurons, the blue circles perceptron neurons and the red circles un-scaling neurons.

Fig 10. Final architectures
Finally, you can see the errors based on different loss functions such as SSE, MSE and etc. in Table (12).

Artificial Neural Network results
ANN is used to find optimal solution. Input variables of ANN are those variables that found and obtained using GA. Network parameters and algorithms are as Table (13): After training network by considered parameters which mentioned in section3, the following progress and results are obtained:  Figure A1 in the appendix). The last step is regression. It is including three parts such as training, validation and testing. Figure (12) shows the regression (fitted data) for each datasets:

Fig 12. Regression analysis (Actual vs. predicted data)
There are some metrics which can show the goodness of fit. One of them is R-squared. As you can see, in all three startups, R-squared is more than 99% and it means the high predictability of ANN.

Econometric model results
As we mentioned earlier, econometric models have different assumptions and hypothesis like normality, linearity, stationarity and etc. in this paper, because logarithmic return is used, the series are normal and stationary. As a result, there is no need for a stationarity test. After doing regression, Figure (13 (13) shows that there is a collinearity between some variables. We need to solve this problem. One of the main solutions is correlation matrix. By using correlation matrix, we can identify variables that have perfect correlation to each other and then eliminate them.
As you can see, in DBX startup, there is a perfect collinearity between TEAM, HIGH, BUSINESS MODEL, CLOSE, FUNDING, LOW, IDEA, TIMING. In G24.DE company, this collinearity is between TEAM, HIGH, CLOSE, LOW, IDEA, TIMING, OPEN. In TIE.AS, there is a collinearity between TEAM, HIGH, BUSINESS MODEL, CLOSE, FUNDING, LOW, TIMING, OPEN. After eliminating determined variables, we did regression again and the following results obtained.   Due to different probability, it is clear that values less than 0.05 are important. So, in DBX, C (2), C (7) and in G24.DE C (5), C (7) coefficients are more important than others. As it is clear, for all three startups, the rate of R-squared is very low and it means that these variables are not relevant to the return and we should find other related and more important variables.

Fig 14. actual vs. Predicted
The red-line shows the actual data and the green-line shows the predicted data. The blue-line shows the residual too. As it is clear, fitted data are too far from actual data and couldn't predict volatility.

VaR estimation
The next step is the calculation of VaR with specified parameters. Here, you can see the return chart of portfolio:

Fig 15. Periodic return
Note that, return will be essentially different according to the selected interval. For return calculation in VaR, the following formula is used: Where:  Return(t) is the return shown in the graph for the observation number t, on date Date(t)  Value(t) is the value of the portfolio on the observation number t  Interval is the selected observations interval  Date(t) is the real date index from observations number t  NumDays VaRAnalysis is the VaR horizon (in days), used as the unit of time to express the returns.
VaR parameters and VaR results can be observed in Table (19): The results are shown in percentage and monetary units. Based on the portfolio value on the date selected. The VaR is calculated both in absolute terms (actual loss) and of the historical returns. Figure (16) shows the portfolio periodic returns histogram:

Fig 18. VaR along time
The simulation uses what is usually called "moving window" approach. This means that a fixed number of past observations will be used to calculate the VaR at all possible dates inside the sample. The window size (the number of observations used for the simulation) is a critical parameter. A large window will reduce the possible dates for simulation (because the first dates of the sample will lack enough past data to be used). The window size (obs) is 50 and the empirical alpha is 6.657%. For testing the results and confidence, backtesting is used:

CVaR estimation
Like VaR calculation and analysis, the related steps should be passed. VaR parameters and VaR results can be observed in Table (22): The portfolio is not likely more than 18.27 of value after 7 days following 02/07/2019 with 95% of confidence. The results are shown in percentage and monetary units. Based on the portfolio value on the date selected. The C-VaR is calculated both in absolute terms (actual loss) and of the historical returns. Figure (23) shows the portfolio periodic returns histogram:

Fig 23. Return histogram
This is a histogram that marks in red the losses below the specified CVaR significance level (the Conditional Value at Risk limit). Figure (24) shows a simulation of the portfolio value (on the right axis) and the C-VaR (in monetary units, on the left axis) along the sample.

Fig 24. C-VaR at different dates
For testing the results and confidence, back-testing is used:

Fig 25. C-VaR back-testing
The empirical alpha is equal 3.541%. In the next steps, we have optimized the C-VaR and portfolio which has the lowest risk and highest return.

Fig 26. Optimum C-VaR portfolio composition
The method contains multiple steps: The first step tests 100,000 random portfolios and chooses the best of them to begin the optimization process. Then, the optimizer applies an adaptive gradient-oriented algorithm that improves the precision of the result each time.

CVaR Backtesting
NOTES: Returns taken f rom prices 1 observ ations apart, conv erted to a 7-day s basis Using current portf olio composition Historical CVaR (%) Next day return (%) The graph shows the weight (in market value) of the most important assets considered into the optimum C-VaR portfolio.  The last step is about risk/return portfolio simulation. Figure27 shows the current portfolio using C-VaR optimized after 1,000,000 times simulations:

Fig 27. Risk-return portfolio simulation
As it is obvious, X-axis shows the minimum and maximum of C-VaR and Y-axis represents minimum and maximum of return respectively. The min and max of C-VaR and return is -10.88%, -35.58% and -0.29%, 2.90% respectively.

Conclusions and results
One of the main factors which facilitating economic growth are startups. Because of their unique characteristics and traits such as innovation, technology, knowledge and etc. they can create value. In these companies or teams, financial issue and funding for going concern and avoid the Death Valley is significant.
There are numerous resources that can be helpful: I. family and friends II. Crowdfunding (i.e. people) III. Angel investors IV. Venture capitals and etc. Investors consider multiple factors such as idea, timing, team and etc. in their choices. They do financial analysis to examine whether the company has potential growth or not. One of the main tasks that they do is startup valuation. There are multiple startup valuation models such as Berkus model, DCF model, venture capital method and etc. Because startups mostly do not have information and financial statements at the beginning, we have to predict the growth rate of startups. Startups may be in different stages such as pre-seed, seed, series-A and etc. The last stage is when a startup enters the stock market.
Since, there is not any information about startups such as sale, market size, profit and etc. and most of the models works with database, so, we have tried to analyze startups that are in stock markets and passed IPO stage. In this paper, we have tried to valuate startups using artificial intelligence based model like artificial neural network (ANN) and genetic algorithm (GA) and econometric models such as regression analysis. GA used as feature selection and ANN used to find optimal solution. Finally, we make a portfolio of these three companies means Dropbox, Inc. (DBX), Scout24 SE (G24.DE) and TIE.AS and optimized it using Value at Risk (VaR) and Conditional Value at Risk (C-VaR) based on risk and return. The results showed that if you want to increase your return and risk, you would better invest in G24.DE and DBX respectively.
We found that artificial intelligence based models having high predictability based on the following characteristics:  Speed up calculations  Improve by training  No assumption  Ease of use But econometric models have some qualifications and assumptions such as normality, linearity, stationarity and etc. which are the limitation.
As recommendations and remarks for future researches, AI based models such as ANN may face with a situation which called local minima or maxima trap. to avoid, there are solutions.
 One of them is using meta-heuristic algorithms as optimization algorithms. These algorithms can increase the capability of the network such as exploitation and exploration. So, you can increase the search space and increase your chance and speed to find the optimal solution.  You can do a widespread literature review and finding the most important indicators in startups which constitute their value. By doing this, you can increase your model predictability with high Rsquared and estimation error.