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Abstract

Risk tolerance can be defined as the maximum amount of risk by investment that an individual is ready to take. In this paper, we explore the relationship between demographic features and risk tolerance pertaining to an individual using the KMeans Algorithm. We also propose a novel architecture using graph embeddings in Graph Convolutional Networks (GCNs) to contrast the use of demographics and try to predict an outcome based on previous investments.

Introduction

Risk Tolerance can be different for individuals from different demographics. The premise of this concept lays in the fact that different people may agree on the riskiness of a gamble, but may however prefer to go for other gambles according to their tolerance. The demographics used include Gender, Age, Education, Marital Status and Race.

Deep learning has indeed revolutionized many tasks in the recent years, ranging from image processing to speech recognition. These problems can be represented in Euclidean space but graphs are n-dimensional, which cannot be represented on a Euclidean space. Graph neural networks come in play here where we can map these graphs to Euclidean space without disrupting their connections.

Here we propose a new method of detecting the risk an investor can take in an investment using graph neural network, especially graph convolution network. For this we have classified the user into three main categories, namely:

Aggressive Risk Taker. Aggressive riskers tend to be market-savvy. They have a deep understanding of their propensities and reach for maximum returns with maximum risks.
Moderate Risk Taker. They accept some risk to the principal but adopt a balanced approach. They often purchase a 50/50 structure.
Conservative Risk Taker. They accept little to no volatility in their investment. Mostly, retired people who do not have a constant source of income tend to incline in this category. They opt for mutual funds.

Literature Survey

In this section we outline each and every criterion which influences investor risk tolerance and review literature which outlines the effect of every option.

Gender

According to Slovic (1966), a prevalent belief in our culture is that men should, and do, take greater risks than women (p. 169). This assumption has been confirmed by other researchers (Higbee & Lafferty, 1972). Blume (1978), when reporting the results of a unique national study of New York Stock Exchange (NYSE) investors that employed a combination of descriptive and multivariate statistics, indicated that men who own and invest in equities avoided risk less than women with similar characteristics. This finding was affirmed by Coet and McDermott (1979) who studied the effects of gender, type of instruction, and group composition on general risk-taking behavior using an experimental method with 200 college students, and by Rubin and Paul (1979) who designed an experimental study to examine systematic risk taking by gender over the life cycle as part of a larger model of risk-tolerance behavior. Rubin and Paul found that males consistently demonstrated greater risk-taking behaviors than did females.

Xiao and Noring (1994) each used a version of the Survey of Consumer Finances (SCF)10 to obtain data for regression type analyses (e.g., Ordinary Least Squares, logit, probit, and tobit), where willingness to take financial risks was defined as the dependent variable, and gender (among a number of other variables) was operationalized as an independent variable. These researchers concluded that men were more willing than women to take financial risks. Bajtelsmit and Bernasek (1996), in reporting findings from a survey of literature, concluded that women invest their pensions more conservatively than men, and that, in general, women are less risk tolerant than men. Lytton and Grable (1997) analyzed gender differences in financial attitudes from a random sample of 592 tax payers from a mid-Atlantic state; they found that males expressed more confidence in their financial situation(s) and higher risk-taking propensities in relation to financial management strategies than women.

As indicated above, there is evidence to suggest that a relationship exists between gender and investor risk tolerance, with men tending to take more risks than women. Furthermore, it is commonly accepted that gender can be used effectively to classify individuals into investor risktolerance categories; however, researchers have not reached consensus on this point. There are, however, a number of empirical studies which indicate that there are no differences between men and women in relation to risk tolerances.

Race

There are few empirical studies concerning the relationship between race and investor risk tolerance. Lefcourt (1965) was the first researcher to explore risk-taking differences between Black and White adults. Using a risk-taking experiment using 30 Blacks and 30 Whites, Lefcourt concluded that Blacks choose fewer low probability bets, made less shifts of bets, and generally took less risks than Whites.Recently there has been a renewed focus on the relationship between risk-taking propensities and race. Haliassos and Bertaut (1995), Hawley and Fujii (1993-1994), Lee and Hanna (1995), and Sung and Hanna (1996a) each used the 1983 and 1986 Surveys of Consumer Finance to conduct logit and probit analyses of multistage area-probability samples (N = 3,824). Each of these research teams found that White respondents had a higher probability of taking investment risks. Investment managers and researchers generally accept the notion that there is a relationship between race and investor risk tolerance. Controlling for other factors, Whites are considered to have higher risk tolerances than non-Whites. This difference may be attributable to cultural values, preferences, and tastes. According to Zhong and Xiao (1995) further investigation will be helpful to enhance the understanding of the investment behaviour between Whites and non-Whites

Education

Education, as used in investor risk-tolerance research, has been defined as the level of formal education completed by an individual (Masters, 1989). Numerous researchers have concluded that greater levels of attained education are associated with increased risk tolerance. Baker and Haslem (1974), using data from 851 respondents to a risk-tolerance questionnaire that was randomly distributed to customers of five brokerage firms, determined that investors with less education found price stability more important than those with at least some college training. Baker and Haslem acknowledged that their findings conflicted with findings from other researchers that suggested that those with little education were desirous of quick profits from risky trading (Potter, 1971). Hammond et al. (1967) used a general regression model to consider life insurance premium expenditures by household. Although it is generally accepted by investment managers and researchers that increased educational levels are associated with increased levels of investor risk tolerance, there is research to suggest otherwise. Blume (1978), using results from a large random national survey of NYSE investors, concluded that educated heads of households were somewhat less willing than others to take substantial risks, but at the same time, they reported a less than average propensity for reducing financial risks to the barest minimum, preferring some intermediate trade-off between risk and expected return (p. 124). McInish (1982), as a result of a regression of betas against Rotter scores and demographic variables, found that educational levels showed a predicted positive relationship with risk tolerance, but that education coefficients were not significant in any of the regressions. The literature suggests that a positive relationship between attained education and increased investor risk tolerance is reasonable. However, as with the implications derived from research concerning other demographics, this relationship is not definite, and additional research is warranted.

Scoring for Classification

This section converges the information obtained literature reviews from the previous section and provides a ranking to the categories given above.

Gender, Gender was included as an independent variable, because gender has been found to be an important investor risk-tolerance classification factor, with more men than women tending to fit the personality trait called thrill seeker or sensation seeker (Roszkowski et al., 1993).

A dataset was generated from the Survey of Consumer Finances 2016, by the Federal Reserve United States. Selected questions were taken separately and the dataset was then scored according to the numbers given in Section 2. The database consists of replies from 31241 people all across United States. A small portion of the table is shown in the below figure.

Using Elbow method we try and assess the optimal number of clusters required to divide the given dataset. It gives us the following output. Looking at the output we take 6 as the number of clusters as looking at the plot we understand that the observed difference in the within-cluster dissimilarity is not much after this point.

Hence from the above result we obtain at very basic classification for risk tolerance analysis and can given each person a score based on their answers of the survey. We value the risk tolerance based on the volatility of the stock which is generally measured with beta value. The beta value in the market ranges from 0.0 1.9 usually. We took a simple method of dividing the beta value into six weighted [image: ]segments as follows: –

Graph Convolutional Networks (GCNs)

In this method we use graphs to classify if an investor when investing in a new venture is able to take risk and in which category he is using his previous investments. The transactions made by an individual are represented in a graph with the Nodes representing the transactions and the Edges represent directed flows. We assume graphs to be directed. Each node holds the amount of the transaction and each edge holds the directed flow of that transaction. Any incoming node will be classified among the three categories stated above based on the threshold done by taking the first quartile of the transactions done by an individual. Any transaction within the first quartile range is classified as Conservative risk, second quartile as Moderate risk and third quartile as Aggressive risk. The topology of the investments is done by collating investments and the dependency of these among each others can be digitized as a directed graph.

Using node embedding we map the nodes so that similarity in the embedding and the embedding space approximates the similarity in the original network.

We generate node embedding based on local neighborhood. Nodes aggregate information from their neighbors using neural network. Network neighbor defines a computation graph. Neighborhood representation using average neighbor. After K-layers of neighborhood aggregation, we get output embedding for each node. We can feed these embedding into any loss function and run stochastic gradient descent to train the aggregation parameters.

Conclusion

This experiment provides a very conservative estimate to an investors risk tolerance by asking very few questions. This method can be incorporated into any investment portal and used to provide efficient investment advice as well as by algorithms to judge the investment decisions on the basis of the risk tolerance of the institution or individual using it. We can conclude that data mining approach allows us to improve our decision making process by a significant extent.

Graph convolution networks can easily classify the risk tolerance level of investors replacing the tiresome task of questionnaires. These provide better prediction and classification results because of the interdependency of the transactions of an individual and is also individual specific.

Graph convolution networks are recently developed and are computationally expensive if the number of edges increases. The forming of an adjacency matrix is a challenging task. We can improve the results using hybrid structure including random forest with GCN.

References

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