The purpose of this document is to provide a more technical description of the econometric, quantitative and financial methods that we use. The scope of RiskDynaMetrics is the estimation (based on econometric models) and the forecasting of risk aversion. We also perform some preliminary investment advice based on our evaluation of investors’ risk aversion. Our results can lead to a variety of other applications, such as portfolio positioning (on which you can ask for detail by sending a mail to info@RiskDynaMetrics.com).
The key scope of RiskDynaMetrics is large-scale data collection. A large amount of reliable data is needed in order to estimate risk aversion models, identify risk profiles and determine key variables which explain risk aversion.
The factors which can potentially explain risk aversion include:
There are several factors that we wish to test and the respondents are invited to visit our Website again, with the same identifier and password (for the time being, only one out of four different sessions is implemented). After each session, the respondent is provided with an evaluation of his/her level of risk aversion and with investment advice. With panel data, we expect a better understanding of the dynamics of risk tolerance.
This questionnaire includes four series of three successive lotteries (only one series is implemented at this time). Each lottery offers a choice between a risky alternative and a risk-free alternative. These lotteries are carefully designed in order to allow a comparison of the standard utility functions. Each respondent faces different series of lotteries and their returns are randomized in order to maximize the statistical efficiency of our estimates.
RiskDynaMetrics is constantly evolving as we regularly feed our models with additional data, in order to obtain better estimates. We can statistically identify the most relevant explanatory variables and therefore select and fine-tune the best questions on a statistical basis. We can further optimize the lottery questions (which are based, at the beginning of the data collection, on our subjective estimates).
RiskDynaMetrics uses a standard scheme, which has been tested previously in experimental economics. Each series of lotteries can be represented as a tree. The risk-free alternative is the same for each question and the risky alternative varies as a function of the previous answers. The four series of lotteries that we envisage are based on different probability distributions for the risky alternatives.
The approach used here is meaningful at an ordinal as well as a cardinal level. As a consequence, we can use the data to rank the respondents according to their levels of risk aversion. Moreover, we can test specific utility functions, that were suggested by our finance team, compare them and estimate their parameters, and in particular the absolute or relative levels of risk aversions. Since the lotteries are naturally ranked, we use an ordered discrete choice model (for example an ordered Logit or an ordered Probit).
The answers to each series of lotteries is described by a discrete choice model as initially introduced and studied by D. McFadden, Economics Nobel Laureate in 2000.
For a family of utility functions, and for a lottery j, the threshold S(j) corresponds to the value of risk aversion which makes the individual indifferent between the risk-free and the risky alternatives. This threshold equalizes the (expected) utility of the risky and of the risk-free alternatives.
Risk aversion depends on a set of explanatory factors, specific to the investors and on parameters that we wish to estimate. Those parameters tell us the importance of the explanatory factors. As the number of answers increases, we are able to identify the most relevant questions. Our analysis allows to have an estimation of risk aversion, which depends at the same time on the lottery series (which will themselves evolve over time) and on the relevant explanatory factors.
We constructed tests to check whether or not the absolute (or the relative) risk aversion is constant over time. One first scope of this analysis is to compare, for example, CARA and CRRA utility functions.
Moreover, we plan to check how the respondent is able to deal with very small or very large probabilities. Our initial analysis is based on expected utility theory. However, we are also interested in testing other types of behavior, involving, for example, biases in the perception of probabilities.
Finally, we plan to use our results to predict the risk aversion of individuals in the next few years. The idea is that the investor who uses a time horizon of 15 years, for example, should make his/her investment choices according to his/her risk aversion after this 15-year period.
We have developed an exact formula for the analytical computation of the portfolio breakdown over a specific time horizon. We have used the four most well-known utility functions (Logarithmic, CARA, HARA and exponential). The utility functions are tested empirically with our data. We are then able to provide investment recommendations for the most relevant utility function. Three asset types are considered: stocks indices, bond indices and money market funds. These three asset types are modelled as standard random motions. The optimal balance maximizes the expected utility at the time horizon. It is based on a continuous rebalance over time of the portfolio and ignores transaction costs.
The solution depends on several parameters which describe market conditions. We have estimated these parameters by standard econometric methods currently used by financial institutions.
As our Website evolves, we will test other types of utility functions which will be associated to other investment recommendations.
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