- Published 2012

In this paper we discuss popular risk measures of risk, their attractions and limitations. In the first chapter, we consider classical approaches to risk management. There we can see the development of measures of risk and moreover, we consider the index options of statistical estimates of quantile measures of risk. On their analysis my diploma thesis was based. The main purpose was the formation of investment portfolio based on such combinations of measures of risk. In the second chapter, the future work is represented. There we present the prospect and cumulative prospect theories. We discuss again the previous models under behavioral finance framework. We propose a new measure based on Value at Risk by using assumptions of behavioral finance and try to make suggestions on other measures. Background Nowadays the analysis and estimation of market risks becomes one of the most actual problems at the formation of a portfolio of securities. Strengthening of economic intensity all over the world, instability and large-scale changes of economy force to improve methods of an estimation of risks. For the first time portfolio theory has been mentioned in 1952 in the work of American mathematician-economist Harry Markowitz "Portfolio Selection". It has served as the beginning of prompt development and problem studying of optimization an investment portfolio. Modern theory of investments developed, trying to correct the lacks inherent in model suggested by Markowitz. The theory of the follower of Markowitz William Sharpe became one of alternative approaches. He has suggested dividing risk of a financial active on two components: market risk of a portfolio and own risk of a portfolio. Besides change in the approach to the risk, the model of Sharpe simplifies a method of a choice of an optimum portfolio; the problem of square-law optimization (model of Markowitz) is reduced to the linear. For variety of different financial technologies on management of risk and the profitableness, as a theoretical basis the model of an estimation of profitableness of the shares serves. It has been developed by William Sharpe, John Lintner and Jan Mossin independently in the mid-sixties of XX century and it is called CAPM (Capital Asset Pricing Model). Within the limits of this approach profitableness of shares depending on behavior of the market is considered as a whole and it is supposed that investors make decisions, considering only expected profitableness and risk. Another equilibrium pricing model – Arbitrage Pricing Theory serves as an alternative of CAPM. It has been created in the beginning of 80-th years by Stefan Ross. The basic assumption of the given model that each investor tries to use possibility of increase in profitableness of the portfolio without risk increase. The mechanism promoting given possibility, is an arbitrage. The arbitrage is a reception of riskless profits at use of the different prices for identical production or securities. In real life of the arbitrage doesn't exist, as it is the ideal situation assuming obligatory reception of profit at absence of risk of loss of investments. The main difference between CAPM and APT is that the last one takes more than one factor into consideration. More seriously the question on necessity of management of risks has risen owing to a train of large financial crashes in the early nineties . After a series of scandalous ruins of such giants as Orange Country, Barings, Metallgesellschaft, Daiwa, economists were convinced once again that the large sums of money can be lost owing to underestimation of importance of control and absence of adequate mechanisms of management of financial risks. Many financial institutions were engaged in researches in the field of a risk management. As a result, the middle of 90th years was marked by two important events in the theory and practice of the application of the financial markets: wide use of quantile measures of risk VaR (Value-at-Risk), that was offered for the first time by the company J.P.Morgan as alternatives of a dispersion dominating before as a risk measure, and allocation of axiomatic classes of measures of risk, first of which was the class of coherent measures of the risk, entered by Artzner, Delbaen, Eber and Heath . Then other classes of measures of risk (convex, additive, revolted, limited to an average) have been entered also. The measure that was suggested by J.P.Morgan was derived from a system based on standard portfolio theory. It was using estimates of the standard deviations and various correlations between the returns to different traded instruments. Other financial institutions that were also working on their own internal models considered VaR systems that were not based on Portfolio Theory. For example, there were VaR systems that were built using a historical simulation approach that estimate VaR from a histogram of past profit and loss data for the institution as a whole. Another system was developed by using method Monte-Carlo. It is much more sophisticated and powerful than previous two systems. The measure of risk VaR is used widely not only by securities houses and investment banks, but also by commercial banks, pension funds and other financial institutions, and non-financial corporate. It is recommended for applying by Basel Committee on Banking Supervision. One of the shortcomings of VaR is that all VaR systems are backward-looking. All of them use past data for future forecasting. But there is no confidence that the past relationships will continue in the future. For example, the one of the difficulties that we can have is a market crash. In these cases, we should remain aware of the limitation and supplement VaR analysis with scenario analyses that tell us what we might lose under hypothetical circumstances. Secondly, all VaR systems are based on the assumptions that may not be valid in real situations. However, the correct action will be aware of limitations and behave accordingly. The measure of risk VaR ignores the weight of tails of distribution of profitablenesses (or losses) – doesn't consider possible big profits (losses) which can occur to small probabilities. One more essential shortcoming: VaR isn't a coherent measure; in particular, it doesn't possess property of subadditivity. It is possible to result examples, when VaR a portfolio more than sum VaR of parts of portfolio of which it consists. It contradicts common sense. Really, if to consider a risk measure as the size of the capital reserved for a covering of market risk for a covering of risk of all portfolio there is no necessity to reserve more than the sum of reserves of components of portfolio. VaR encourages trading strategy which gives the good income at the majority of scenarios, but can sometimes lead to catastrophic losses. S. Uryasev has been offered a coherent measure of the risk Conditional Value-atRisk (CVaR). CVaR is the expectation of income, lower than VaR. This method of risk assessment can take into account the huge losses that can occur with small probability. While this measure of risk does not become common in risk assessments. Conditional Value at Risk (CVaR) is also called expected shortfall, average value at risk (AVaR), and expected tail loss (ETL).The "expected shortfall at q% level" is the expected return on the portfolio in the worst q% of the cases. For high values of q CVaR ignores the most profitable but unlikely possibilities, for small values of q it focuses on the worst losses. On the other hand, unlike the discounted maximum loss even for lower values of q expected shortfall does not consider only the single most catastrophic outcome. A value of q often used in practice is 5%. CVaR estimates the value (or risk) of investments in conservative manner, focusing on the less favorable results. CVaR has two important properties. Firstly, it is coherent measure of risk. Secondly, it is a spectral measure of financial portfolio risk. It requires a quantilelevel q, and is defined to be the expected loss of portfolio value given that a loss is occurring at or below the q-quantile. CVaR could be easily decomposed and optimized, while VaR is not. Moreover, CVaR requires a larger size of sample than VaR for the same level of accuracy. In my diploma thesis I considered two index options of statistical estimates quantile measures of risk (VaR-CVaR). The main purpose was to develop the methodology for formation of the investment portfolios. For achievement necessary results n portfolios were generated by using the gage of pseudo-random numbers of Uichman-Hill. After that the values of measures of risk M1, M2 for all generated portfolios on time interval T were calculated. We investigate two new measures of risk based on left and right tails of distribution:

@inproceedings{Kovaleva2012BEHAVIOURALAT,
title={BEHAVIOURAL APPROACH TO THE RISK MANAGEMENT Research Proposal for PhD Advisory Committee, Behavioral Economics Program, University of Trento},
author={Svetlana Kovaleva},
year={2012}
}