# 1 The improper use of risk management: three issues for a new agenda Francesco Betti Head of Risk, Accounting & Financial Controls Aletti Gestielle SGR.

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1 The improper use of risk management: three issues for a new agenda Francesco Betti Head of Risk, Accounting & Financial Controls Aletti Gestielle SGR

2 Three proposals for a new agenda Stress Testing Liquidity Risk Model Risk

3 First issue: rethinking stress testing Improper use of stress testing: is it only a backtesting tool? Stress testing techniques should be used after (and not besides) backtesting tools. Their outcome is the estimate of stress events’ likelihood (if the model is perfectly accurate).

4 First issue: rethinking stress testing

5 Improper use of stress testing: is it only a backtesting tool? Stress testing techniques should be used after (and not besides) backtesting tools. Their outcome is the estimate of stress events’ likelihood (if the model is perfectly accurate). Stress testing “out of the model” is not a coherent measure of risk. What is useful for?

6 A well known test examines whether the observed exception rate is statistically equal to the expected one. Under the null hypothesis that the model is adequate, the appropriate likelihood ratio statistic is: where x is the number of days over a period n that a violation occured and p is the desired coverage rate and LR is asyntotically distributed in accordance with a T- Student with one degree of freedom. A more elaborate criterior examines simultaneously if the total number of failures is equal to the expected one and is the VaR failure process is independently distributed: LR CC = LR UC + LR IND con LR CC ~χ 2 (2) The likelihood ratio test of the first hypothesis is given by the previous equation, and the second one by the following equation: First issue: rethinking stress testing

7 Improper use of stress testing: is it only a backtesting tool? Stress testing techniques should be used after (and not besides) backtesting tools. Their outcome is the estimate of stress events’ likelihood (if the model is perfectly accurate). Stress testing “out of the model” is not a coherent measure of risk. What is useful for? The proper uses of stress testing are (at least): To estimate the likelihood of stress events (not forecast them…) To perform reverse stress testing To infer fat tail behaviors from risk mispricing

8 Second issue: liquidity risk Three sources of liquidity risk: portfolio liquidity risk, market liquidity risk and systemic liquidity risk. Traditionally a portfolio is supposed to be a sum of values. As a consequence: - there exists a unique value for each security - portfolios live in a vector space spanned by assets - the value is a linear function in the space of portfolios In the presence of liquidity risk, the value of portfolios is no more necessarily a linear map in the vector space of portfolios. The value of assets becomes a vague concept.

9 Second issue: liquidity risk Each asset on the market has its own marginal supply/demand curve. The value of the sum of two assets simply does not exist: the market simply does not quote bids and asks on any collection of assets (is not a complete set of contracts). So, the market does not exhibit any structure of linear space. The hypotesis that the value of a portfolio is equal to the sum of the values of its single assets is compatible only with the assumption of perfect liquidity of the market.

10 Second issue: liquidity risk Secondly, in the presence of liquidity risk, is not possible to define the value or liquidity risk of the portfolio in the absence of a liquidity policy. The value of a portfolio depends on the type of the liquidity policy (regulatory, economic, ALM…. set of liquidity constraints). The granularity in the liquidity space produces a new diversification principle which is not linked to correlation of assets: the value of a blend of portfolios is larger than the blend of the portfolios values Translational subvariance holds: the injection of cash reduces the risk more than its nominal value because it improves the portfolio liquidity (under a well defined liquidity policy). Liquidity creates a concave map on the space of portfolios. Optimization problems rarely admits analytical solution but numerically they are solvable by convex optimization methods.

11 Second issue: liquidity risk The definition of a liquidity policy implies that the policy setter must know: the liquidity outflows (that is, the portfolio’s metrics) the securities’ marginal supply-demand curve (the market’s metrics, including not traded assets) the liquidity risk behavior of market participants (the systemic approach) The last argument is directly linked to the third issue.

12 Third issue: risk models in a leveraged market

13 Third issue: risk models in a leveraged market Markets are adaptive and temporary inefficient. Are risk models adaptive? ARCH/GARCH modeling for covariance behavior is still on discussion. In the meantime, our models fail to suit financial risk factors in the presence of increasing correlation, in a credit crunch environment and in a leveraged market. Risk models in a leveraged markets break down missing the big picture of the systemic risk. They don’t recognize that idiosyncratic risk is linked to global risk. Can connectivity (as in a small world network) and market capacity (including the balance of short/long term investors) be included in our local factor models? We have to recognize that financial systems are complex, thus nonlinear dynamics or heterogeneity of beliefs produce inverse power law distributions and chaotic behaviors.

14 Concluding remarks: the improper use  We need robust models, but risk management is a thermometer  We need to abandon the risk neutral framework because in a risk neutral framework liquidity risk simply does not exist  We need to develop new adaptive models, able to live in leveraged, connected, complex markets  We don’t need less but different quant analysis

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