Beta lives - some statistical perspectives on the capital asset pricing model

This note summarizes some technical issues relevant to the use of the idea of excess return in empirical modelling. We cover the case where the aim is to construct a measure of expected return on an asset and a model of the CAPM type is used. We review some of the problems and show examples where the basic CAPM may be used to develop other results which relate the expected returns on assets both to the expected return on the market and other factors

"Better Safe than Sorry" - Individual Risk-free Pension Schemes in the European Union - Macroeconomic Benefits, the Mobile Working Citizen's Perspective and Why Nots

Variations between the diverse pension systems in the member states of the European Union hamper labour market mobility, across country borders but also within the countries of the European Union. From a macroeconomic perspective, and in the light of demographic pressure, this paper argues that allowing individual instead of collective pension building would greatly improve labour market flexibility and thus enhance the functioning of the monetary union. I argue that working citizens would benefit, for three reasons, from pension saving in a risk-free savings account. First, citizens would have a clear picture of the accumulation of their own pension savings throughout their working life. Second, they would pay hardly any extra costs and, third, once retired they would not be subject to the whims of government or other pension fund managers. This paper investigates the feasibility of individual pension building under various parameter settings by calculating the pension saved during a working life and the pension dis-saved after retirement. The findings show that there are no reasons why the European Union and individual member states should not allow individual risk-free pension savings accounts. This would have macroeconomic benefits and provide a solid pension provision that can enhance mobility, instead of engaging workers in different mandatory collective pension schemes that exist around in the European Union

Derivatives and Credit Contagion in Interconnected Networks

The importance of adequately modeling credit risk has once again been highlighted in the recent financial crisis. Defaults tend to cluster around times of economic stress due to poor macro-economic conditions, {\em but also} by directly triggering each other through contagion. Although credit default swaps have radically altered the dynamics of contagion for more than a decade, models quantifying their impact on systemic risk are still missing. Here, we examine contagion through credit default swaps in a stylized economic network of corporates and financial institutions. We analyse such a system using a stochastic setting, which allows us to exploit limit theorems to exactly solve the contagion dynamics for the entire system. Our analysis shows that, by creating additional contagion channels, CDS can actually lead to greater instability of the entire network in times of economic stress. This is particularly pronounced when CDS are used by banks to expand their loan books (arguing that CDS would offload the additional risks from their balance sheets). Thus, even with complete hedging through CDS, a significant loan book expansion can lead to considerably enhanced probabilities for the occurrence of very large losses and very high default rates in the system. Our approach adds a new dimension to research on credit contagion, and could feed into a rational underpinning of an improved regulatory framework for credit derivatives.Comment: 26 pages, 7 multi-part figure

Regularizing Portfolio Optimization

The optimization of large portfolios displays an inherent instability to estimation error. This poses a fundamental problem, because solutions that are not stable under sample fluctuations may look optimal for a given sample, but are, in effect, very far from optimal with respect to the average risk. In this paper, we approach the problem from the point of view of statistical learning theory. The occurrence of the instability is intimately related to over-fitting which can be avoided using known regularization methods. We show how regularized portfolio optimization with the expected shortfall as a risk measure is related to support vector regression. The budget constraint dictates a modification. We present the resulting optimization problem and discuss the solution. The L2 norm of the weight vector is used as a regularizer, which corresponds to a diversification "pressure". This means that diversification, besides counteracting downward fluctuations in some assets by upward fluctuations in others, is also crucial because it improves the stability of the solution. The approach we provide here allows for the simultaneous treatment of optimization and diversification in one framework that enables the investor to trade-off between the two, depending on the size of the available data set

Implementing natural capital credit risk assessment in agricultural lending

Agriculture has critical impacts and dependencies on natural capital, and agriculturallenders are therefore exposed to natural capital credit risk through their loans tofarmers. Currently, however, lenders lack any detailed guidance for assessing naturalcapital credit risk in agriculture and are challenged by the fact that the relevant material risks vary considerably by agricultural sector and geography. This paper developsa natural capital credit risk assessment framework based on a bottom‐up review ofthe material risks associated with natural capital impacts and dependencies forAustralian beef production. It demonstrates that implementing natural capital creditrisk assessment is feasible in agricultural lending, using a combination of quantitativeand qualitative inputs. Implementation challenges include the complexity and interconnectedness of natural capital processes, data availability and cost, spatial data analytical capacity, and the need for transformational change, both within lendingorganisations and across the banking sector