Seminars for 2020-2022

The stochastic modelling and aggregation of dependent risks is a central risk management task  for many financial institutions. After an introduction illustrating some basic mathematical challenges, we will review Poisson approximation, the collective model from actuarial science, Panjer distributions, and the extended multivariate Panjer recursion. To assure numerical stability, we introduce weighted convolutions combined with the Panjer recursion, thereby widening the class of mixture distributions. The aim is to discuss a multi-business-line variant of the collective model, mixed by a convex combination of non-negative (mainly unbounded) claim number intensities to obtain an arbitrary linear dependence structure — and still use recursive methods to calculate the loss distribution of the portfolio.

Time permitting, an implementation will be presented, which is available online

Corporate bond market participants are increasingly worried about liquidity. However, bid-ask spreads and other standard measures indicate liquidity has not deteriorated significantly. This paper proposes a potential reconciliation. We show credit yields became four times more sensitive to bid-ask spreads in 2019 than in 2005. We then provide a model that connects this change to the rapid growth of mutual funds in the corporate bond market. The model features heterogeneous investors with different trading needs who choose between a risk-free asset and illiquid bonds. As the risk-free rate declines, more short-term investors reach for yield and enter the bond market. These short-term investors reduce the selling pressure in each sub-market and so the bid-ask spreads. However, their greater trading needs amplify the sensitivity of credit yields to the bid-ask spreads, leading to a larger liquidity component. We next test the model’s predictions using detailed data on investor holdings in the U.S. As predicted, we find investor turnover amplifies the effect of illiquidity on credit yields. Bonds with more short-term investors are traded at lower bid-ask spreads and their credit yields are more sensitive to the bid-ask spreads. Finally, we look across countries and show that, consistent with the model, larger declines in risk-free rates are associated with higher growth in mutual fund shares. These results highlight the key role that investor heterogeneity plays in determining corporate bond yields and ultimately firms’ financing conditions.

We relax the absence of near-arbitrage bound by recognizing the statistical limits to arbitrage — the ignorance of population parameters in linear asset pricing models. We then classify the new maximal arbitrage-free space by the strength and sparsity of alphas. Standard statistical methods that are designed for identifying potentially strong alphas miss vast investment opportunities of the weaker ones. We propose a new approach to construction of portfolios that optimally exploit both strong alphas and weaker ones. We demonstrate how individually impotent alphas can collectively lead to large investment gains. For illustration we construct optimal portfolios with large-cap US stocks, for which strong investment opportunities are less obvious, and our approach leads to a substantial 50% gain in Sharpe ratios compared to widely used alternatives.

Permanent components of income and  consumption are obtained by functional Beveridge-Nelson decomposition of U.S. Consumer Expenditure Survey data. From the permanent income distribution, we identify two factors the level (aggregate) and the spread (redistribution) that affect permanent consumption. Longrun consumption is most positively affected by households with monthly earnings of around $2,000, households with lower income have negative effects on aggregate consumption, and those with $5,000 or more respond little to income redistribution. Limited income sharing across households, high entry barriers, and nontrivial adjustment costs associated with both human and physical capital accumulation may contribute to the empirical findings. Taking the estimated longrun response function as the optimal behavior of households, counterfactual taxation exercises suggest that purely redistributive policies can increase the permanent component of aggregate consumption by 250%.