On the existence of bivariate moments of lower order given the existence of moments of higher order

Dit artikel geeft een voorbeeld van een twee-dimensionale waarschijnlijkheidsdcht-heid met de eigenschap, dat het bestaan van momenten van de vorm E(g^ky^l ) niet het bestaan garandeert van alle momenten van lagere orde, E(g^myⁿ ) met 0myⁿ ) met 0 < m < k en 0 < n < l is, dat de drie momenten E(x^k), E(y^l ) en E(x^ky^l ) bestaan, alsmede een iets algemener resultaat.     

Direct density estimation as an ill-posed inverse estimation problem

A possible definition of ill-posedness in statistical estimation is the lack of qualitative robustness. In this sense direct density estimation shares ill-posedness with the more obviously ill-posed indirect density estimation models, of which it is a special case. A general construction pattern for estimators is proposed, based on suitable preconditioning, that works for both direct and indirect density estimation. Special emphasis is on its application to the direct case, where in general it yields delta-sequence estimators. More specifically both kernel and series type estimators are included depending on the choice of preconditioning operator. In particular sinc and other flattop kernel estimators emerge in a natural way.     

Islamic investing

Using a large international sample of 35 developed and emerging markets, we analyze whether Islamic indices exhibit a different performance to conventional benchmarks. While there is no compelling evidence of performance differences in robust Sharpe ratio tests and after controlling for market risk, we find a significantly positive four-factor alpha for the aggregate developed markets region. This outperformance stems, however, mainly from the U.S. and is largely attributable to the exclusion of financial stocks in Sharia-screened portfolios. As the extensive downturn of financials is related to the recent financial crisis, we do not argue that this outperformance will continue over time. The style analysis reveals that Islamic indices invest mainly in growth stocks and positive momentum stocks. This, for a passive portfolio intriguing result can, however, be explained by the strong sector allocation towards energy firms and their strong momentum characteristic during the sample period.     

Modelling and forecasting liquidity supply using semiparametric factor dynamics

We model the dynamics of ask and bid curves in a limit order book market using a dynamic semiparametric factor model. The shape of the curves is captured by a factor structure which is estimated nonparametrically. Corresponding factor loadings are modelled jointly with best bid and best ask quotes using a vector error correction specification. Applying the framework to four stocks traded at the Australian Stock Exchange (ASX) in 2002, we show that the suggested model captures the spatial and temporal dependencies of the limit order book. We find spill-over effects between both sides of the market and provide evidence for short-term quote predictability. Relating the shape of the curves to variables reflecting the current state of the market, we show that the recent liquidity demand has the strongest impact. In an extensive forecasting analysis we show that the model is successful in forecasting the liquidity supply over various time horizons during a trading day. Moreover, it is shown that the model's forecasting power can be used to improve optimal order execution strategies.     

Predicting credit spreads

Predictions of firm-level credit spreads based on the current spot and forward credit spreads can be significantly improved upon by using the information contained in the shape of the credit-spread curve. However, the current credit-spread curve is not a sufficient statistic for predicting future out-of-sample credit spreads; predictions can be significantly improved upon by exploiting the information contained in the shape of the riskless yield curve. In the presence of credit-spread and riskless factors, other macroeconomic, marketwide, and firm-specific risk variables do not significantly improve predictions of credit spreads. These results have important implications for credit-spreads modeling as well as for better understanding corporate capital structure and risk management policies.     

A note on wealth effect under CARA utility

There is a simple but overlooked way of capturing the wealth effect under CARA utility via making the absolute-risk aversion parameter wealth-dependent. We implement this approach in the asymmetric information setting of Verrecchia (1982), and compare it with the alternative approach of changing the utility function (Peress, 2004). Ours is a straightforward tractable extension of Verrecchia, while Peress has to resort to approximate methods. Importantly, our closed-form solution reveals that the relation between wealth and wealth share invested in a risky asset can be negative, while Peress’s main result is that this relation is uniquely positive.