This paper examines the impact of the 2005 hurricane season, particularly Hurricane Katrina, on the pricing of CAT bonds. We examine whether highly rated CAT bonds demonstrate a different relationship than subinvestment bonds between objective risk measures and the spread. The theoretical framework for this relationship is based on the Lance Financial (LFC) model, introduced by Lane (Rationale and results with the LFC cat bond pricing model, Discussion paper, Lane Financial LLC, Wilmette, 2003). The empirical results of treed Bayesian estimation confirm that the severity component of the spread has an increased impact, indicating a shift in investor perception during the pricing process. The impact of the conditional expected loss also significantly increases, but it contributes through its interaction with the attachment probability rather than through its variance. Finally, we show that the influence of conditional expected loss is also increased by investment-grade ratings, because investors who demand highly rated bonds may be more concerned about possible losses than junk bond investors.

This paper develops and applies a novel estimation procedure for quantile regressions with time-varying coefficients based on a fully parametric, multifactor specification. The algorithm recursively filters the multifactor dynamic coefficients with a Kalman filter and parameters are estimated by maximum likelihood. The likelihood function is built on the Skewed-Laplace assumption. In order to eliminate the non-differentiability of the likelihood function, it is reformulated into a non-linear optimization problem with constraints. A relaxed problem is obtained by moving the constraints into the objective, which is then solved numerically with the Augmented Lagrangian Method. In the context of an application to electricity prices, the results show the importance of modelling the time-varying features and the explicit multi-factor representation of the latent coefficients is consistent with an intuitive understanding of the complex price formation processes involving fundamentals, policy instruments and participant conduct. We demonstrated the value of a well specified dynamic model for quantile estimation by means of an application to electricity price risk. Electricity prices are a commodity in which price formation is nonlinear in its relationship to fundamentals, dynamic in the relative influences of drivers, with further complications introduced by policy interventions for supporting specific technologies and opportunities for participant conduct to be influential at high and low prices. Despite these complications careful consideration of the shape of the supply function with its concave, flat and convex regions, together with the information that is available to market participants day ahead allows plausible expectations for the price dynamics to be considered, and these explain very well the signs and significance of the parameters in the estimated models. Nevertheless, the models need to have a detailed specification with the various quantiles being related to multiple factors through coefficients which have dynamic properties themselves related to some of the exogenous factors. This modelling requirement motivates the development of quantile models that need fully parametric specifications to capture dynamics through exogenous factors and time-varying coefficients. A novel general methodology has therefore been developed in which time-varying multi factor coefficients are recursively estimated with a Kalman filter using maximum likelihood. Since the likelihood function is non-differentiable, the problem is re-formulated as a non-linear optimization with constraints, and furthermore re-formulated again by moving the constraints into the objective function to solve an augmented Lagrangian method. With careful selection of starting values, maximum likelihood estimates were thereby acquired. As a general approach, we would expect this to be useful in many applications of risk management and quantile estimation where there is dynamic complexity in price formation and plausible exogenous price drivers.

We present a geometric approach to discrete time multiperiod mean variance portfolio optimization that largely simplifies the mathematical analysis and the economic interpretation of such model settings. We show that multiperiod mean variance optimal policies can be decomposed in an orthogonal set of basis strategies, each having a clear economic interpretation. This implies that the corresponding multiperiod mean variance frontiers are spanned by an orthogonal basis of dynamic returns. Specifically, in a k-period model the optimal strategy is a linear combination of a single k-period global minimum second moment strategy and a sequence of k local excess return strategies which expose the dynamic portfolio optimally to each single-period asset excess return. This decomposition is a multi period version of Hansen and Richard (Econometrica (1987)) orthogonal representation of single-period mean variance frontiers and naturally extends the basic economic intuition of the static Markowitz model to the multiperiod context. Using the geometric approach to dynamic mean variance optimization we obtain closed form solutions in the i.i.d. setting for portfolios consisting of both assets and liabilities (AL), each modelled by a distinct state variable. As a special case, the solution of the mean variance problem for the asset only case in Li and Ng (Mathematical Finance 10 (2000)) follows directly and can be represented in terms of simple products of some single period orthogonal returns. We illustrate the usefulness of our geometric representation of multiperiods optimal policies and mean variance frontiers by discussing specific issues related to AL portfolios: The impact of taking liabilities into account on the implied mean variance frontiers, the quantification of the impact of the rebalancing frequency and the determination of the optimal initial funding ratio.

This paper proposes a novel approach to portfolio revision. The current literature on portfolio optimization uses a somewhat naïve approach, where portfolio weights are always completely revised after a predefined fixed period. However, one shortcoming of this procedure is that it ignores parameter uncertainty in the estimated portfolio weights, as well as the biasedness of the in-sample portfolio mean and variance as estimates of the expected portfolio return and out-of-sample variance. To rectify this problem, we propose a Jackknife procedure to determine the optimal revision intensity, i.e. the percent of wealth that should be shifted to the new, in-sample optimal portfolio. We find that our approach leads to highly stable portfolio allocations over time, and can significantly reduce the turnover of several well established portfolio strategies. Moreover, the observed turnover reductions lead to statistically and economically significant performance gains in the presence of transaction costs.

The paper presents a robust version of a simple two-assets Merton (1969, Review of Economics and Statistics 51, 247-57) model where the optimal choices and the implied shadow market prices of risk for a representative robust decision maker (RDM) can be easily described. With the exception of the log-utility case, precautionary behaviour is induced in the optimal consumption-investment rules through a substitution of investment in risky assets with both current consumption and riskless saving. For the log-utility case, precautionary behaviour arises only through a substitution between risky and riskless assets. On the financial side, the decomposition of the market price of risk in a standard consumption based component and a further price for model uncertainty risk (which is positively related to the robustness parameter) is independent of the underlying risk aversion parameter.

A typical problem arising in financial planning for private investors consists in the fact that the initial investor's portfolio, the one determined by the consulting process of the financial institution and the universe of instruments made available to the investor have to be matched/optimised when determining the relevant portfolio choice. We call this problem the three-portfolios matching problem. Clearly, the resulting portfolio selection should be as close as possible to the optimal asset allocation determined by the consulting process of the financial institution. However, the transition from the investor's initial portfolio to the final one is complicated by the presence of transaction costs and some further more specific constraints. Indeed, usually the portfolios under consideration are structured at different aggregation levels, making portfolios comparison and matching more difficult. Further, several investment restrictions have to be satisfied by the final portfolio choice. Finally, the arising portfolio selection process should be sufficiently transparent in order to incorporate the subjective investor's trade-off between the objectives ‘optimal portfolio matching' and ‘minimal portfolio transition costs'. In this paper, we solve the three-portfolios matching problem analytically for a simplified setting that illustrates the main features of the arising solutions and numerically for the more general situation.

This article uses regime-switching models of the threshold type to analyze the adjustment process of rental prices for three U.K. commercial real estate sectors over the period 1974-2008. The nonlinear models outperform their linear counterparts in in-sample fit. Their out-of-sample forecasting ability is better whenever the corresponding linear models contain a significant amount of neglected nonlinearity. Regime switches are triggered when the growth rates of rental price exceed certain threshold levels. For the industrial and retail sectors such regime switches occur in situations of strong excess demand, for the office sector they occur when there is strong excess supply.

To estimate the bid-ask spread, we propose a new method that resembles the Roll measure (1984) but has some key advantages: it is fully independent of bid-ask bounces and benefits from a wider information set, namely, close, high, and low prices, which are readily available. Assessed against other low-frequency estimates, our estimator generally provides the highest cross-sectional and average time-series correlations with the TAQ effective spread benchmark. Moreover, it delivers the most accurate estimates for less liquid stocks. Finally, our estimator improves the measurement of systematic liquidity risk and commonality in liquidity for individual stocks and sorted portfolios.

We propose a new method to estimate the bid-ask spread when quote data are not available. Compared to other low-frequency estimates, it utilizes a wider information set, namely, close, high, and low prices, which are readily available. In the absence of end-of-day quote data, it generally provides the highest cross-sectional and average time-series correlations with the TAQ effective spread benchmark. Moreover, it delivers the most accurate estimates for less liquid stocks. Our estimator has many potential applications including an accurate measurement of transaction cost, systematic liquidity risk, and commonality in liquidity for U.S. stocks dating back almost one century.