This paper combines a behavioral reward-risk model based on prospect theory with multiple investment accounts to explain the asset allocation puzzle, that is, the observation that investors violate the two-fund separation property of optimal mean-variance allocations. In a empirical analysis with U.S. data, the authors show that investors with preference according to the behavioral reward-risk model and multiple investment accounts, invest a higher proportion into bonds and large cap stocks as their risk tolerance diminishes, consistently with the empirical findings.

We provide theoretical and empirical arguments in favor of a concave shape for the security market line, or a diminishing marginal premium for market risk. In capital market equilibrium with binding portfolio restrictions, different investors generally hold different sets of risky securities. Despite the differences in composition, the optimal portfolios generally share a joint exposure to systematic risk. Equilibrium in this case can be approximated by a concave relation between expected return and market beta rather than the traditional linear relation. An empirical analysis of U.S. stock market data confirms the existence of a significant and robust, concave cross-sectional relation between average return and estimated past market beta. We estimate that the market-risk premium is at least five to six percent per annum for the average stock, substantially higher than conventional estimates.

We provide theoretical and empirical arguments in favor of a diminishing marginal premium for market risk. In capital market equilibrium with binding portfolio restrictions, investors with different risk aversion levels generally hold different sets of risky securities. Whereas the traditional linear relation breaks down, equilibrium can be described or approximated by a concave relation between expected return and market beta, and a concave relationship between market alpha and market beta. An empirical analysis of U.S. stock market data confirms the existence of a significant concave cross-sectional relation between average return and estimated market beta. We estimate that the market risk premium is at least four to six percent per annum, substantially above traditional estimates. A practical implication for active portfolio managers is that the alpha of ``betting against beta'' strategies seems dominated by the medium-minus-high-beta spread rather than the low-minus-medium-beta spread. The success of such strategies thus largely depends on underweighting or short selling high-beta stocks.

Equity index implied volatility functions are known to be excessively skewed in comparison with implied volatility at the single stock level. We study this stylized fact for the case of a major German stock index, the DAX, by recovering index implied volatility from simulating the 30-dimensional return system of all DAX constituents. Option prices are computed after risk neutralization of the multivariate process which is estimated under the physical probability measure. The multivariate models belong to the class of copula asymmetric dynamic conditional correlation models. We show that moderate tail dependence coupled with asymmetric correlation response to negative news is essential to explain the index implied volatility skew. Standard dynamic correlation models with zero tail dependence fail to generate a sufficiently steep implied volatility skew.

A multivariate methodology based on functional gradient descent to estimate and forecast time-varying expected bond returns is presented and discussed. Backtesting this procedure on US monthly data, empirical evidence of its strong forecasting potential in terms of the accuracy of the predictions is collected. The proposed methodology clearly outperforms the classical univariate analysis used in the literature.

We apply the recently introduced generalized tree-structured (GTS) model to the analysis and forecast of stock market diversity. Diversity is a measure of capital concentration across a market that plays a central role in the search for arbitrage. The GTS model allows for different conditional mean and volatility regimes that are directly related to the behavior of macroeconomic fundamentals through a binary threshold construction. Testing on US market data, we collect empirical evidence of the model's strong potential in estimating and forecasting diversity accurately in comparison with other standard approaches. In addition, the GTS model allows for the construction of very simple portfolio strategies that systematically beat the standard cap-weighted S&P500 index.

We introduce a new multivariate GARCH model with multivariate thresholds in conditional correlations and develop a two-step estimation procedure that is feasible in large dimensional applications. Optimal threshold functions are estimated endogenously from the data, and the model conditional covariance matrix is ensured to be positive definite. We study the empirical performance of our model in two applications using US stock and bond market data. In both applications our model has, in terms of statistical and economic significance, higher forecasting power than several other multivariate GARCH models for conditional correlations

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=487942

http://ideas.repec.org/p/usg/dp2005/2005-04.html

A life cycle model with pension benefits and taxes is analyzed by means of stochastic control. In the phase of employment an individual earns a stochastic income, contributes to a pension plan and chooses an optimal consumption and investment strategy under a tax system. At the end of the phase of employment the individual decides to fully or partially withdraw capital from the pension plan or to retire with no reduced pension benefits. During retirement an optimal consumption and investment strategy is chosen. It is shown that the individual profits from the financial protection against the uncertainty of her life span. Further, the decision on partial or full capital withdrawal from the pension fund depends crucially on the specification of the tax scheme. Under a uniform linear tax scheme and a fair pension benefit there will be no capital withdrawal. Under a more sophisticated tax scheme no, partial or full withdrawal may occur.

It is difficult to compute Value-at-Risk (VaR) using multivariate models able to take into account the dependence structure between large numbers of assets and being still computationally feasible. A possible procedure is based on functional gradient descent (FGD) estimation for the volatility matrix in connection with asset historical simulation. Backtest analysis on simulated and real data provides strong empirical evidence of the better predictive ability of the proposed procedure over classical filtered historical simulation, with a resulting significant improvement in the measurement of risk.

This paper presents a general reward-risk portfolio selection model and derives sufficient conditions for two-fund separation. In particular we show that many reward-risk models presented in the literature satisfy these conditions.

We propose a semiparametric factor model, which approximates the implied volatility surface (IVS) in a finite dimensional function space. Unlike standard principal component approaches typically used to reduce complexity, our approach is tailored to the degenerated design of IVS data. In particular, we only fit in the local neighborhood of the design points by exploiting the expiry effect present in option data. Using DAX index option data, we estimate the nonparametric components and a low-dimensional time series of latent factors. The modeling approach is completed by studying vector autoregressive models fitted to the latent factors.

We suggest a simple and general approach to fitting the discount curve under no-arbitrage constraints based on a penalized shape-constrained B-spline. The approach accommodates B-splines of any order and fitting both under the L1 and the L2 loss functions. An application to US STRIPS data from 2001-2015 suggests that polynomial splines of order three and four are mandatory to obtain reasonable fits. The choice of the loss function appears to be less relevant.

We evaluate the relevance of covariances in the transmission mechanism of variance spillovers across the US stock, US bond and gold markets from July 2003 to December 2012. For that purpose, we perform a comparative spillover analysis between a model that considers covariances and a model that considers only variances. Our results emphasise the importance of covariances. Including covariances leads to an overall increase of the spillover level and detects the beginnings of the financial crisis and of the US debt ceiling crisis earlier than the spillover measure that considers only variances. Even for the low-dimensional system that we consider, one misses important variance spillover channels when covariances are excluded.

http://ideas.repec.org/p/usg/dp2007/2007-24.html

We propose a multivariate nonparametric technique for generating reliable short-term historical yield curve scenarios and confidence intervals. The approach is based on a Functional Gradient Descent (FGD) estimation of the conditional mean vector and covariance matrix of a multivariate interest rate series. It is computationally feasible in large dimensions and it can account for nonlinearities in the dependence of interest rates at all available maturities. Based on FGD we apply filtered historical simulation to compute reliable out-of-sample yield curve scenarios and confidence intervals. We back-test our methodology on daily USD bond data for forecasting horizons from 1 to 10 days. Based on several statistical performance measures we find significant evidence of a higher predictive power of our method when compared to scenarios generating techniques based on (i) factor analysis, (ii) a multivariate CCC-GARCH model, or (iii) an exponential smoothing covariances estimator as in the RiskMetricsTM approach.