Moody's correlated binomial default distributions for inhomogeneous portfolios

This paper generalizes Moody's correlated binomial default distribution for homogeneous (exchangeable) credit portfolios, which was introduced by Witt, to the case of inhomogeneous portfolios. We consider two cases of inhomogeneous portfolios. In the first case, we treat a portfolio whose assets have uniform default correlation and non-uniform default probabilities. We obtain the default probability distribution and study the effect of inhomogeneity. The second case corresponds to a portfolio with inhomogeneous default correlation. Assets are categorized into several different sectors and the inter-sector and intra-sector correlations are not the same. We construct the joint default probabilities and obtain the default probability distribution. We show that as the number of assets in each sector decreases, inter-sector correlation becomes more important than intra-sector correlation. We study the maximum values of the inter-sector default correlation. Our generalization method can be applied to any correlated binomial default distribution model that has explicit relations to the conditional default probabilities or conditional default correlations, e.g. Credit Risk⁺, implied default distributions. We also compare some popular CDO pricing models from the viewpoint of the range of the implied tranche correlation.     

Systematic Risk and Empirical Research

We show here that risky asset returns generating processes stated in terms of factors which include both accounting and non-accounting based measures of risk (e.g. book to market ratios) imply, under fairly standard regularity conditions, that the Sharpe-Lintner-Black asset pricing model beta is a 'sufficient' statistic in the sense that it captures all important attributes of the returns generating process in a single number. We then derive the parametric relationship between betas based on inefficient index portfolios and betas based on the market or tangency portfolio. We demonstrate that the relationship between risky asset expected returns and betas computed on the basis of inefficient index portfolios is both consistent with the predictions of the Capital Asset Pricing Model and the multi-factor asset pricing models of Fama and French (1992, 1993, 1995 and 1996). The 'trick' is to realise that inefficient index portfolios are composed of the market portfolio and a collection of inefficient but self financing 'kernel' or 'arbitrage' portfolios. It then follows that there is a perfect linear cross sectional relationship between risky asset expected returns, betas based on inefficient index portfolios and the arbitrage portfolios. Hence, if we happen to stumble across variables that span the same subspace as the vectors representing the arbitrage portfolios, it is easy to create the illusion that risky asset expected returns depend on variables other than 'beta'.     

Performance based mortgage-backed securities indexing

The traditional approaches to indexing first developed for equities and then adapted to bonds are not effective for mortgage-backed securities. This paper details a new technique for indexing portfolios of mortgage-backed securities which rectifies the deficiencies of the older cellular method. By focusing on the performance characteristics of the bonds adjusted for their embedded options, we at once simplify the process of portfolio selection and increase the accuracy of performance tracking.     

Options on portfolios with higher-order moments

We develop a simple calibration approach to generate return distributions for multivariate asset distributions and use this technique to price options on portfolios given the first four co-moments of the joint distribution of returns. The technique is fast and captures the impact of covariance, and the co-skewness and co-kurtosis tensors on the value of these options. Given the technique works for a portfolio, the same is also applicable to options on individual securities as a special simpler case.     

The value of asset allocation advice: Evidence from The Economist's quarterly portfolio poll

This study analyzes the economic importance of portfolio advice for an investor with an international and multiple-asset investment strategy. We construct portfolios based upon the asset allocation and security market advice of major international investment bankers and analyze the performance using weight-based techniques. Our results indicate that portfolio advisers are not able to outperform passive benchmarks. They do not realize superior performance either through appropriate timing or selection skills. Apparent market timing skills as measured by the Portfolio Change Measure are to a large extent an artifact caused by serial correlation in the return indices used. Likewise, the apparent short-run performance persistence is more due to the serial correlation in returns than to active portfolio selection strategies.     

REITs风险收益特征及其资产配置作用

REITs具有“长期收益率高于股票、波动性低于股票”的风险／收益特征，更为重要的是REITs与股票、债券的相关系数低。机构投资者的传统组合中通常只包括债券、股票类证券，加AREITs可使组合优化，即组合有效边界向左上方移动，意味着在相同风险水平下，增加REITs后的组合可获得更高收益，或是为取得相同收益水平，增加REITs后的组合只承担更低风险。     

Options Trading and the CAPM

This article studies equilibrium asset pricing when agents facenonnegative wealth constraints. In the presence of these constraintsit is shown that options on the market portfolio are nonredundantsecurities and the economy's pricing kernel is a function ofboth the market portfolio and the nonredundant options. Thisimplies that the options should be useful for explaining riskyasset returns. To test the theory, a model is derived in whichthe expected excess return on any risky asset is linearly related(via a collection of betas) to the expected excess return onthe market portfolio and to the expected excess returns on thenonredundant options. The empirical results indicate that thereturns on traded index options are relevant for explainingthe returns on risky asset portfolios.     

Mean–variance and mean–semivariance portfolio selection: a multivariate nonparametric approach

While univariate nonparametric estimation methods have been developed for estimating returns in mean-downside risk portfolio optimization, the problem of handling possible cross-correlations in a vector of asset returns has not been addressed in portfolio selection. We present a novel multivariate nonparametric portfolio optimization procedure using kernel-based estimators of the conditional mean and the conditional median. The method accounts for the covariance structure information from the full set of returns. We also provide two computational algorithms to implement the estimators. Via the analysis of 24 French stock market returns, we evaluate the in-sample and out-of-sample performance of both portfolio selection algorithms against optimal portfolios selected by classical and univariate nonparametric methods for three highly different time periods and different levels of expected return. By allowing for cross-correlations among returns, our results suggest that the proposed multivariate nonparametric method is a useful extension of standard univariate nonparametric portfolio selection approaches.     

SYMMETRIC VERSUS ASYMMETRIC CONDITIONAL COVARIANCE FORECASTS: DOES IT PAY TO SWITCH?

Volatilities and correlations for equity markets rise more after negative returns shocks than after positive shocks. Allowing for these asymmetries in covariance forecasts decreases mean‐variance portfolio risk and improves investor welfare. We compute optimal weights for international equity portfolios using predictions from asymmetric covariance forecasting models and a spectrum of expected returns. Investors who are moderately risk averse, have longer rebalancing horizons, and hold U.S. equities benefit most and may be willing to pay around 100 basis points annually to switch from symmetric to asymmetric forecasts. Accounting for asymmetry in both variances and correlations significantly lowers realized portfolio risk.     

Correlation expansions for CDO pricing

This paper develops numerical approximations for pricing collateralized debt obligations (CDOs) and other portfolio credit derivatives in the multifactor Normal Copula model. A key aspect of pricing portfolio credit derivatives is capturing dependence between the defaults of the elements of the portfolio. But, compared with an independent-obligor model, pricing in a model with correlated defaults is more challenging. Our approach strikes a balance by reducing the problem of pricing in a model with correlated defaults to calculations involving only independent defaults. We develop approximations based on power series expansions in a parameter that scales the underlying correlations. These expansions express a CDO tranche price in a multifactor model as a series of prices in independent-obligor models, which are easy to compute. The approach builds on a classical approximation for multivariate Gaussian probabilities; we introduce an alternative representation that greatly reduces the number of terms required to evaluate the coefficients in the expansion. We also apply this method to the underlying problem of computing joint probabilities of multivariate normal random variables for which the correlation matrix has a factor structure.     

Optimal asset allocation using a combination of implied and historical information

This paper investigates the contribution of option-implied information for strategic asset allocation for individuals with minimum-variance preferences and portfolios with a variety of assets. We propose a covariance matrix that exploits a mixture of historical and option-implied information. Implied variance measures are proposed for those assets for which option-implied information is available. Historical variance and correlation measures are applied to the remaining assets. The performance of this novel approach for constructing optimal investment portfolios is assessed out-of-sample using statistical and economic measures. An empirical application to a sophisticated portfolio comprised by a combination of equities, fixed income, alternative securities and cash deposits shows that implied variance measures with risk premium correction outperform variance measures constructed from historical data and implied variance without correction. This result is robust across investment portfolios, volatility and portfolio performance metrics, and rebalancing schemes.     

DIVERSIFICATION AND SKEWNESS IN OPTION PORTFOLIOS

Skewness in returns is relevant to option investors. Because options possess positively skewed distributions, the traditional maxim of diversification, which can destroy positive skewness, is not necessarily consistent with investment objectives. The results indicate that the majority of skewness in option portfolios is diversified with a relatively small portfolio size, suggesting a strategy of antidiversification for option investors. Even though the investment performance of options is inferior to stocks on a risk-return basis, the data indicate the suitability of option portfolios in an environment where an investor's utility is measured by the return, risk, and skewness of the return distribution.     

Hedge fund portfolio construction: A comparison of static and dynamic approaches

This article studies the impact of modeling time-varying covariances/correlations of hedge fund returns in terms of hedge fund portfolio construction and risk measurement. We use a variety of static and dynamic covariance/correlation prediction models and compare the optimized portfolios’ out-of-sample performance. We find that dynamic covariance/correlation models construct portfolios with lower risk and higher out-of-sample risk-adjusted realized return. The tail-risk of the constructed portfolios is also lower. Using a mean-conditional-value-at-risk framework we show that dynamic covariance/correlation models are also successful in constructing portfolios with minimum tail-risk.     

Using industry momentum to improve portfolio performance

Minimum-variance portfolios, which ignore the mean and focus on the (co)variances of asset returns, outperform mean–variance approaches in out-of-sample tests. Despite these promising results, minimum-variance policies fail to deliver a superior performance compared with the simple 1/N rule. In this paper, we propose a parametric portfolio policy that uses industry return momentum to improve portfolio performance. Our portfolio policies outperform a broad selection of established portfolio strategies in terms of Sharpe ratio and certainty equivalent returns. The proposed policies are particularly suitable for investors because portfolio turnover is only moderately increased compared to standard minimum-variance portfolios.     

Asset Allocation by Variance Sensitivity Analysis

This article provides a solution to the curse of dimensionalityassociated to multivariate generalized autoregressive conditionallyheteroskedastic (GARCH) estimation. We work with univariateportfolio GARCH models and show how the multivariate dimensionof the portfolio allocation problem may be recovered from theunivariate approach. The main tool we use is "variance sensitivityanalysis," the change in the portfolio variance induced by aninfinitesimal change in the portfolio allocation. We suggesta computationally feasible method to find minimum variance portfoliosand estimate full variance-covariance matrices. An applicationto real data portfolios implements our methodology and comparesits performance against that of selected popular alternatives.     

Issues in Islamic Equities: A Literature Survey

This article reviews the current literature on Islamic equities. Our survey indicates that the bulk of articles is quantitative or empirical in nature, with a notable dearth of theoretical works. Among the common research themes explored by these articles are comparative performances of Islamic equities vis-à-vis their conventional counterparts, comparisons of Islamic portfolios with SRI funds, and empirically articulating portfolio diversification benefits associated with Islamic equities. In addition, numerous articles discuss idiosyncrasies of Shari’ah compliant stocks and portfolios under subthemes such as volatility, risk factors, and performance attributes. This survey also includes articles addressing efficiency perspectives, calendar anomalies, and issues in Shari’ah stock screening norms. We summarize general findings and offer suggestions for future research. Literature surveys on Islamic equities are few and far between, and this article, to date, represented the most recent and comprehensive attempt at that.     

Markowitz efficiency and size effect: evidence from the UK stock market

Academics and practitioners have frequently debated the relationship between market capitalization and expected return. We apply the Markowitz efficient frontier approach to develop a portfolio performance measure that compares the return of a portfolio to its optimal return, using data from the UK stock market over the period 1985–2012. Our results show that there is a negative relationship between portfolio size and portfolio return during the period under study. When comparing actual portfolio return with achievable return for the same level of risk, we find that as the portfolio size expands, underperformance of the portfolio increases, i.e. the larger the portfolio size, the greater the underperformance. This indicates that Markowitz efficiency is difficult to achieve, particularly in large portfolios. Changing model parameters leads to alternative efficient frontiers that impact upon the measurement of performance. However, the use of alternative efficient frontiers does not affect our result of the size effect on the relative performance of portfolios. Our study shows that the size effect is present over the full period. Our findings also suggest that the excess returns found in small portfolios are likely to be associated with higher levels of diversifiable risk in comparison with larger portfolios. Furthermore, in contrast to other studies, we find no evidence to support the size reversal effect in the data.     

Multistep predictions for multivariate GARCH models: Closed form solution and the value for portfolio management

This paper derives the closed form solution for multistep predictions of the conditional means and covariances for multivariate ARMA-GARCH models. These predictions are useful e.g. in mean-variance portfolio analysis when the rebalancing frequency is lower than the data frequency. In this situation the conditional mean and the conditional covariance matrix of the cumulated higher frequency returns are required as inputs in the mean-variance portfolio problem. The empirical value of the result is evaluated by comparing the performance of quarterly and monthly rebalanced portfolios using monthly MSCI index data across a large set of GARCH models. Using correct multistep predictions generally results in lower risk and higher returns.     

Comparisons of aggregate claim numbers and amounts: a study of heterogeneity

In this paper, we investigate how the heterogeneity among occurrence probabilities and claim severities affects the aggregate claim numbers and aggregate claim amount for an insurance portfolio. We show that higher heterogeneity (and dependence) among occurrence probabilities results in both smaller aggregate claim numbers and aggregate claim amount in the sense of the mean residual lifetime order. We also prove that as the heterogeneity among the claims increases, the aggregate claim amount increases in the sense of the usual stochastic order when the vector of occurrence probabilities is left tail weakly stochastic arrangement increasing. These theoretical findings are applied to (i) study ordering properties of convolutions of binomial random variables, (ii) provide upper bounds for the mean residual lifetime functions of the aggregate claim numbers and amount, and (iii) compare stop-loss premiums and risk capital of different insurance portfolios.