Typical Portfolio Research Articles

Empirical investigation of insurance claim dependencies using mixture models

For several years now, there continues to be attention in the modeling of insurance and other similar type of risks, such as the risk of credit default, to incorporate the presence of dependencies. Some of the early papers appearing in the literature demonstrate that for a typical portfolio of such risks, ignoring dependencies can have a direct impact on the tail or extremes of the resulting portfolio loss distribution. The tail of the loss distribution is something not to be ignored by the actuary or the risk manager. To date, in spite of this growing number of papers in the literature on dependence modeling, we find that there is no known published work that provides for an empirical evidence to validate the presence of dependencies in an insurance portfolio. In this paper, we use mixture models, customarily suggested to model dependent credit default risks, to facilitate the investigation of claim dependencies. The empirical data used to calibrate these models came from a portfolio of automobile insurance policies drawn from a randomly selected insurance provider. In order to measure the presence of claim dependencies, one of the most reasonable statistic to use is the relative risk ratio, a measure that is widely popular in medical statistics and is used to gauge how the claim occurrence of a particular insurance risk induces claim of another insurance risk. Our calibration results indicate some presence of positive dependencies; relative risk is in the neighborhood of 1.4 and resulting pair-wise correlation is 0.04. The model naturally extends to capture policyholder heterogeneity through the presence of covariates by introducing mixture models with covariates as explained in this article. Not surprisingly, because the premium is the actuary’s best guess of the degree of riskiness of an insurance risk, at least on an a priori basis, it provides for the single most important factor that influences the presence of claim dependencies.

Simulating Pension's Assets and Liabilities in a Regime Switching Framework

In this paper we build a simple ALM model where future scenarios are generated assuming a Markov switching framework. Using the Shiller database of monthly equity returns and interest rate data since 1870, two regimes are revealed by the data that clearly correspond to a normal regime where returns behave like expected from economic theory, and a volatility we may also refer to as a crisis Given the evidence of the non-stationarity of economic variables, we investigate the added value of reducing risk in the portfolio when the model indicates a high probability of a shift. The persistence of each of the regimes is high. This framework gives, each month and for each scenario, the probability of being in one of the two regimes, and hence the multivariate distribution of the simulated variables that pertains to the relevant regime. These variables are 1) equity returns, 2) long term (10-year) interest rates, 3) realized inflation, and 4) short term (6-month) interest rates. We then investigate a number of relevant statistics of the terminal wealth achieved after a 20-year period for two typical portfolios: a long-only portfolio well-diversified over stocks and bonds where the relevant metric is the portfolio’s value (for instance, an endowment fund), and a pension fund’s coverage ratio where the fund’s liabilities are valued by a market interest rate curve. We show that both types of investors greatly benefit from adjusting their exposure to equities and interest rates conditionally on the expected risk regime. Finally, we show the consequence when both the endowment fund manager and the pension fund board members optimize their own reward/risk ratio from their job. We argue that in such a case they seek to minimize the probability of large losses (either in absolute terms or relative to the pension fund’s liabilities), while maximizing the minimum level of wealth (or coverage ratio for the pension fund) achieved with a given (say 95%) confidence level. We quantify the added value of the risk-regime depending allocations for such managers.

The Impact of Currency Exposure on Institutional Investment Performance: The Good, the Bad, and the Ugly

Institutional investor portfolios typically hold a significant allocation of foreign currency denominated assets. Very often at least some of this currency exposure has been viewed as bad or unwanted. On the other hand, recent studies have concluded that currency is itself an asset class that offers investors favorable risk-adjusted returns that could benefit a typical portfolio of stocks and bonds. There are two basic types of currency management mandates. In a currency hedging mandate (currency overlay), investors strive to manage (usually meaning reduce) the risk associated with the foreign currency exposure in their international assets. With an absolute return mandate (currency alpha), investors seek to earn a positive return subject to acceptable risk levels. The existing literature analyses these two basic types of currency management mandates separately. In this study, we investigate their impact on institutional investment performance simultaneously. We find that both absolute return and currency hedging mandates can have a positive impact on the portfolio risk/return characteristics. Absolute return mandates have the potential to increase the portfolio return with little impact on volatility. Risk reduction mandates tend to reduce portfolio volatility with little impact on returns. Due to the safe haven status of the U.S. Dollar, higher hedge ratios provide diversification for US dollar based investors when needed most, namely in periods of negative equity returns. Combining both currency hedging and absolute return mandates improves overall investment performance while allowing managers to stay within their portfolio risk budget.

Empirical Investigation of Insurance Claim Dependencies Using Mixture Models

For several years now, there continues to be attention in the modeling of insurance and other similar type of risks, such as the risk of credit default, to incorporate the presence of dependencies. Some of the early papers appearing in the literature demonstrate that for a typical portfolio of such risks, ignoring dependencies can have a direct impact on the tail or extremes of the resulting portfolio loss distribution. The tail of the loss distribution is something not to be ignored by the actuary or the risk manager. To date, in spite of this growing number of papers in the literature on dependence modeling, we find that there is no known published work that provides for an empirical evidence to validate the presence of dependencies in an insurance portfolio. In this paper, we use mixture models, customarily suggested to model dependent credit default risks, to facilitate the investigation of claim dependencies. The empirical data used to calibrate these models came from a portfolio of automobile insurance policies drawn from a randomly selected insurance provider. In order to measure the presence of claim dependencies, one of the most reasonable statistic to use is the relative risk ratio, a measure that is widely popular in medical statistics and is used to gauge how the claim occurrence of a particular insurance risk induces claim of another insurance risk. Our calibration results indicate some presence of positive dependencies; relative risk is in the neighborhood of 1.4 and resulting pair-wise correlation is 0.04. The model naturally extends to capture policyholder heterogeneity through the presence of co-variates by introducing mixture models with co-variates as explained in this article. Not surprisingly, because the premium is the actuary's best guess of the degree of riskiness of an insurance risk, at least on an a priori basis, it provides for the single most important factor that influences the presence of claim dependencies.

Economic capital model validation: a comparative study

Using a long history of public firm defaults, this study illustrates a validation approach for jointly testing the impact of probability of default and correlation upon economic capital model performance. We construct predicted default distributions using a variety of probability of default and correlation inputs and examine how the predicted distribution compares with the realized distribution. We conduct the comparison by looking at the percentile of realized defaults with respect to the predicted default distribution. We compare the performance of two typical portfolio parameterizations: a through-the-cycle style parameterization using agency-ratings-based long-term average default rates and Basel II correlations; and a point-in-time style parameterization using the public "expected default frequency" credit measure and the global correlation model (GCorr) of Moody's Analytics. We find that a through-the-cycle style parameterization results in a less conservative view of economic capital and substantial serial correlation in capital estimates; when point-in-time measures are used, the tested economic capital model produces consistent and conservative economic capital estimates over time.

A brain information-aided intelligent investment system

Recent advancements in neuroeconomics have revealed that specific sites of brain activity provide beneficial information regarding future risks and expected rewards. Given such advances in neuroscience, this paper studies the use of brain information in the financial system. This study explores the extent to which investment performance can be improved by using brain information in investment decision making. To examine this question, we developed a self-managed investment system that selectively employs useful brain information obtained from multiple individuals. The findings show the validity of brain information. Our system accomplishes superior performances of the investments based on a typical portfolio selection model and financial time-series models. The results of this study indicate the possibility of applying brain information to the field of finance.

Performance Analysis and Optimal Selection of Large Minimum Variance Portfolios Under Estimation Risk

We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of assets remains comparable in magnitude to the sample size, we provide a characterization of the estimation risk by providing deterministic equivalents of the portfolio out-of-sample performance in terms of the underlying investment scenario. The previous estimates represent a means of quantifying the amount of risk underestimation and return overestimation of improved portfolio constructions beyond standard ones. Well-known for the latter, if not corrected, these deviations lead to inaccurate and overly optimistic Sharpe-based investment decisions. Our results are based on recent contributions in the field of random matrix theory. Along with the asymptotic analysis, the analytical framework allows us to find bias corrections improving on the achieved out-of-sample performance of typical portfolio constructions. Some numerical simulations validate our theoretical findings.

Continuous-Time Optimal Portfolio Selection Strategy with Redemption Based on Stochastic Control

In this paper a continuous-time portfolio optimization decision with the redemption is made, a typical portfolio selection model is established by use of Bellman principle of optimality and HJB equation, we derive the optimal strategy and efficient frontier with general stochastic control technique. Its research methodologies can be applied in the practical work such as investment funds management and financial risk management to raise the scientificity of decisions. It is of great referential and inspirational value to provide solutions to practical problem in real investment process.

Management Insights

Management Insights

The Pricing of Risk-Neutral Systematic Moments in the Cross-Section of Expected Returns

This study investigates if changes in risk-neutral systematic volatility, skewness, and kurtosis, are priced, either symmetrically or asymmetrically, as systematic risk factors in the cross-section of stock returns. The moments are constructed using options on the S&P 500, and represent investors' expectation of the distribution of future market returns. Portfolio analyses reveal positive changes in implied market skewness are priced between -5% to -11% annually, while negative changes in implied market skewness are not priced. Additionally, when accounting for an asymmetric relation between returns and implied market skewness, changes in implied market volatility and kurtosis are not priced. The results are robust to portfolio weighting, market capitalization, book-to-market equity ratio, idiosyncratic volatility, and idiosyncratic skewness. Time-series and cross-sectional analyses confirm the portfolio results and associate positive changes in implied market skewness with a negative price of risk. An implied market skewness tracking portfolio possesses a great deal of power to price a variety of portfolio returns, and subsumes other typical hedge portfolios used in asset pricing. The results present a challenge to the theoretical asset pricing models, since the asymmetric results cannot be accounted for in an ICAPM framework, and the pricing of only positive skewness changes is inconsistent with the predictions of prospect theory.

Linear Generalized Stochastic Systems for Insurance Portfolios

We consider a typical portfolio of different insurance products and investigate the pricing process using the framework of a linear time invariant generalized stochastic discrete-time model. Moreover, we assume that, due to regulatory constraints, the resulting system is (regular) descriptor and calculate the solution using the tools of matrix pencil theory. Finally, we present a numerical application for two different portfolios.

Meaningful key performance indicators: Real or illusory?

Whether it is measuring the performance of a service provider or providing an accurate picture of organisational performance to senior management, the real estate executive must reconsider how performance is defined, measured and managed. This paper argues that typical portfolio measurements provide managers with little actionable information, and that the specific performance of the organisation is often indiscernible from other influencing factors. To address this critical problem, a framework for implementing a robust performance management system is laid out. The paper discusses the importance of defining critical processes, building effective measures, and balancing the demands of cost, quality and schedule. A structure for linking these measurements to strategy is discussed, as is the methodology for aggregating the measurements in a way that provides appropriate visibility for the different levels of management. With these principles in mind, a truly useful balanced scorecard can be created. The effort required to build a legitimate performance management framework is extensive but necessary. Organisational survival demands key performance indicators that are predictive, actionable and concise. Simply put, without appropriate attention to performance management, corporate real estate organisations will not survive.

Risk Governance for Funds

The typical portfolio theory does not distinguish investors and asset managers. Most of investments, however, are delegated to asset managers, which leads to an Agency problem. Moreover, the Agency problem faced by the investment industry is specific as the managers can manipulate the performance of funds. In that respect, the governance specificities of investment funds have not been adequately addressed by the academic literature. The aim of this paper is to rationalize the notion of benchmark and risk management through agency problems. We then give guidance on how a consistent risk limit and attribution system can be developed. We suggest a new approach based on shortfall measures which can be integrated to a portfolio optimization system.

A Tractable Model to Measure Sector Concentration Risk in Credit Portfolios

This paper explores a simplified version of the analytic value-at-risk approximation developed by Pykhtin (2004) which only requires risk parameters on a sector level. This approach is applied to measure the impact of credit concentrations in business sectors on the economic capital of credit portfolios. The sector composition of the portfolios is based on credit information from the German central credit register. Sensitivity analyses with various input parameters show that the analytic approximation formulae perform very well for fine-grained portfolios which are homogeneous on a sector level in terms of PD and exposure size. Furthermore, we explore the robustness of our results for portfolios which are heterogeneous in terms of these two characteristics. We find that low granularity ceteris paribus causes the analytic approximation formulae to underestimate economic capital, whereas heterogeneity in individual PDs causes overestimation. Indicative results imply that in typical credit portfolios of banks, PD heterogeneity will at least compensate for the granularity effect. This suggests that the analytic approximations estimate economic capital reasonably well and/or err on the conservative side.

Portfolio optimisation under changing risk via time‐varying beta

PurposeThe paper is aimed at modelling time varying betas via a state space representation in order to decompose the marginal contribution to risk of downside and upside deviations of asset returns in portfolio optimisation.Design/methodology/approachThe approach enables to take into account the relationship between risk and excess returns in up‐side and down‐side markets and to arrange a flexible asset allocation model which directly incorporates the investor risk tolerance to positive or negative expected market moves. The model volatility through state space models and the Kalman filter, widely used to recursively and optimally estimate time varying betas.FindingsThe study shows that the application of an asset allocation model which splits beta in two parts, one related to Bear and the other to Bull markets, and reconciles them with a non negative risk aversion parameter may produce interesting financial results if compared with typical passive portfolios. The proposed model was tested by conducting extensive empirical evaluations on a set securities belonging to eight different markets. The outcomes show that active strategies can be developed and can lead to better performances.Research implicationsThe research affects optimisation models in particular considering the volatility indicators usually estimated not only by researchers but also by practitioners.Originality/valueIn financial literature we find empirical evidence that the constant beta model may be inaccurate and hazardous to use in asset allocation decisions and many statistical techniques have been developed to estimate time dependent betas. Rolling regression procedures allow to capture beta dynamics but require the definition of the estimation period. The paper provides an empirical analysis referred both to European and American market data which let us to allocate assets avoiding the usual limits of standard volatility indicators.

Mean-Coherent Risk and Mean-Variance Approaches in Portfolio Selection: An Empirical Comparison

We empirically analyze the implementation of coherent risk measures in portfolio selection.First, we compare optimal portfolios obtained through mean-coherent risk optimization with corresponding mean-variance portfolios.We find that, even for a typical portfolio of equities, the outcomes can be statistically and economically different.Furthermore, we apply spanning tests for the mean-coherent risk efficient frontiers, which we compare to their equivalents in the meanvariance framework.For portfolios of common stocks the outcomes of the spanning tests seem to be statistically the same.

Capitalization of Farm Policy Benefits and the Rate of Return to Policy-Created Assets: Evidence from California Dairy Quota

The rate of return to ownership of California dairy quota is about 27% per year-well above that of typical financial assets, but in line with other measured returns to agricultural quotas. Ownership of dairy quota does not contribute positively to total variation of typical portfolios, including those of dairy farm assets, and so contributes little or no portfolio risk. A plausible alternative hypothesis for the high rate of return is that quota owners see significant risk of policy change that would reduce future quota values. That is, they face default risk in quota ownership. T he capitalization of farm program benefits and the effects of policy on the rate of return to investments in farm assets have long been important to agricultural policy analysis. The issues arise in the context of the influence of policy on prices of farmland, other physical assets, and policy-created assets such as farm program quota. Basic economic principles tell us that the benefits of government programs will affect returns to and prices of resources connected to a program. The incidence of flow benefits depends, in part, on the elasticities of supply of these resources, with the prices of inelastic resources affected most. The capital prices of assets do not depend directly on past returns, but on expectations about future returns. Of course, in many practical cases, the history of past returns is a crucial source of information used to form expectations. Johnson assessed the literature on returns to farm quota, stating, Roughly speaking, the discount rate used to value future earnings from [farm-program created] quotas is approximately 25%. Thus, individuals who have recently

A Comparison of Two Widely Applied Models of Shareholder Returns in the Context of Takeover Offer Gains for Australian Bidders

The impact of different modelling and testing procedures is explored on inferences concerning expected acquisition benefits to bidding shareholders. Two widely accepted return models are examined and found to imply different outcomes for Australian bidding shareholders, despite controlling for potential size- and survivor-related biases and also curbing the influence of extreme observations. A comparison of bidder returns with typical reference portfolio values, via the (0, 1) market model, finds significant wealth gains for bidding shareholders. Those gains evaporate when bidder returns are measured against their own performance standards, via the market model. The choice of return model is not the only decision affecting conclusions. Traditional tests are also examined and found to be unreliable. Conflicting conclusions are reached, under the market model, according to the chosen return measure. The inadequacy of traditional tests is demonstrated and the conflict eliminated when more robust bootstrapping tests are applied. Conclusions are more consistent for traditional tests when the (0, 1) market model is used.

Project portfolio selection through decision support

Project portfolio selection is a crucial decision in many organizations, which must make informed decisions on investment, where the appropriate distribution of investment is complex, due to varying levels of risk, resource requirements, and interaction among the proposed projects. In this paper, we discuss the implementation of an organized framework for project portfolio selection through a decision support system (DSS), which we call Project Analysis and Selection System (PASS). We describe the results of laboratory tests undertaken to measure its usability and quality, compared to manual selection processes, in typical portfolio selection problems. We also discuss the potential of PASS in supporting corporate decision making, through exposure this system has received through demonstrations for several companies.

On the Optimality of Long–Short Strategies

We consider the optimality of portfolios not subject to short-selling constraints and derive conditions that a universe of securities must satisfy for an optimal active portfolio to be dollar neutral or beta neutral. We find that following the common practice of constraining long–short portfolios to have zero net holdings or zero betas is generally suboptimal. Only under specific unlikely conditions will such constrained portfolios optimize an investor's utility function. We also derive precise formulas for optimally equitizing an active long–short portfolio using exposure to a benchmark security. The relative sizes of the active and benchmark exposures depend on the investor's desired residual risk relative to the residual risk of a typical portfolio and on the expected risk-adjusted excess return of a minimum-variance active portfolio. We demonstrate that optimal portfolios demand the use of integrated optimizations.