An alternative measure of the “world market portfolio”: Determinants, efficiency, and information content

The world market portfolio plays an important role in international asset pricing, but is unobservable in practice. We first propose a framework for constructing a market proxy that corresponds to the “market portfolio” of financial theory. We then construct this proxy, analyze its determinants and test its efficiency and explanatory power over the period 1975-2007 with respect to the return generating processes of a broad asset universe. We show that its major determinants are traded assets and that it is not efficient. However, it is significant for explaining individual asset returns over an asset universe that includes stocks, bonds, money markets and commodities. The explanatory information is incremental to what is available in traded asset prices and the significance of this information is robust with respect to diversified portfolios generated by factor analysis and to characteristic-sorted portfolios as well as to various model specifications, including the single-index model, the Fama-French (1992) three factor model for stocks, and various specifications of multi-index models hedged and unhedged for foreign currency risk.     

A Note on the Three–Portfolios Matching Problem

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.     

The diversification effects of volatility-related assets

We examine whether investors can improve their investment opportunity sets through the addition of volatility-related assets into various groupings of benchmark portfolios. By first analyzing the weekly returns of three VIX-related assets over the period 1996-2008 and then applying mean-variance spanning tests, we find that adding VIX-related assets does lead to a statistically significant enlargement of the investment opportunity set for investors. Our empirical findings are robust and have two implications. First, there is scope for the further development of financial products relating to volatility indexes. Second, hedge fund managers can utilize VIX futures contracts or VIX-squared portfolios to enhance their equity portfolio performance, as measured by the Sharpe ratio.     

Portfolio credit-risk optimization

This paper evaluates several alternative formulations for minimizing the credit risk of a portfolio of financial contracts with different counterparties. Credit risk optimization is challenging because the portfolio loss distribution is typically unavailable in closed form. This makes it difficult to accurately compute Value-at-Risk (VaR) and expected shortfall (ES) at the extreme quantiles that are of practical interest to financial institutions. Our formulations all exploit the conditional independence of counterparties under a structural credit risk model. We consider various approximations to the conditional portfolio loss distribution and formulate VaR and ES minimization problems for each case. We use two realistic credit portfolios to assess the in- and out-of-sample performance for the resulting VaR- and ES-optimized portfolios, as well as for those which we obtain by minimizing the variance or the second moment of the portfolio losses. We find that a Normal approximation to the conditional loss distribution performs best from a practical standpoint.     

Do Socially Responsible Index Investors Incur an Opportunity Cost?

We construct index‐tracking portfolios using integer programming and then compare the tracking errors and performances of portfolios formed from an unrestricted and socially screened stock universe. We find that one can construct a portfolio of socially responsible stocks that deliver market performance. Thus, the exclusion of a set of stocks from consideration does not exhaust the existence of efficient index‐tracking portfolios, especially when the exclusionary screen is for nonfinancial reasons. Our results are robust to various specifications in constructing the portfolio, for example, number of stocks included in the portfolio and weighting schemes, and robust to alternative tracking error measurement; we show that the difference induced from conducting socially responsible screen is never statistically significant.     

Ethical Investing Has No Portfolio Performance Cost

We guide investors in three ethical investment applications by comparing ethically constrained versus unconstrained optimal portfolio methods that force well-behaved weights. With optimal readjustment upon constrained investing, in Sharpe ratio analysis, we find no evidence of a performance cost for sin-free, carbon-free, or Shariah portfolios even though, in the most exacting case, Shariah investing excludes roughly 65% of common shares from security selection. In each case, we identify the specific portfolio adjustments needed to prevent an ethical portfolio performance cost.     

The impact of terrorism on financial markets: An empirical study

The main focus of this paper is to study empirically the impact of terrorism on the behavior of stock, bond and commodity markets. We consider terrorist events that took place in 25 countries over an 11-year time period and implement our analysis using different methods: an event-study approach, a non-parametric methodology, and a filtered GARCH-EVT approach. In addition, we compare the effect of terrorist attacks on financial markets with the impact of other extreme events such as financial crashes and natural catastrophes. The results of our analysis show that a non-parametric approach is the most appropriate method among the three for analyzing the impact of terrorism on financial markets. We demonstrate the robustness of this method when interest rates, equity market integration, spillover and contemporaneous effects are controlled. We show how the results of this approach can be used for investors’ portfolio diversification strategies against terrorism 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.     

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.     

Risk adjustment and momentum sources

We show that the conventional procedure of risk adjustment by running full-sample time-series Fama-French three-factor regressions is not appropriate for momentum portfolios because the procedure fails to allow for the systematic dynamics of momentum portfolio factor loadings. We propose a simple procedure to adjust risks associated with the Fama-French three factors for momentum portfolios. Using our proposed method, the Fama-French three factors can explain approximately 40% of momentum profits generated by individual stocks and nearly all of momentum returns from style portfolios.     

Thematic portfolio optimization: challenging the core satellite approach

In recent years, thematic exchange-traded funds (ETF) have increased in economic significance. Investors in thematic ETFs have more than just financial objectives and gain a non-monetary added value from a thematic portion in their portfolios. Therefore, traditional portfolio optimization models which target only financial criteria cannot suit these investors’ needs anymore. Nevertheless, to account for their thematic interests, investors adapt a core satellite strategy in which conventional core portfolios and thematic satellite portfolios are combined. Thus, these portfolios are separately optimized without further considering inter-portfolio correlation effects. Since modern portfolio theory has originally been established to, inter alia, optimize these correlation effects, portfolios can only be efficient by chance. Therefore, this study targets the correlation effects between conventional and thematic portfolios and uses a tri-criterion thematic portfolio optimization model as an overall framework. Throughout a two-part analysis with tradable ETFs and a simulation with 250,000 draws and 1,750,000 portfolio optimizations performed, the status quo is compared to the tri-criterion model. Quantifying the suboptimality, simulation results show a mean portfolio improvement of 6.23% measured as relative yield enhancement. Further, our analysis concludes that the more narrowly a theme is defined and the more particular it is, relative yield enhancements can increase up to 46.88%.

     

Forecasting portfolio-Value-at-Risk with nonparametric lower tail dependence estimates

We propose to forecast the Value-at-Risk of bivariate portfolios using copulas which are calibrated on the basis of nonparametric sample estimates of the coefficient of lower tail dependence. We compare our proposed method to a conventional copula-GARCH model where the parameter of a Clayton copula is estimated via Canonical Maximum-Likelihood. The superiority of our proposed model is exemplified by analyzing a data sample of nine different bivariate and one nine-dimensional financial portfolio. A comparison of the out-of-sample forecasting accuracy of both models confirms that our model yields economically significantly better Value-at-Risk forecasts than the competing parametric calibration strategy.     

Efficient portfolios when housing needs change over the life cycle

We address the issue of the efficiency of household portfolios in the presence of housing risk. We treat housing stock as an asset and rents as a stochastic liability stream: over the life cycle, households can be short or long in their net-housing position. Efficient financial portfolios are the sum of a standard Markowitz portfolio and a housing risk hedge term that multiplies net housing wealth. Our empirical results show that net housing plays a key role in determining which household portfolios are inefficient. The largest proportion of inefficient portfolios obtains among those with positive net housing, who should invest more in stocks.     

Performance of technical analysis in growth and small cap segments of the US equity market

A large universe of technical trading rules applied to a set of technology industry and small cap sector portfolios over the 1995-2010 period yields superior predictability after adjusting for data snooping bias in the first half of the sample period and delivers statistically significant profits for a number of portfolios when the transaction cost is assumed to be of small to moderate size. Technical analysis is not able to outperform the buy-and-hold approach for any portfolio in the set in the second half of the sample period. The finding that the short-term return predictability becomes much weaker in the more recent period suggests that the underlying segments of the equity market have become more efficient over time. The fact that mechanical trading strategies have been futile after adjusting for data snooping bias for two samples of portfolios where technical analysis is most anticipated to succeed suggests that it is unlikely to have delivered abnormal returns in any other segment of the domestic equity market in the last decade.     

Portfolio performance gauging in discrete time using a Luenberger productivity indicator

This paper proposes a pragmatic, discrete time indicator to gauge the performance of portfolios over time. Integrating the shortage function (Luenberger, 1995) into a Luenberger portfolio productivity indicator (Chambers, 2002), this study estimates the changes in the relative positions of portfolios with respect to the traditional Markowitz mean-variance efficient frontier, as well as the eventual shifts of this frontier over time. Based on the analysis of local changes relative to these mean-variance and higher moment (in casu, mean-variance-skewness and mean-variance-skewness-kurtosis) frontiers, this methodology allows to neatly separate between on the one hand performance changes due to portfolio strategies and on the other hand performance changes due to the market evolution. This methodology is empirically illustrated using a mimicking portfolio approach (22 and 23) using US monthly data from January 1931 to August 2007.     

Why does junior put all his eggs in one basket? A potential rational explanation for holding concentrated portfolios

Empirical studies of household portfolios show that young households, with little financial wealth, hold underdiversified portfolios that are concentrated in a small number of assets, a fact often attributed to behavioral biases. We present a potential rational alternative: we show that investors with little financial wealth, who receive labor income, rationally limit the number of assets they invest in when faced with financial constraints such as margin requirements and restrictions on borrowing. We provide theoretical and numerical support for our results and identify the ratio of financial wealth to labor income as a useful control variable for household portfolio studies.     

Long-horizon event studies and event firm portfolio weights: Evidence from U.K. rights issues re-visited

Empirical results, in long-horizon event studies, are sensitive to whether equal- or value-weighting schemes are used to form event firm portfolios. In this paper we propose, as a first step, an evaluation of the economic value to investing in an equal-weighted and a value-weighted event firm portfolio prior to the event study. Using tests for mean-variance spanning we find in our data a significant improvement in an investor's investment opportunity set to investing in an equal-weighted portfolio. We then re-visit the long-run post-offer performance for rights issuers in the U.K. where we find, as in other studies, differences in both the magnitude and statistical significance of abnormal performance for value-weighted and equal-weighted event firm portfolios. We then use the results from our first step to provide an economic rationale for interpreting our results. A general conclusion we draw is that it may be useful to first ascertain, in long-horizon event studies, the economic value of portfolio weighting schemes as this can then provide some guidance to the use of a specific portfolio weighting scheme and thereby to interpretation of often conflicting results.     

On systematic mortality risk and risk-minimization with survivor swaps

A new market for so-called mortality derivatives is now appearing with survivor swaps (also called mortality swaps), longevity bonds and other specialized solutions. The development of these new financial instruments is triggered by the increased focus on the systematic mortality risk inherent in life insurance contracts, and their main focus is thus to allow the life insurance companies to hedge their systematic mortality risk. At the same time, this new class of financial contract is interesting from an investor's point of view, since it increases the possibility for an investor to diversify the investment portfolio. The systematic mortality risk stems from the uncertainty related to the future development of the mortality intensities. Mathematically, this uncertainty is described by modeling the underlying mortality intensities via stochastic processes. We consider two different portfolios of insured lives, where the underlying mortality intensities are correlated, and study the combined financial and mortality risk inherent in a portfolio of general life insurance contracts. In order to hedge this risk, we allow for investments in survivor swaps and derive risk-minimizing strategies in markets where such contracts are available. The strategies are evaluated numerically.     

Hedge Fund Indices: Reconciling Investability and Representativity

Following a growing concern among investors about the quality of hedge fund index return data, this paper addresses the question of whether designing hedge fund indices that fulfil the usual requirements (in particular representative and investable) is or not a feasible task, given a variety of features that are specific to that industry. To test whether or not investability should necessarily come at the cost of representativity, we use a well‐known methodology in the asset pricing literature based on the concept of factor replicating portfolios. Our results suggest that it is actually possible to construct representative indices based on a limited number of funds that are open to new investments, except perhaps in the case of equity market neutral strategies, provided that: i) these funds are suitably selected and ii) a portfolio is constructed with the objective of replicating the common trend in hedge fund returns for a given strategy. A range of robustness tests are performed that show that high correlation of the factor replicating portfolios with the common factor of returns for each strategy is remarkably stable with respect to modifying the number of funds in the replicating portfolio or changing the frequency of rebalancing.     

Spectral risk measures and portfolio selection

This paper deals with risk measurement and portfolio optimization under risk constraints. Firstly we give an overview of risk assessment from the viewpoint of risk theory, focusing on moment-based, distortion and spectral risk measures. We subsequently apply these ideas to an asset management framework using a database of hedge funds returns chosen for their non-Gaussian features. We deal with the problem of portfolio optimization under risk constraints and lead a comparative analysis of efficient portfolios. We show some robustness of optimal portfolios with respect to the choice of risk measure. Unsurprisingly, risk measures that emphasize large losses lead to slightly more diversified portfolios. However, risk measures that account primarily for worst case scenarios overweight funds with smaller tails which mitigates the relevance of diversification.