Do ADRs enhance portfolio performance for a domestic portfolio? Evidence from the 1990s

American depository receipts (ADRs) represent an increasingly popular and convenient mechanism for international investing. We analyze ADRs traded throughout the 1990s and find that these securities offer a diversification and portfolio performance benefit when combined with a domestic portfolio (proxied by the S&P 500). While we find that emerging market ADRs are effective instruments for reducing portfolio risk, they do not improve portfolio performance as measured by the Sharpe ratio. Developed market ADRs do improve portfolio performance as measured by the Sharpe ratio. The asset allocation which maximizes the Sharpe ratio is 84 percent domestic stocks, 16 percent developed ADRs, and 0 percent emerging ADRs. Further, due to problems in defining an appropriate market index for ADRs, the Sharpe ratio is viewed to be the preferred performance measure. Other measures such as Jensen’s alpha and the Treynor measure are susceptible to being “gamed” to distort portfolio performance.     

Credit portfolios: What defines risk horizons and risk measurement?

The strong autocorrelation between economic cycles demands that we analyze credit portfolio risk in a multiperiod setup. We embed a standard one-factor model in such a setup. We discuss the calibration of the model to Standard & Poor’s ratings data in detail. But because single-period risk measures cannot capture the cumulative effects of systematic shocks over several periods, we define an alternative risk measure, which we call the time-conditional expected shortfall (TES), to quantify credit portfolio risk over a multiperiod horizon.     

Two-sided coherent risk measures and their application in realistic portfolio optimization

By using a different derivation scheme, a new class of two-sided coherent risk measures is constructed in this paper. Different from existing coherent risk measures, both positive and negative deviations from the expected return are considered in the new measure simultaneously but differently. This innovation makes it easy to reasonably describe and control the asymmetry and fat-tail characteristics of the loss distribution and to properly reflect the investor’s risk attitude. With its easy computation of the new risk measure, a realistic portfolio selection model is established by taking into account typical market frictions such as taxes, transaction costs, and value constraints. Empirical results demonstrate that our new portfolio selection model can not only suitably reflect the impact of different trading constraints, but find more robust optimal portfolios, which are better than the optimal portfolio obtained under the conditional value-at-risk measure in terms of diversification and typical performance ratios.     

An Analytical Confidence Interval for the Treynor Index: Formula, Conditions and Properties

The Treynor index, a well-known, widely-used measure of portfolio performance, is the ratio of the mean excess rate of return of the portfolio to the portfolio's beta. We derive an analytical formula that is designed to yield rigorous confidence intervals on the index. Necessary and sufficient conditions for the Treynor index to be statistically different from zero, are provided. We illustrate our approach with detailed examples and include simulations to help analysts choose the number of periods to study. Finally, some interesting properties of the interval and some sensitivity results are provided.     

Optimal Portfolio Selection Based on Expected Shortfall Under Generalized Hyperbolic Distribution

This paper discusses optimal portfolio selection problems under Expected Shortfall as the risk measure. We employ multivariate Generalized Hyperbolic distribution as the joint distribution for the risk factors of underlying portfolio assets, which include stocks, currencies and bonds. Working under this distribution, we find the optimal portfolio strategy.     

Asset pricing models with errors-in-variables

This paper revisits Fama and French [Fama, Eugene F., French, Kenneth R., (1993) Common risk factors in the returns on stock and bonds. Journal of Financial Economics 33 (1), 3–56] and Carhart [Carhart, Mark M., 1997. On persistence in mutual fund performance. Journal of Finance 52 (1), 57–82] multifactor model taking into account the possibility of errors-in-variables. In their well known paper, Fama and French [Fama, Eugene F., French, Kenneth R., 1997. Industry costs of equity. Journal of Financial Economic 43 (2), 153–193] concluded that estimates of the cost of equity for the three-factor model of FF (1993) were imprecise. We argue that this imprecision is even more severe because of the pervasive effects of measurement errors. We propose Dagenais and Dagenais [Dagenais, Marcel G., Dagenais, Denyse L., 1997. Higher moment estimators for linear regression models with errors in the variables. Journal of Econometrics 76 (1–2), 193–221] higher moments estimator as a solution. Our results show that estimates of the cost of equity obtained with Dagenais and Dagenais estimator differ sharply from popular OLS estimates and shed a new light on performance attribution and abnormal performance (α). Adapting the Generalized Treynor Ratio, recently developed by Hübner [Hübner, Georges, 2005. The generalized treynor ratio. Review of Finance 9 (3), 415–435], we show that the performance of managed portfolios with multi-index models should be revisited in presence of errors-in-variables.     

Commercial Real Estate Return Performance: A Cross-Country Analysis

This paper investigates the return performance of publicly traded real estate companies. The analysis spans the 1984–1999 time period and includes return data on over 600 companies in 28 countries. The return data reveal a substantial amount of variation in mean real estate returns and standard deviations across countries. Moreover, standard Treynor ratios, which scale country excess returns by the estimated beta on the world wealth portfolio, also reveal substantial variation across countries in excess real estate returns per unit of systematic risk. However, when we estimate Jensens alphas using both single and multifactor specifications, we detect little evidence of abnormal, risk-adjusted returns at the country level. We do, however, find evidence of a strong world-wide factor in international real estate returns. Furthermore, even after controlling for the effects of world-wide systematic risk, an orthogonalized country-specific factor is highly significant. This suggests that real estate securities may provide international diversification opportunities.     

Liquidity risk,leverage and long-run IPO returns

We examine the risk-return characteristics of a rolling portfolio investment strategy where more than 6000 Nasdaq initial public offering (IPO) stocks are bought and held for up to 5 years. The average long-run portfolio return is low, but IPO stocks appear as “longshots”, as 5-year buy-and-hold returns of 1000% or more are somewhat more frequent than for non-issuing Nasdaq firms matched on size and book-to-market ratio. The typical IPO firm is of average Nasdaq market capitalization but has relatively low book-to-market ratio. We also show that IPO firms exhibit relatively high stock turnover and low leverage, which may lower systematic risk exposures. To examine this possibility, we launch an easily constructed “low-minus-high” (LMH) stock turnover portfolio as a liquidity risk factor. The LMH factor produces significant betas for broad-based stock portfolios, as well as for our IPO portfolio and a comparison portfolio of seasoned equity offerings. The factor-model estimation also includes standard characteristic-based risk factors, and we explore mimicking portfolios for leverage-related macroeconomic risks. Because they track macroeconomic aggregates, these mimicking portfolios are relatively immune to market sentiment effects. Overall, we cannot reject the hypothesis that the realized return on the IPO portfolio is commensurable with the portfolio's risk exposures, as defined here.     

Portfolio performance evaluation with generalized Sharpe ratios: Beyond the mean and variance

This paper presents a theoretically sound portfolio performance measure that takes into account higher moments of distribution. This measure is motivated by a study of the investor’s preferences to higher moments of distribution within Expected Utility Theory and an approximation analysis of the optimal capital allocation problem. We show that this performance measure justifies the notion of the Generalized Sharpe Ratio (GSR) introduced by Hodges (1998). We present two methods of practical estimation of the GSR: nonparametric and parametric. For the implementation of the parametric method we derive a closed-form solution for the GSR where the higher moments are calibrated to the normal inverse Gaussian distribution. We illustrate how the GSR can mitigate the shortcomings of the Sharpe ratio in resolution of Sharpe ratio paradoxes and reveal the real performance of portfolios with manipulated Sharpe ratios. We also demonstrate the use of this measure in the performance evaluation of hedge funds.     

Equity portfolio diversification with high frequency data

Investors wishing to achieve a particular level of diversification may be misled on how many stocks to hold in a portfolio by assessing the portfolio risk at different data frequencies. High frequency intradaily data provide better estimates of volatility, which translate to more accurate assessment of portfolio risk. Using 5-min, daily and weekly data on S&P500 constituents for the period from 2003 to 2011, we find that for an average investor wishing to diversify away 85% (90%) of the risk, equally weighted portfolios of 7 (10) stocks will suffice, irrespective of the data frequency used or the time period considered. However, to assure investors of a desired level of diversification 90% of the time (in contrast to on average), using low frequency data results in an exaggerated number of stocks in a portfolio when compared with the recommendation based on 5-min data. This difference is magnified during periods when financial markets are in distress, as much as doubling during the 2007–2009 financial crisis.     

Market timing: A global endeavor

This paper employs daily fund and index data, the classical Treynor and Mazuy timing model, and two multi-factor extensions to measure the market timing ability of global asset allocation funds. These funds differ from traditional global or international funds in that they face fewer investment constraints and are known to actively shift funds across a wide variety of asset classes. When using the classical Treynor and Mazuy timing models, I find evidence of poor market timing ability. However, this evidence disappears when timing ability is examined using two multi-factor models. The results from Treynor and Mazuy are spurious since both multi-factor extensions do a much better job in explaining the variation in average fund returns.     

Economic capital for nonperforming loans

A portfolio of nonperforming loans requires economic capital. We present two models for forecasting the portfolio loss and its probability distribution. In the first model, the loss for each nonperforming loan entails a change in provision over the risk horizon. The risk determinants are the single-name concentration, measured by the Herfindahl–Hirschmann index, as well as a systematic factor and the idiosyncratic risk. Our second model allows for interportfolio diversification with a portfolio of performing loans because banks typically own both performing and nonperforming loans. In this model, the nonperforming loan is identified with its systematic risk. Both models allow for closed-form expressions of economic capital and for the capital charge of the single loan. We calibrate the macroeconomic model parameters statistically with a loss panel; the microeconomic parameters depend on the portfolio. The portfolio risk for nonperforming loans mainly depends on the volatility of the systematic economic factor. The dependence becomes more pronounced when interportfolio diversification is taken into account. The magnitude of interportfolio diversification is also marked. Finally, we calculate regulatory capital charges according to Basel II for past-due loans. The regulatory charges are on average smaller than our economic charges and, additionally, take the volatility of economic activity into account only implicitly.     

All Guts,No Glory: Trading and Diversification among Online Investors

I explore cross‐sectional portfolio performance in a sample containing 324,736 transactions conducted by 16,831 Swedish investors at an Internet discount brokerage firm during the period May 1999 to March 2002. On average, investors hold undiversified portfolios, show a strong preference for risk, and trade aggressively. I measure performance using a panel data model, and explain the cross‐sectional variation using investors' turnover, portfolio size and degree of diversification. I find that turnover is harmful to performance due to fees, and is therefore more predominant among investors with small portfolios. I argue that the degree of diversification is a proxy for investor skill, and it has a separate and distinct positive effect on performance. Investors underperform the market by about 8.5% per year on average, of which half can be attributed to trading costs.     

A bootstrap-based comparison of portfolio insurance strategies

This study presents a systematic comparison of portfolio insurance strategies. We implement a bootstrap-based hypothesis test to assess statistical significance of the differences in a variety of downside-oriented risk and performance measures for pairs of portfolio insurance strategies. Our comparison of different strategies considers the following distinguishing characteristics: static versus dynamic protection; initial wealth versus cumulated wealth protection; model-based versus model-free protection; and strong floor compliance versus probabilistic floor compliance. Our results indicate that the classical portfolio insurance strategies synthetic put and constant proportion portfolio insurance (CPPI) provide superior downside protection compared to a simple stop-loss trading rule and also exhibit a higher risk-adjusted performance in many cases (dependent on the applied performance measure). Analyzing recently developed strategies, neither the TIPP strategy (as an ‘improved’ CPPI strategy) nor the dynamic VaR-strategy provides significant improvements over the more traditional portfolio insurance strategies.     

Risk measure pricing and hedging in incomplete markets

This article attempts to extend the complete market option pricing theory to incomplete markets. Instead of eliminating the risk by a perfect hedging portfolio, partial hedging will be adopted and some residual risk at expiration will be tolerated. The risk measure (or risk indifference) prices charged for buying or selling an option are associated to the capital required for dynamic hedging so that the risk exposure will not increase. The associated optimal hedging portfolio is decided by minimizing a convex measure of risk. I will give the definition of risk-efficient options and confirm that options evaluated by risk measure pricing rules are indeed risk-efficient. Relationships to utility indifference pricing and pricing by valuation and stress measures will be discussed. Examples using the shortfall risk measure and average VaR will be shown. The work of Mingxin Xu is supported by the National Science Foundation under grant SES-0518869. I would like to thank Steven Shreve for insightful comments, especially his suggestions to extend the pricing idea from using shortfall risk measure to coherent ones, and to study its relationship to utility based derivative pricing. The comments from the associate editor and the anonymous referee have reshaped the paper into its current version. The paper has benefited from discussions with Freddy Delbaen, Jan Večeř, David Heath, Dmitry Kramkov, Peter Carr, and Joel Avrin.     

Optimal portfolios when stock prices follow an exponential Lévy process

We investigate some portfolio problems that consist of maximizing expected terminal wealth under the constraint of an upper bound for the risk, where we measure risk by the variance, but also by the Capital-at-Risk (CaR). The solution of the mean-variance problem has the same structure for any price process which follows an exponential Lévy process. The CaR involves a quantile of the corresponding wealth process of the portfolio. We derive a weak limit law for its approximation by a simpler Lévy process, often the sum of a drift term, a Brownian motion and a compound Poisson process. Certain relations between a Lévy process and its stochastic exponential are investigated.Received: January 2003Mathematics Subject Classification: Primary: 60F05, 60G51, 60H30, 91B28; secondary: 60E07, 91B70JEL Classification: C22, G11, D81We would like to thank Jan Kallsen and Ralf Korn for discussions and valuable remarks on a previous version of our paper. The second author would like to thank the participants of the Conference on Lévy Processes at Aarhus University in January 2002 for stimulating remarks. In particular, a discussion with Jan Rosinski on gamma processes has provided more insight into the approximation of the variance gamma model.     

Killing the Law of Large Numbers: Mortality Risk Premiums and the Sharpe Ratio

We provide an overview of how the law of large numbers breaks down when pricing life‐contingent claims under stochastic as opposed to deterministic mortality (probability, hazard) rates. In a stylized situation, we derive the limiting per‐policy risk and show that it goes to a non‐zero constant. This is in contrast to the classical situation when the underlying mortality decrements are known with certainty, per policy risk goes to zero. We decompose the standard deviation per policy into systematic and non‐systematic components, akin to the analysis of individual stock (equity) risk in a Markowitz portfolio framework. Finally, we draw upon the financial analogy of the Sharpe Ratio to develop a premium pricing methodology under aggregate mortality risk.     

An Empirical Investigation of the Option-Adjusted Realized Return

The issue of meaningful evaluation of professionally managed portfolios remains to be resolved satisfactorily within the investment community. The fact that many of the current procedures for evaluating portfolio performance are deeply rooted in conventional mean-variance (M-V) analysis raises serious concerns from a theoretical perspective. The primary objective of this paper is an empirical investigation (as differentiated from a thorough empirical test) of an ordinal portfolio performance measure, called the Option-adjusted Realized (average rate of) Return or ORR, developed recently by Smith and Kokoska (1998). The ORR is a leverage- and risk-adjusted average realized rate of return that can be used directly in evaluating portfolio performance.Using returns data for June 1992 to May 1998, we estimate ORRs for two portfolios—the CREF Stock Fund and a hypothetical market index portfolio whose composition is identical to that of the S&P 500 Index. Also, we estimate Sharpe and Treynor ratio values for each portfolio and compare rankings provided by these methods for the two portfolios with rankings provided by the ORR method. For the interval of time from June 1995 to May 1998, the rankings provided by the three methods are not consistent. The ORR rankings for this time period indicate the CREF Fund underperformed the S&P Index on a risk-adjusted basis. Additional partitioning of the data creates other multiple intervals or holding periods for which the evaluation results (ex post) support at least moderate likelihood of unambiguous inconsistency ex ante. We argue that, given our set of assumptions, the ORR rankings, founded in option-pricing theory, are more reliable than the others that are M-V based.     

How much do firms hedge with derivatives?

For 234 large non-financial corporations using derivatives, we report the magnitude of their risk exposure hedged by financial derivatives. If interest rates, currency exchange rates, and commodity prices change simultaneously by three standard deviations, the median firm's derivatives portfolio, at most, generates $15 million in cash and $31 million in value. These amounts are modest relative to firm size, and operating and investing cash flows, and other benchmarks. Corporate derivatives use appears to be a small piece of non-financial firms’ overall risk profile. This suggests a need to rethink past empirical research documenting the importance of firms’ derivative use.     

The Pollution Premium

This paper studies the asset pricing implications of industrial pollution. A long-short portfolio constructed from firms with high versus low toxic emission intensity within an industry generates an average annual return of 4.42%, which remains significant after controlling for risk factors. This pollution premium cannot be explained by existing systematic risks, investor preferences, market sentiment, political connections, or corporate governance. We propose and model a new systematic risk related to environmental policy uncertainty. We use the growth in environmental litigation penalties to measure regime change risk and find that it helps price the cross section of emission portfolios' returns.