The Generalized Treynor Ratio

This paper extends the Treynor performance ratio for a single index to the case of multiple indexes. The new measure, called the Generalized Treynor Ratio, preserves the same key geometric and analytical properties of the original Treynor Ratio. The Generalized Treynor Ratio is defined as the abnormal return of a portfolio per unit of premium-weighted average systematic risk, normalized by the premium-weighted average systematic risk of the benchmark. Numerical simulations reveal that the portfolio rankings produced with this measure are more precise and more stable than the ones provided by Jensen’s alpha and the Information Ratio.I wish to thank Wayne Ferson, Pascal François, Eric Jacquier, Lars Tyge Nielsen, Nicolas Papageorgiou, Peter Schotman, Marco Pagano (the Editor) and three anonymous referees, as well as participants at the 2003 International AFFI Conference (Lyon), the 2003 NFA Conference (Qu’ebec) and seminars at Maastricht University and CORE (Louvain-la-Neuve) for helpful comments. The author acknowledges financial support from Deloitte Luxemburg and a research grant of the Belgian National Funds for Scientific Research (FNRS). Part of this research was completed while I was visiting HEC Montr’ eal. All errors remaining are mine.     

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.     

Performance Measurement under Asymmetric Information and Investment Constraints

The fact that investment policies are often restricted appears to have been neglected in the performance measurement literature. This paper, using a standard information model, shows how the introduction of constraints on the proportion of assets to be invested in the market affects the expected portfolio returns and the value of a portfolio manager's performance. The results are related to the classical Treynor and Mazuy (1966) conjectures about characteristic lines.     

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.     

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.     

Economically significant stock market forecasts

It has been known for some time that a small, but statistically significant portion of the monthly variation in excess returns on the S&P 500-stock index is predictable using ex ante information. This paper presents a model whose out-of-sample forecasts have economic significance. Specifically, a switching rule conditioned on out-of-sample forecasts of stock excess returns, produces investment outcomes that mean-variance dominate the buy-and-hold. The switching strategy yields superior risk-adjusted returns as judged by the composite performance measures of Treynor, Sharpe, and Jensen.     

Global Property Market Diversification

This paper examines global diversification benefits provided by developed property markets over 1992–2007. We employ a cointegration methodology, invariant to pair-wise correlational instability plaguing MPT approaches, to investigate regional and country property market diversification benefits for U.S. domiciled global real estate investors. We show, theoretically and empirically, the cointegration procedure aptly identifies markets integrated by common trends that mitigate diversification potential. We show global property markets are interregionally independent but find intraregional market cointegration. A portfolio of markets independent of cointegrating relationships performs best during the period but is insufficiently diversified relative to a cointegrated portfolio. Independent country markets do account for the bulk of global property diversification gains but cointegrated markets, particularly from the North American and Asia Pacific regions, retain some diversifying qualities. We also show cointegrated markets converge toward benchmark characteristics, reducing their attraction as portfolio candidates.     

Portfolio risk management in a data-rich environment

We study risk assessment using an optimal portfolio in which the weights are functions of latent factors and firm-specific characteristics (hereafter, diffusion index portfolio). The factors are used to summarize the information contained in a large set of economic data and thus reflect the state of the economy. First, we evaluate the performance of the diffusion index portfolio and compare it to both that of a portfolio in which the weights depend only on firm-specific characteristics and an equally weighted portfolio. We then use value-at-risk, expected shortfall, and downside probability to investigate whether the weights-modeling approach, which is based on factor analysis, helps reduce market risk. Our empirical results clearly indicate that using economic factors together with firm-specific characteristics helps protect investors against market?risk.     

Portfolio optimization with stochastic dominance constraints

We consider the problem of constructing a portfolio of finitely many assets whose return rates are described by a discrete joint distribution. We propose a new portfolio optimization model involving stochastic dominance constraints on the portfolio return rate. We develop optimality and duality theory for these models. We construct equivalent optimization models with utility functions. Numerical illustration is provided.     

Return performance volatility and adaptation in an automated technical analysis approach to portfolio management

This paper discusses the design of a quantitative computational intelligence portfolio management system and evaluates the advantages of some adaptive mechanisms to enable the system to adjust its management approach as market conditions change. A detailed analysis of the performance of the system outside is also provided. It is found that an adaptive methodology where trading rules are able to adjust to market conditions performs better, having greater excess returns and lower volatility than a fixed rule approach. We consider several performance metrics, including portfolio alpha and information content. Copyright © 2009 John Wiley & Sons, Ltd.     

Do low-carbon investments in emerging economies pay off? Evidence from the Brazilian stock market

Climate change has created both challenges and opportunities for investors worldwide. Investing in carbon-efficient assets, for instance, may reduce investors' climate risks while contributing to global efforts for climate change mitigation. Investors need updated and robust information on the financial performance of low-carbon investments, especially in emerging markets, where climate finance initiatives are still scattered. In this work, we provide a first insight into the financial performance of a portfolio of shares from Brazilian carbon-efficient companies. To that end, we use as reference the Carbon Efficient Index (ICO2) and assess its financial performance from 2010 to 2019 through the lens of several classic and modern portfolio metrics. We find that the index outperformed both the Brazilian market benchmark and the country's broad sustainability index, and provided competitive risk-adjusted returns compared with other sectorial indices. The results thus indicate that investing in carbon-efficient companies in Brazil has so far positively contributed to portfolio performance while offering investors an opportunity to reduce climate risk exposure in stock markets.     

A COMPARISON OF RISK MEASURES WHEN USED IN A SIMPLE PORTFOLIO SELECTION HEURISTIC

Assuming that a portfolio manager selects a portfolio by maximizing the returnto-risk ratios of the securities that constitute the portfolio, the performance of this "heuristic" is sensitive to the choice of risk measure in the return-to-risk ratio. Using sixty month holding periods and second degree stochastic dominance to evaluate the performance of the portfolio selection heuristic; the mean absolute deviation, beta and target semivariance were found to be superior to the variance and the mean semivariance. In addition, the heuristic with the superior risk measures provided performance comparable to the optimal single index model.     

Comment on “Optimal portfolio selection in a value-at-risk framework”

This comment discusses some errors in [Journal of Banking and Finance 25 (2001) 1789]. Given the portfolio rate of return is normally distributed, the following can be inferred. First, taking expected portfolio return rate as the benchmark of value-at-risk (VaR), the risk–return ratio collapses to a multiple of the Sharpe index. However, using risk-free rate as the benchmark, then above inference does not hold. Second, whether the benchmark of VaR is expected portfolio return rate or the risk-free rate, the optimal asset allocations for maximizing the risk–return ratio and Sharpe index are identical.     

An analysis of the importance of S&;P 500 discretionary constituent changes

The main purpose of this paper is to investigate the impact of the S&P 500 index committee’s decisions to change the constituent firms in the index on benchmark risk measures. The index is managed and changed discretionally by the index committee to make it as representative of the market condition as possible. In addition, the index constantly changes due to important corporate events such as bankruptcies, mergers and acquisitions, and spin-offs. We reconstruct market portfolios by retaining all discretionally deleted firms in a 3 and 5 year periods. We estimate betas at every deletion date in terms of reconstructed market portfolios; we found that these estimate betas are significantly different from the betas obtained from the constantly updated S&P 500 portfolio. We also found that such portfolios are less representative of the business cycle than the actual S&P 500 portfolio. Finally, we found that the portfolio returns obtained by retaining all discretionally deleted firms deviate significantly from the returns of the actual S&P 500 index over the studied period, October 1989 to December 2007.     

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.     

基于规模与风格的证券投资基金最优组合构建研究

本文选择中国2004年10月1日前成立的8种投资风格共133只证券投资基金,根据其在2005年1月1日-2008年3月31日共161周的数据,依照非回置等权抽样方法构建基金组合。在研究了基金组合规模与组合风险和绩效关系的基础上,着重探讨了基金组合所含风格类型以及基金组合风格丰富化指标与组合风险和绩效的关系。在上述研究的基础上,论文提出了综合规模和风格双因素的基金最优组合构建原则,并得出了最适度风格类型模型和最适度风格丰富化指标模型。     

Forecasting market turbulence using regime-switching models

We propose an early warning system to timely forecast turbulence in the US stock market. In a first step, a Markov-switching model with two regimes (a calm market and a turbulent market) is developed. Based on the time series of the monthly returns of the S&P 500 price index, the corresponding filtered probabilities are successively estimated. In a second step, the turbulent phase of the model is further specified to distinguish between bullish and bearish trends. For comparison only, a Markov-switching model with three states (a calm market, a turbulent bullish market, and a turbulent bearish market) is examined as well. In a third step, logistic regression models are employed to forecast the filtered probabilities provided by the Markov-switching models. A major advantage of the presented modeling framework is the timely identification of the factors driving the different phases of the capital market. In a fourth step, the early warning system is applied to an asset management case study. The results show that explicit consideration of the models’ signals yields better portfolio performance and lower portfolio risk compared to standard buy-and-hold and constant proportion portfolio insurance strategies.     

They're back! Post-financialization diversification benefits of commodities

Do alternative assets such as commodities improve portfolio diversification? The empirical evidence is generally positive but mixed, and almost exclusively focuses on U.S. data. Using several distinct commodity indexes over the period 1993–2019, we investigate the case of an investor in Canada, a commodity-currency country where equities are already exposed to commodity beta. We use spanning tests and several out-of-sample performance measures for both risk-averse and disappointment-averse investors. Overall, we find that while the diversification potential of commodities was limited in Canada before and during financialization, the post-financialization period offers new opportunities. The evidence suggests that portfolio performance is significantly improved using some, but not all, commodity indexes. Thus, the choice of a relevant commodity index matters as a vehicle for diversification. Finally, compounding an international component to the sectorial diversification of the portfolio can significantly improve its performance.     

The 4% strategy revisited: a pre-commitment mean-variance optimal approach to wealth management

In contrast to single-period mean-variance (MV) portfolio allocation, multi-period MV optimal portfolio allocation can be modified slightly to be effectively a down-side risk measure. With this in mind, we consider multi-period MV optimal portfolio allocation in the presence of periodic withdrawals. The investment portfolio can be allocated between a risk-free investment and a risky asset, the price of which is assumed to follow a jump diffusion process. We consider two wealth management applications: optimal de-accumulation rates for a defined contribution pension plan and sustainable withdrawal rates for an endowment. Several numerical illustrations are provided, with some interesting implications. In the pension de-accumulation context, Bengen (1994)’s [J. Financial Planning, 1994, 7, 171–180], historical analysis indicated that a retiree could safely withdraw 4% of her initial retirement savings annually (in real terms), provided that her portfolio maintained an even balance between diversified equities and U.S. Treasury bonds. Our analysis does support 4% as a sustainable withdrawal rate in the pension de-accumulation context (and a somewhat lower rate for an endowment), but only if the investor follows an MV optimal portfolio allocation, not a fixed proportion strategy. Compared with a constant proportion strategy, the MV optimal policy achieves the same expected wealth at the end of the investment horizon, while significantly reducing the standard deviation of wealth and the probability of shortfall. We also explore the effects of suppressing jumps so as to have a pure diffusion process, but assuming a correspondingly larger volatility for the latter process. Surprisingly, it turns out that the MV optimal strategy is more effective when there are large downward jumps compared to having a high volatility diffusion process. Finally, tests based on historical data demonstrate that the MV optimal policy is quite robust to uncertainty about parameter estimates.     

Portfolio size and information disclosure: An analysis of startup accelerators

We study the information-gathering role of a startup accelerator and consider the accelerator's incentives to choose a portfolio size and disclose information about participating ventures. We show that in a rational-expectations equilibrium, the resultant portfolio size is smaller than the first-best (efficient) level, consistent with some real-world observations. We further show that when some signals are uninformative and the portfolio consists of mostly high-quality ventures, the accelerator may choose to disclose only positive signals (and conceal negative signals) about its portfolio firms — a strategy we refer to as partial disclosure. Moreover, coupled with pursuing this strategy of partial disclosure, we demonstrate that the accelerator may possess incentives to exit its portfolio firms early.