Performance Participation Strategies: OBPP versus CPPPJournal articlePhilippe Bertrand and Jean-Luc Prigent, Finance, Volume 43, Issue 1, pp. 123-150, 2022

The goal of this paper is to provide and examine an important extension of the usual portfolio insurance, namely to study the notion of portfolio performance participation. In this framework, the portfolio is based on two risky assets: the first one corresponds to a reserve asset, while the second one is considered as an active asset which has usually both a higher mean and a higher variance. We aim at insuring a given percentage of the reserve asset return, whatever the market fluctuations. The two main performance participation methods are the Option-Based Performance Participation (OBPP) and the Constant Proportion Performance Participation (CPPP). We compare these two portfolio strategies by means of various criteria such as their payoffs at maturity, their four first moments and their cumulative distributions functions. We also compare their dynamic hedging properties by computing in particular their deltas and vegas.

On the optimality of path-dependent structured funds: The cost of standardizationJournal articlePhilippe Bertrand and Jean-Luc Prigent, European Journal of Operational Research, Volume 277, Issue 1, pp. 333-350, 2019

This paper examines the suitability of an important class of standard financial structured products, namely those whose performances are based on smoothing the return of a given risky underlying asset while providing a guarantee at maturity. Using various assumptions about the customers attitudes towards risk, we show that such standardized products are not optimal, even if the financial market volatility is constant. As a by-product, we provide in particular the optimal portfolio value in the regret/rejoice framework to go further with the notion of aversion of getting a return smaller than the risk-free one. Using the notion of compensating variation, we determine for the first time, the monetary losses of providing these standardized products instead of the optimal ones to the customers. We show that these monetary losses can be very significant when the volatility of the risky asset is stochastic. From the operational point of view, such results highly suggest to trade on the Volatility Index (VIX) and/or to introduce derivatives written on it, when selling standardized funds in order to better meet investors needs and preferences.

Option-Based performance participationJournal articleRudi Zagst, Julia Kraus and Philippe Bertrand, Journal of Banking & Finance, Volume 105, Issue C, pp. 44-61, 2019

The purpose of this article is to introduce and analyze the option-based performance participation (OBPP) as performance participation method based on a portfolio consisting of two risky assets. By generalizing the provided guarantee to a participation in the performance of a second risky underlying, this new kind of strategies allows to cope with well-known problems associated with standard portfolio insurance methods, especially in times of low or even negative interest rates. However, the minimum guaranteed portfolio value at the end of the investment horizon is not deterministic anymore, but subject to systematic risk instead. Hence, we compare the newly introduced OBPP with the option-based portfolio insurance (OBPI) in various dimensions such as terminal payoffs, mean-variance efficiency and stochastic dominance. To do this, general analytical expressions for all moments of the payoff distributions of the two strategies are derived. Furthermore, we show how an OBBP can be designed so that it stochastically dominates a given OBPI (with a given probability) while retaining the potential for a participation in rising markets via a so-called reserve asset. Numerical case studies show how the proposed concept can be easily implemented for practical applications.

Mixed-asset portfolio allocation under mean-reverting asset returnsJournal articleCharles-Olivier Amédée-Manesme, Fabrice Barthélémy, Philippe Bertrand and Jean-Luc Prigent, Annals of Operations Research, Volume 281, Issue 1-2, pp. 65-98, 2019

Standard results about portfolio optimization suggest that the allocation to real estate in a mixed-asset portfolio should be around 15–20%. However, the institutional investors share in real estate is significantly smaller, around 7–9%. Many researches have addressed this point even if as of today no consensus has emerged. In this paper, we built-up an allocation model that can explain the empirical observed weights. For this purpose, we account for the term structure of all standard financial assets and also of real estate asset class (expected returns, volatilities and correlations depending on the time to maturity). We propose a dynamic portfolio optimization model that allows analyzing portfolio weights with respect to the whole term structure modelling, due to its tractability and its good fit when being adequately calibrated. In this framework, we provide explicit and operational solutions to the dynamic mixed-asset portfolio allocation (cash, real estate, stock and bond). The results show that accounting for investment horizon and mean-reverting dynamics allows to better examine how portfolio allocations depend on both risk aversion and investment horizon.

Residential real estate in a mixed-asset portfolioJournal articlePhilippe Bertrand and Jean-Luc Prigent, Bankers, Markets & Investors, Volume 150, Issue 1, 2018

Mixed-asset portfolio optimization consists in determining the best allocation among standard financial assets such as money market accounts, bonds, stocks and real estate asset as well. For this latter kind of asset, computing the optimal weight can be challenging. First, there is the need to specify the kind of real estate included in the portfolio (commercial, industrial, residential, direct, REIT shares). Second, the prices used to calibrate real estate values need to be chosen from alternatives like: appraisal values, actual real estate transactions, repeated sales, indices. In this paper we focus on private residential real estate returns, investigating the optimal weight of the real asset with respect to standard financial assets. Using quarterly data on housing indices for four European countries, France, Germany, UK and Spain, we address the question of how investing in housing affects the composition of an investor’s portfolio. We show in particular under which conditions we recover the typical 15%-20% real asset allocation.

Risk-based strategies: the social responsibility of investment universes does matterJournal articlePhilippe Bertrand and Vincent Lapointe, Annals of Operations Research, Volume 262, Issue 2, pp. 413-429, 2018

In this article we extend the research on risk-based asset allocation strategies by exploring how using an SRI universe modifies properties of risk-based portfolios. We focus on four risk-based asset allocation strategies: the equally weighted, the most diversified portfolio, the minimum variance and the equal risk contribution. Using different estimators of the matrix of covariances, we apply these strategies to the EuroStoxx universe of stocks, the Advanced Sustainability Performance Index (ASPI) and the complement of the ASPI in the EuroStoxx universe from March 15, 2002 to May 1, 2012. We observe several impacts but one is particularly important in our mind. We observe that risk-based asset allocation strategies built on the entire universe, concentrate their solution on non-SRI stocks. Such risk-based portfolios are therefore under-weighted in socially responsible firms.

Equilibrium of financial derivative markets under portfolio insurance constraintsJournal articlePhilippe Bertrand and Jean-Luc Prigent, Economic Modelling, Volume 52, Issue Part A, pp. 278-291, 2016

This paper examines the equilibrium of financial portfolios under insurance constraints on terminal wealth. We consider a single period economy in which agents search to maximize the expected utilities of their wealth at maturity. Three main classes of financial assets are considered: a riskless asset (usually the bond), a risky asset (the stock) and European options of all strikes (corresponding to financial derivatives). Both partial and general optimal financial equilibria are determined and analyzed for quite general utility functions and insurance constraints.

Portfolio Insurance: The Extreme Value Approach Applied to the CPPI MethodBook chapterPhilippe Bertrand and Jean-Luc Prigent, In: Extreme Events in Finance: A Handbook of Extreme Value Theory and its Applications, Francois Longin (Eds.), 2016-10, pp. 465-482, Wiley, 2016


Risk Attribution AnalysisBook chapterPhilippe Bertrand, In: Investment Risk Management, H. K. Baker and G. Filbeck (Eds.), 2015, pp. 387-407, Oxford University Press, 2015

A common practice in the financial management industry is to combine portfolio risk attribution with performance attribution. Performance attribution considered alone is insufficient and can be misleading. Tracking-error attribution is only consistent with some types of efficient portfolios. The next step in the portfolio evaluation process combines performance attribution and risk attribution in a single measure of risk-adjusted performance attribution. Given three levels in the analysis of information ratio attribution that can possibly lead to conflicting results, analysts must exercise care in interpretation. Component information ratios are particularly useful in assessing whether equilibrium between expected returns and relative risk has been reached.

On Path-Dependent Structured Funds: Complexity Does Not Always Pay (Asian versus Average Performance Funds)Journal articlePhilippe Bertrand and Jean-Luc Prigent, Finance, Volume 36, Issue 2, pp. 67-105, 2015

As emphasized by the U.S. Dodd-Frank Act and the European MiFID directive, financial institutions are required to ?categorise their clients and assess their suitability for each type of investment product.? In this framework, this paper examines several standard financial structured products whose performances are based on smoothing the return of an underlying risky asset and providing a guarantee at maturity. We use various criteria such as probabilities of providing merely the guarantee at maturity and Kappa measures. Surprisingly, our study reveals that funds based on averages of calls generally do better than Asian funds.

Overreaction and momentum in the Vietnamese stock marketJournal articleLe Quy Duong and Philippe Bertrand, Managerial Finance, Forthcoming

Although the solid empirical proof of momentum is documented in various stock markets, there are many debates among academics with respect to the source of momentum profit. The first aim of this paper is intensively re-examine the momentum profit in Vietnam, an important emerging market. Secondly, the authors study the return predictability of a measure of investors’ overreaction, then examine whether the momentum effect in Vietnam is explained by overreaction.
Using the weekly data of more than 300 non-financial Vietnamese stocks during 2009–2019, the authors build a measure of investors’ overreaction, which is based on trading volume and the sign of stock returns. Consequently, to investigate whether momentum exits after controlling for overreaction, the authors carefully compare trading strategies based on overreaction with price momentum strategies using adjusted returns and double sorts on past returns and levels of overreaction.
The article makes three main findings. Firstly, the authors discover the empirical evidence of momentum in the Vietnamese equity market. Secondly, the measure of overreaction could be a predictor of Vietnamese stock returns. Stocks that have experienced a stronger upward overreaction provide a higher average return. Finally, returns on trading strategies based on overreaction are robust after adjusting for momentum, while returns on momentum portfolios become insignificant after adjusting for overreaction. By double-sorting, the authors document that holding past returns constant, the average returns of portfolios rise monotonically with their measure of overreaction. Hence, the momentum profit in Vietnam arises from investors’ overreaction.
The paper extends previous research on the behavioral explanation of momentum in emerging stock markets, which has not been fully exploited in the literature.

Black-Scholes Approximation of Warrant Prices: Slight Return in a Low Interest Rate EnvironmentJournal articlePhilippe Bertrand, Annals of Operations Research, Forthcoming

The objective of this paper is to emphasize the differences between a call and a warrant as well as the different valuation methods of warrants which have been introduced in the financial literature. For the sake of simplicity and applicability, we only consider a debt-free equity-financed firm. More recently a formal distinction between structural and reduced form pricing models has been introduced. This distinction is important whether one wishes to price a new warrant issue or outstanding warrants. If we are interested in pricing a new issue of warrants, e.g. in the context of a management incentive package, one has to rely on a structural model. However most of practitioners use the simple Black-Scholes formula. In this context, we analyze the accuracy of the approximation of the “true” price of a warrant by the Black-Scholes formula. We show that in the current low interest rate environment, the quality of the approximation deteriorates and the sensitivity of this approximation to the volatility estimate increases.

The role of investor behavior in emerging stock markets: Evidence from VietnamJournal articleThi Nha Truc Phan, Philippe Bertrand, Hong Hai Phan and Xuan Vinh Vo, The Quarterly Review of Economics and Finance, Forthcoming

Exloring the role of different types of investors on stock market is crticial since different types of investors react and behave differently when making investment decision. The role of investor behavior is a very important issue in an immature stock market like Vietnam stock market because the market is characterized by a large number of individual investors and low reporting standard. Institutional and foreign investors however play an influential role due to their large exposure and strong investment expertise. Clearly, examining the role of investor behavior and its impact on the stock market in Vietnam is an important topic in finance. A significant body of empirical research has shown that investor behavior is an essential factor to explain stock price that the classical financial theory cannot explain. This research examines the role of investor behavior in stock market by examining the relationship between investor behavior and stock return using the Vietnamese stock exchange data. We create a sentiment index using the principal components analysis (PCA). Consistent with the sentiment and stock return literature, the research shows a negative contemporaneous relationship between investor sentiment and market return.

The size effect and default risk: Evidence from the Vietnamese stock marketJournal articleLe Quy Duong and Philippe Bertrand, Review of Financial Economics, Volume n/a, Issue n/a, Forthcoming

The literature is inconclusive on the source of the size effect. Our paper contributes to extant studies by investigating the relationship between the size premium and default risk in Vietnam, an important frontier emerging market. The debt-to-equity ratio and distance-to-default of Merton (1974, The Journal of Finance, 29, 449) are used as distress-risk proxies. Based on more than 300 listed stocks over 2009–2019, we discover that the small portfolio delivers the highest average return. The excess return on the small portfolio is concentrated in firms with high distress risk. Furthermore, neutral size factors are built to dissect returns on the Fama-French size factor from the default-risk premium. Empirical results prove that the explanatory power of the size factor is negatively affected when the default-risk neutrality is applied. Given this backdrop, the size premium in Vietnam is likely to be compensation for distress risk, consistent with a risk-based point of view.