On the optimality of path-dependent structured funds: The cost of standardizationJournal articlePhilippe Bertrand et 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 et 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 et 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 et Jean-Luc Prigent, Bankers, Market & Investors, Issue 150, 2018
Risk-based strategies: the social responsibility of investment universes does matterJournal articlePhilippe Bertrand et 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 et Jean-Luc Prigent, Economic Modelling, Volume 52, 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.

On Path-Dependent Structured Funds: Complexity Does Not Always Pay (Asian versus Average Performance Funds)Journal articlePhilippe Bertrand et Jean-Luc Prigent, Finance, 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.

How performance of risk-based strategies is modified by socially responsible investment universe?Journal articlePhilippe Bertrand et Vincent Lapointe, International Review of Financial Analysis, Volume 38, Issue C, pp. 175-190, 2015

Risk-based allocation strategies, also known as Smart Beta allocations, define the weights of assets in portfolios as functions of the individual and common asset risk. In this paper we focus on the Minimum Variance (MV), Maximum Diversification (MD), Equal Risk Contribution (ERC) and Equal-Weight (EW) risk-based allocation strategies. The popularity of risk-based strategy is commonly justified by their good record of out-performing the cap-weighted (CW) allocation strategy. Because of the low-volatility profile of risk-based allocations this is especially true when crises occur. From March 15, 2002 to May 1, 2012 we investigate how using a socially responsible investment universe impacts performance of risk-based allocation strategies. We use different measures of performance, included risk-adjusted one (multi-factor models), and we propose to disentangle the effect of using a SRI universe from the effect of using risk-based allocations. SRI universe only contains firms that have good environmental, social and governance performance. This kind of filtering is increasingly popular among institutional investors. On the estimation period, using European stocks, we find that the use of the SRI universe has a positive contribution to risk-adjusted performance of risk-based allocations. However this contribution is not uniform among all the risk-based allocation strategies and, can represent only a small part of the total alpha that is observed.

French Retail Financial Structured Products: A Typology and Assessment of Their Fair PricingJournal articlePhilippe Bertrand et Jean-Luc Prigent, Bankers, Markets & Investors, Issue 135, pp. 4-18, 2015

This paper deals with the pricing of financial structured products. We examine French retail structured products, “OPCVM. Formule”, from a sample including about 650 funds. First, we detail the main characteristics of this market and propose a simplified typology of all these products. Second, we analyze some of the most common contracts with portfolio insurance, which correspond to specific portfolio profiles based on performances of given underlying assets, usually the major French or European stock indices. Using the standard Black and Scholes pricing with appropriate financial parameters, we compute the initial values of such products. Our numerical results on the fair pricing of French financial structured products agree with previous studies in other countries, for example those for the German and Swiss markets. The magnitude of mispricing lies between 2 % and 7 %.

Raising Companies’ Profile with Corporate Social Performance: Variation in Investor Recognition and Liquidity Linked to Vigeo CSP Rating Disclosure.Journal articlePhilippe Bertrand, Alexis Guyot et Vincent Lapointe, Bankers, Markets & Investors, Issue 130, pp. 41-54, 2014

This paper examines whether the initiation of Vigeo Corporate Social Performance (CSP) rating impacts company profiles. Using a sample of European listed firms, we confirm that there is a positive and significant relationship between CSP rating and a firm’s liquidity and investor base. Consistent with the neglected stock effect, this relationship is sensitive to firm size. Our results have important implications for practitioners. Firstly, investment in Corporate Social Responsibility (CSR) could represent an alternative method of improving a company’s stock market quality alongside liquidity provider contracting or market listing transfer. Secondly, when a firm’s board investigates the opportunity to invest in CSR, it should consider the benefits of lowering the company’s cost of capital through the aforementioned effects. Finally, from an asset manager’s perspective, any change in CSP should be taken into account, as it can affect company valuation and therefore portfolio performance.

The size effect and default risk: Evidence from the Vietnamese stock marketJournal articleLe Quy Duong et 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.