Are structured products ‘fairly’ priced? An analysis of the German market for equity-linked instruments

Based on a unique data set, this paper examines the pricing of equity-linked structured products in the German market. The daily closing prices of a large variety of structured products are compared to theoretical values derived from the prices of options traded on the Eurex (European Exchange). For the majority of products, the study reveals large implicit premiums charged by the issuing banks in the primary market. A set of driving factors behind the issuers’ pricing policies is identified, for example, underlying and type of implicit derivative(s). For the secondary market, the product life cycle is found to be an important pricing parameter.     

Portfolio choices and VaR constraint with a defaultable asset

We consider a Constant Elasticity of Variance (CEV) model for the asset price of a defaultable asset showing the so-called leverage effect (high volatility when the asset price is low). We show that a VaR constraint re-evaluated over time induces an agent more risk averse than a logarithmic utility to take more risk than in the unconstrained setting.     

Optimal portfolio positioning within generalized Johnson distributions

Many empirical studies have shown that financial asset returns do not always exhibit Gaussian distributions, for example hedge fund returns. The introduction of the family of Johnson distributions allows a better fit to empirical financial data. Additionally, this class can be extended to a quite general family of distributions by considering all possible regular transformations of the standard Gaussian distribution. In this framework, we consider the portfolio optimal positioning problem, which has been first addressed by Brennan and Solanki [J. Financial Quant. Anal., 1981, 16, 279–300], Leland [J. Finance, 1980, 35, 581–594] and further developed by Carr and Madan [Quant. Finance, 2001, 1, 9–37] and Prigent [Generalized option based portfolio insurance. Working Paper, THEMA, University of Cergy-Pontoise, 2006]. As a by-product, we introduce the notion of Johnson stochastic processes. We determine and analyse the optimal portfolio for log return having Johnson distributions. The solution is characterized for arbitrary utility functions and illustrated in particular for a CRRA utility. Our findings show how the profiles of financial structured products must be selected when taking account of non Gaussian log-returns.     

Optimal payoffs under state-dependent preferences

Most decision theories, including expected utility theory, rank-dependent utility theory and cumulative prospect theory, assume that investors are only interested in the distribution of returns and not in the states of the economy in which income is received. Optimal payoffs have their lowest outcomes when the economy is in a downturn, and this feature is often at odds with the needs of many investors. We introduce a framework for portfolio selection within which state-dependent preferences can be accommodated. Specifically, we assume that investors care about the distribution of final wealth and its interaction with some benchmark. In this context, we are able to characterize optimal payoffs in explicit form. Furthermore, we extend the classical expected utility optimization problem of Merton to the state-dependent situation. Some applications in security design are discussed in detail and we also solve some stochastic extensions of the target probability optimization problem.     

Optimal insurance contract under a value-at-risk constraint

This study develops an optimal insurance contract endogenously under a value-at-risk (VaR) constraint. Although Wang et al. [2005] had examined this problem, their assumption implied that the insured is risk neutral. Consequently, this study extends Wang et al. [2005] and further considers a more realistic situation where the insured is risk averse. The study derives the optimal insurance contract as a single deductible insurance when the VaR constraint is redundant or as a double deductible insurance when the VaR constraint is binding. Finally, this study discusses the optimal coverage level from common forms of insurances, including deductible insurance, upper-limit insurance, and proportional coinsurance. JEL Classification G22     

Optimal Time to Sell in Real Estate Portfolio Management

This paper examines the properties of optimal times to sell a diversified real estate portfolio. The portfolio value is supposed to be the sum of the discounted free cash flows and the discounted terminal value (the discounted selling price). According to Baroni et al. (Journal of Property Investment and Finance 25(6):603–625, 2007b), we assume that the terminal value corresponds to the real estate index. The optimization problem corresponds to the maximization of a quasi-linear utility function. We consider three cases. The first one assumes that the investor knows the probability distribution of the real estate index. However, at the initial time, he has to choose one deterministic optimal time to sell. The second one considers an investor who is perfectly informed about the market dynamics. Whatever the random event that generates the path, he knows the entire path from the beginning. Then, given the realization of the random variable, the path is deterministic for this investor. Therefore, at the initial time, he can determine the optimal time to sell for each path of the index. Finally, the last case is devoted to the analysis of the intertemporal optimization, based on the American option approach. We compute the optimal solution for each of these three cases and compare their properties. The comparison is also made with the buy-and-hold strategy.

Pricing,issuance volume,and design of innovative securities: The role of investor information

This study investigates the role of asymmetric information for the pricing, issuance volume, and design of innovative securities. By analyzing the information that structured product issuers provide to the investors of those products, we can identify specific sources of asymmetric information between the issuers and investors in this market. We show that issuers exploit this information friction to offer products to investors that appear more profitable for the issuer. In addition, we find that the friction induces issuers to design products with higher information asymmetry. Our results suggest that product issuers’ behavior increases information frictions in the financial system.     

Asset management with endogenous withdrawals under a drawdown constraint

Asset preservation is a major concern for foundations that are hostile to large wealth downfalls. Implications for optimal consumption and investment policies are explored in a dynamic setting where wealth is restrained from falling below a fraction of its all-time high. Risky investment regulates wealth growth and mitigates the ratchet effect of the constraint, and may decrease as wealth approaches its maximum. The correspondence found between habit formation over consumption and wealth ratcheting provides a rational explanation for the proliferation of capital protection oriented funds.     

Optimal execution strategies in limit order books with general shape functions

We consider optimal execution strategies for block market orders placed in a limit order book (LOB). We build on the resilience model proposed by Obizhaeva and Wang (2005 Obizhaeva, A and Wang, J. 2005. Optimal trading strategy and supply/demand dynamics, Preprint Available online at: http://www.rhsmith.umd.edu/faculty/obizhaeva/OW060408.pdf (accessed 16 February 2009)[Crossref] , [Google Scholar]) but allow for a general shape of the LOB defined via a given density function. Thus, we can allow for empirically observed LOB shapes and obtain a nonlinear price impact of market orders. We distinguish two possibilities for modelling the resilience of the LOB after a large market order: the exponential recovery of the number of limit orders, i.e. of the volume of the LOB, or the exponential recovery of the bid–ask spread. We consider both of these resilience modes and, in each case, derive explicit optimal execution strategies in discrete time. Applying our results to a block-shaped LOB, we obtain a new closed-form representation for the optimal strategy of a risk-neutral investor, which explicitly solves the recursive scheme given in Obizhaeva and Wang (2005 Obizhaeva, A and Wang, J. 2005. Optimal trading strategy and supply/demand dynamics, Preprint Available online at: http://www.rhsmith.umd.edu/faculty/obizhaeva/OW060408.pdf (accessed 16 February 2009)[Crossref] , [Google Scholar]). We also provide some evidence for the robustness of optimal strategies with respect to the choice of the shape function and the resilience-type.     

Portfolio optimisation with jumps: Illustration with a pension accumulation scheme

In this paper, we address portfolio optimisation when stock prices follow general Lévy processes in the context of a pension accumulation scheme. The optimal portfolio weights are obtained in quasi-closed form and the optimal consumption in closed form. To solve the optimisation problem, we show how to switch back and forth between the stochastic differential and standard exponentials of the Lévy processes. We apply this procedure to both the Variance Gamma process and a Lévy process whose arrival rate of jumps exponentially decreases with size. We show through a numerical example that when jumps, and therefore asymmetry and leptokurtosis, are suitably taken into account, then the optimal portfolio share of the risky asset is around half that obtained in the Gaussian framework.     

The dark side of financial innovation: A case study of the pricing of a retail financial product

The offering prices of 64 issues of a popular retail structured equity product were, on average, almost 8% greater than estimates of the products' fair market values obtained using option pricing methods. Under reasonable assumptions about the underlying stocks' expected returns, the mean expected return estimate on the structured products is slightly below zero. The products do not provide tax, liquidity, or other benefits, and it is difficult to rationalize their purchase by informed rational investors. Our findings are, however, consistent with the recent hypothesis that issuing firms might shroud some aspects of innovative securities or introduce complexity to exploit uninformed investors.     

Optimal Bond Portfolio for Investors with Long Time Horizons

We study the optimal bond portfolio for an investor with long time horizonusing Japanese interest rate data. A simple one-factor term structure modelis used for our numerical example. The optimal portfolio is computed using thetechnique of stochastic flows and Monte Carlo simulation. The hedgingportfolio is not negligible and the mean variance portfolio is very sensitiveto parameter values. The optimal portfolio is highly leveraged for a typicalparameter value. The investor holds a zero-coupon bond because of the lowerbound restriction on investor's wealth. The lower bound constraint may makethe optimal portfolio more realistic.     

Optimal portfolios with a positive lower bound on final wealth

We consider the determination of optimal portfolios under a lower bound on the final wealth. Possible applications range from capital guarantee strategies over life insurance investment where part of the benefit is a guaranteed return on capital to continuous-time mean-variance problems with a strictly positive lower bound. Our solution method consists of transforming the original problem into a portfolio problem without a positive lower bound but a transformed utility function and a modified initial wealth.     

Optimal portfolio allocation with higher moments

We model the risky asset as driven by a pure jump process, with non-trivial and tractable higher moments. We compute the optimal portfolio strategy of an investor with CRRA utility and study the sensitivity of the investment in the risky asset to the higher moments, as well as the resulting wealth loss from ignoring higher moments. We find that ignoring higher moments can lead to significant overinvestment in risky securities, especially when volatility is high.      

Optimal Number of Stock Holdings in Mutual Fund Portfolios Based on Market Performance

Among the decisions that most mutual fund portfolio managers make is the number of stocks to hold. We posit that there is an optimal number of stocks for each mutual fund, reflecting the trade‐off between diversification benefits versus transactions and monitoring costs. We find a significant quadratic relation between number of stock holdings and risk‐adjusted returns for U.S. equity mutual fund portfolios during 1992–2000. Moreover, we find that changes in the number of stocks held over time are more highly correlated with mutual fund flows than with funds' investment returns.     

Optimal investment of an insurer with regime-switching and risk constraint

We investigate an optimal investment problem of an insurance company in the presence of risk constraint and regime-switching using a game theoretic approach. A dynamic risk constraint is considered where we constrain the uncertainty aversion to the ‘true’ model for financial risk at a given level. We describe the surplus of an insurance company using a general jump process, namely, a Markov-modulated random measure. The insurance company invests the surplus in a risky financial asset whose dynamics are modeled by a regime-switching geometric Brownian motion. To incorporate model uncertainty, we consider a robust approach, where a family of probability measures is cosidered and the insurance company maximizes the expected utility of terminal wealth in the ‘worst-case’ probability scenario. The optimal investment problem is then formulated as a constrained two-player, zero-sum, stochastic differential game between the insurance company and the market. Different from the other works in the literature, our technique is to transform the problem into a deterministic differential game first, in order to obtain the optimal strategy of the game problem explicitly.     

Portfolio selection under the condition of value preservation

Besides risk and return, investors often are interested in choosing a portfolio such that the portfolio value is preserved. However, the traditional utility-maximizing approach generally fails to provide such a solution. As a different approach value preservation is formulated as an equilibrium problem. Following this approach it is shown that under reasonable assumptions a value preserving solution exists. The solution only depends on the set of feasable portfolio decisions. Contrary to this, the Bernoulli principle in addition requires a utility function that is independent from this set.     

Stock Market Mean Reversion and the Optimal Equity Allocation of a Long-Lived Investor

This paper solves numerically the intertemporalconsumption and portfolio choiceproblem of an infinitely-lived investor whofaces a time-varying equity premium.The solutions we obtain are very similarto the approximate analytical solutionsof Campbell and Viceira (1999), except atthe upper extreme of the state spacewhere both the numerical consumption andportfolio rules flatten out.We also consider a constrained version ofthe problem in which the investor facesborrowing and short-sales restrictions.These constraints bind when the equitypremium moves away from its mean in eitherdirection, and are particularly severe forrisk-tolerant investors. The constraints havesubstantial effects on optimalconsumption, but much more modest effects onoptimal portfolio choice in theregion of the state space where they are notbinding.     

Optimal life insurance with no-borrowing constraints: duality approach and example

We solve an optimal portfolio choice problem under a no-borrowing assumption. A duality approach is applied to study a family’s optimal consumption, optimal portfolio choice, and optimal life insurance purchase when the family receives labor income that may be terminated due to the wage earner’s premature death or retirement. We establish the existence of an optimal solution to the optimization problem theoretically by the duality approach and we provide an explicitly solved example with numerical illustration. Our results illustrate that the no-borrowing constraints do not always impact the family’s optimal decisions on consumption, portfolio choice, and life insurance. When the constraints are binding, there must exist a wealth depletion time (WDT) prior to the retirement date, and the constraints indeed reduce the optimal consumption and the life insurance purchase at the beginning of time. However, the optimal consumption under the constraints will become larger than that without the constraints at some time later than the WDT.