Making inefficient market indices efficient

This paper uses the concept of Marginal Conditional Stochastic Dominance and a generalization of the 50% Portfolio Rule to develop a tractable and parsimonious methodology for constructing a second degree Stochastic Dominance (SSD) efficient portfolio from a given, inefficient index. Because the SSD approach considers the entire probability distributions of asset returns, the resulting portfolios are efficient with respect to all risk-averse, utility-maximizing investors regardless of the form of their utility functions or the distributions of asset returns.     

Optimal co-investment in supply chain infrastructure

This paper considers co-investment in a supply chain infrastructure using an inter-temporal model. We assume that firms’ capital is essentially the supply chain’s infrastructure. As a result, firms’ policies consist in selecting an optimal level of employment as well as the level of co-investment in the supply chain infrastructure. Several applications and examples are presented and open-loop, as well as feedback solutions are found for non-cooperating firms, long- and short-run investment cooperation and non-simultaneous moves (Stackelberg) firms. In particular, we show that a solution based on Nash and Stackelberg differential games provides the same level of capital investment. Thus, selecting the leader and the follower in a co-investment program does not matter. We show that in general, co-investments by firms vary both over time and across firms, and thereby render difficult the implementation of co-investment programs for future capital development. To overcome this problem, we derive conditions for firms’ investment share to remain unchanged over time and thus be easily planned.     

Splitting up value: A critical review of residual income theories

This paper deals with the notion of residual income, which may be defined as the surplus profit that residues after a capital charge (opportunity cost) has been covered. While the origins of the notion trace back to the 19th century, in-depth theoretical investigations and widespread real-life applications are relatively recent and concern an interdisciplinary field connecting management accounting, corporate finance and financial mathematics (Peasnell, 1981, 1982; Peccati, 1987, 1989, 1991; Stewart, 1991; Ohlson, 1995; Arnold and Davies, 2000; Young and O’Byrne, 2001; Martin, Petty and Rich, 2003). This paper presents both a historical outline of its birth and development and an overview of the main recent contributions regarding capital budgeting decisions, production and sales decisions, implementation of optimal portfolios, forecasts of asset prices and calculation of intrinsic values. A most recent theory, the systemic-value-added approach (also named lost-capital paradigm), provides a different definition of residual income, consistent with arbitrage theory. Enfolded in Keynes’s (1936) notion of user cost and forerun by Pressacco and Stucchi (1997), the theory has been formally introduced in Magni (2000a,b,c; 2001a,b; 2003), where its properties are thoroughly investigated as well as its relations with the standard theory; two different lost-capital metrics have been considered, for value-based management purposes, by Drukarczyk and Schueler (2000) and Young and O’Byrne (2001). This work illustrates the main properties of the two theories and their relations, and provides a minimal guide to construction of performance metrics in the two approaches.     

Computational methods for incentive option valuation

Employing stochastic programming, we provide a general framework for option pricing based on marginal bid/ask price valuation. It is applied to numerical analysis of options with European and American style exercise using a double binary tree. Incentive options are valued considering hedging restrictions and other market frictions, such as transaction and short position costs, and different borrowing and lending rates. The framework also includes correlated labor income. The possibility of partial sales is analyzed using ask price functions. Without friction costs and labor income, our model is the discrete-time equivalent of Ingersoll (J Bus 79:453–487, 2006). When labor income and/or market frictions are present, or a fraction of options is sold, the option values are materially different compared to Ingersoll (J Bus 79:453–487, 2006).

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Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.      

Theoretical and empirical estimates of mean–variance portfolio sensitivity

This paper studies properties of an estimator of mean–variance portfolio weights in a market model with multiple risky assets and a riskless asset. Theoretical formulas for the mean square error are derived in the case when asset excess returns are multivariate normally distributed and serially independent. The sensitivity of the portfolio estimator to errors arising from the estimation of the covariance matrix and the mean vector is quantified. It turns out that the relative contribution of the covariance matrix error depends mainly on the Sharpe ratio of the market portfolio and the sampling frequency of historical data. Theoretical studies are complemented by an investigation of the distribution of portfolio estimator for empirical datasets. An appropriately crafted bootstrapping method is employed to compute the empirical mean square error. Empirical and theoretical estimates are in good agreement, with the empirical values being, in general, higher.     

Optimal exercise of jointly held real options: A Nash bargaining approach with value diversion

This paper provides a two-stage decision framework in which two or more parties exercise a jointly held real option. We show that a single party’s timing decision is always socially efficient if it precedes bargaining on the terms of sharing. However, if the sharing rule is agreed before the exercise timing decision is made, then socially optimal timing is attained only if there is a cash payment element in the division of surplus. If the party that chooses the exercise timing can divert value from the project, then the first-best outcome may not be possible at all and the second-best outcome may be implemented using a contract that is generally not optimal in the former cases. Our framework contributes to the understanding of a range of empirical regularities in corporate and entrepreneurial finance.     

The Newsboy problem when customer demand is a compound renewal process

The Newsboy (Newsvendor) problem is probably the simplest of all stochastic inventory problems, involving a one-time purchase decision and a stochastic sales outcome. As an investment, it can be interpreted as the simplest stochastic version of the point-in, point-out investment problem of Jevons [Jevons, W.S., Theory of Political Economy, Macmillan, London 1871].     

Should you stop investing in a sinking fund when it is sinking?

Many people invest regularly in sinking funds that track stock market indices. When stock markets themselves sink significantly, as in the current credit crunch, investors face a decision as to whether they should continue paying into a falling fund, or switch payment to a risk-free deposit account until the market recovers. Most financial advice is to keep investing on the grounds that as the unit price falls more units can be purchased and that this is ultimately beneficial (dollar-cost averaging, DCA) However, most academic studies show that DCA is sub-optimal, at least to a lump sum strategy. In this paper we consider a specific, tax-free fund – the Individual Savings Account (ISA). We demonstrate, both analytically and numerically, that in a situation of perfect information a stop and restart policy can beat DCA. From these results we test some heuristics that could be used by an everyday investor under real-world conditions of uncertainty and volatility.     

Optimal excess-of-loss reinsurance and investment problem for an insurer with jump–diffusion risk process under the Heston model

In this paper, we study the optimal excess-of-loss reinsurance and investment problem for an insurer with jump–diffusion risk model. The insurer is allowed to purchase reinsurance and invest in one risk-free asset and one risky asset whose price process satisfies the Heston model. The objective of the insurer is to maximize the expected exponential utility of terminal wealth. By applying stochastic optimal control approach, we obtain the optimal strategy and value function explicitly. In addition, a verification theorem is provided and the properties of the optimal strategy are discussed. Finally, we present a numerical example to illustrate the effects of model parameters on the optimal investment–reinsurance strategy and the optimal value function.