Measure preserving derivatives and the pricing kernel puzzle

Recent empirical studies have found evidence of nonmonotonicity in the pricing kernels for a variety of market indices. This phenomenon is known as the pricing kernel puzzle. The payoff distribution pricing model of Dybvig predicts that the payoff distribution of a direct investment of $1 in a market index may be replicated by investing less than $1 in some derivative written on that market index whenever the associated pricing kernel is nondecreasing. Using the Hardy–Littlewood rearrangement inequality, we obtain an explicit solution for the cheapest replicating derivative, which we refer to as the optimal measure preserving derivative. The optimal measure preserving derivative is the permutation appearing in Ryff’s decomposition of the pricing kernel with respect to the market payoff measure. We compute optimal measure preserving derivatives corresponding to the estimated physical and risk neutral distributions in the paper by Jackwerth (2000) that first brought attention to the pricing kernel puzzle.     

On pricing and hedging options in regime-switching models with feedback effect

We study the pricing and hedging of European-style derivative securities in a Markov, regime-switching, model with a feedback effect depending on the economic condition. We adopt a pricing kernel which prices both financial and economic risks explicitly in a dynamically incomplete market and we provide an equilibrium analysis. A martingale representation for a European-style index option's price is established based on the price kernel. The martingale representation is then used to construct the local risk-minimizing strategy explicitly and to characterize the corresponding pricing measure.     

Rationalizing investors’ choices

Assuming that agents’ preferences satisfy first-order stochastic dominance, we show how the Expected Utility paradigm can rationalize all optimal investment choices: the optimal investment strategy in any behavioral law-invariant (state-independent) setting corresponds to the optimum for an expected utility maximizer with an explicitly derived concave non-decreasing utility function. This result enables us to infer the utility and risk aversion of agents from their investment choice in a non-parametric way. We relate the property of decreasing absolute risk aversion (DARA) to distributional properties of the terminal wealth and of the financial market. Specifically, we show that DARA is equivalent to a demand for a terminal wealth that has more spread than the opposite of the log pricing kernel at the investment horizon.     

Optimal consumption and investment under partial information

We consider a stock market model where prices satisfy a stochastic differential equation with a stochastic drift process. The investor’s objective is to maximize the expected utility of consumption and terminal wealth under partial information; the latter meaning that investment decisions are based on the knowledge of the stock prices only. We derive explicit representations of optimal consumption and trading strategies using Malliavin calculus. The results apply to both classical models for the drift process, a mean reverting Ornstein-Uhlenbeck process and a continuous time Markov chain. The model can be transformed to a complete market model with full information. This allows to use results on optimization under convex constraints which are used in the numerical part for the implementation of more stable strategies. Supported by the Austrian Science Fund FWF, project P17947-N12. We thank two anonymous referees for their comments which led to a considerable improvement of the paper.     

Optimal rebalance rules for the constant proportion portfolio insurance strategy – Evidence from China

The constant proportion portfolio insurance (CPPI) strategy is one of the most popular asset allocation strategies employed by guaranteed-return financial products investors. Rebalance disciplines play an important role in determining the CPPI performance in practice. This paper examines whether the selection of rebalance rules affects CPPI strategy performance in the context of Chinese equity markets and, if so, in what pattern, and whether an optimal parameter of rebalance exists. We find that, (1) the three alternative rebalance disciplines – time discipline, market move discipline and lag discipline – are indifferent in affecting the performance of CPPI strategy; (2) in terms of optimal parameters of each rebalance rule, the optimal rebalancing period for the time discipline is 3 trading days, the optimal trading threshold of the market move discipline 4%, and the optimal lag factor of the lag discipline 6%. These optimal parameters are not influenced by the length of investment.     

The stock–bond comovements and cross-market trading

We propose an asset pricing model with heterogeneous agents allocating capital to the stock and bond markets to optimize their portfolios, utilizing the dynamic interaction between the two markets. While some agents focus on the stock market and have more expertise in it, the others specialize in the bond market. Based on their comparative advantages in a particular market, heterogeneous agents constantly revise their investment portfolios by taking into account the time-varying stock–bond return comovements and the changing market conditions. Agents׳ collective investment behavior shapes the stock–bond interlinkage, which feedbacks on their subsequent capital allocations. Using monthly US stock and bond data from January 1990 to June 2014, we estimate the vector autoregression model with threshold and Markov switching mechanisms. We find evidence in support of flight-to-quality and show that it is mainly driven by the technical traders who actively sell stocks and buy bonds during periods of high market uncertainty.     

Optimal investment and reinsurance policies for an insurer with ambiguity aversion

In this paper, we study the optimal investment and reinsurance problem for an insurer based on the variance premium principle, in which three cases are considered. First, we assume that the financial market does not exist. The insurer only holds an insurance business, and the optimal reinsurance problem is studied. Subsequently, we assume that there exists a financial market with an accurately modeled risky asset. The optimal investment and reinsurance problem is investigated under these conditions. Finally, we consider the general case in which the insurer is concerned about the model ambiguity of both the insurance market and the financial market. In all three cases, the value function is set to maximize the expected utility of terminal wealth. By employing the dynamic programming principle, we derive the Hamilton–Jacobi–Bellman (HJB) equations, which are satisfied by the value functions and obtain closed-form solutions for optimal reinsurance and investment policies and the value functions in all three cases. Most interestingly, we elucidate how investment improves the insurer’s utility and find that the existence of ambiguity can significantly affect the optimal policies and value functions. We also compare the ambiguities in the two markets and find that ambiguity in the insurance market has much more significant impact on the value function than the ambiguity in the financial market. It implies that it is more valuable for insurer to precisely evaluate the insurance risk. We also provide some numerical examples and economic explanations to illustrate our results.     

Utility indifference valuation for jump risky assets

We discuss utility maximization problems with exponential preferences in an incomplete market where the risky asset dynamics is described by a pure jump process driven by two independent Poisson processes. This includes results on portfolio optimization under an additional European claim. Value processes of the optimal investment problems, optimal hedging strategies and the indifference price are represented in terms of solutions to backward stochastic equations driven by the Poisson martingales. Via a duality result, the solution to the dual problems is derived. In particular, an explicit expression for the density of the minimal martingale measure is provided. The Markovian case is also discussed. This includes either asset dynamics dependent on a pure jump stochastic factor or claims written on a correlated non tradable asset.     

How to Identify and Forecast Bull and Bear Markets?

Because the state of the equity market is latent, several methods have been proposed to identify past and current states of the market and forecast future ones. These methods encompass semi‐parametric rule‐based methods and parametric Markov switching models. We compare the mean‐variance utilities that result when a risk‐averse agent uses the predictions of the different methods in an investment decision. Our application of this framework to the S&P 500 shows that rule‐based methods are preferable for (in‐sample) identification of the state of the market, but Markov switching models for (out‐of‐sample) forecasting. In‐sample, only the mean return of the market index matters, which rule‐based methods exactly capture. Because Markov switching models use both the mean and the variance to infer the state, they produce superior forecasts and lead to significantly better out‐of‐sample performance than rule‐based methods. We conclude that the variance is a crucial ingredient for forecasting the market state. Copyright © 2016 John Wiley & Sons, Ltd.     

Dividends and leverage: How to optimally exploit a non-renewable investment

In this paper we model the situation where a non-renewable investment is given, for instance a resource reservoir, and show how to optimally trade-off between dividends and leverage, in order to maximize a performance indicator for shareholders, up to the bankruptcy time. We then study the way market risk (the volatility of the market price of the resource) impacts the optimal policies and the default risk of the company. The moments when the policies are rebalanced are analyzed and we give a measure of the agency costs which appear between the shareholders and the debt-holders.     

Dynamic portfolio choice under ambiguity and regime switching mean returns

I examine a continuous-time intertemporal consumption and portfolio choice problem under ambiguity, where expected returns of a risky asset follow a hidden Markov chain. Investors with Chen and Epstein's (2002) recursive multiple priors utility possess a set of priors for unobservable investment opportunities. The optimal consumption and portfolio policies are explicitly characterized in terms of the Malliavin derivatives and stochastic integrals. When the model is calibrated to U.S. stock market data, I find that continuous Bayesian revisions under incomplete information generate ambiguity-driven hedging demands that mitigate intertemporal hedging demands. In addition, ambiguity aversion magnifies the importance of hedging demands in the optimal portfolio policies. Out-of-sample experiments demonstrate the economic importance of accounting for ambiguity.     

The R&D Investment–Uncertainty Relationship: Do Strategic Rivalry and Firm Size Matter?

This paper uses a real options perspective to augment a standard research and development (R&D) investment model and implement a firm‐level empirical analysis to assess the practical significance of market uncertainty and its interactions with strategic rivalry and firm size. We use a measure of firm‐relevant market uncertainty along with panel data and find that firms invest less in current R&D as uncertainty about market returns increases. The effect of firm‐specific uncertainty on R&D investment is smaller in markets where strategic rivalry is likely to be more intense. Furthermore, holding access to financing constant, the effect of uncertainty on R&D investment is attenuated for large firms. Copyright © 2012 John Wiley & Sons, Ltd.     

Optimal time-consistent reinsurance and investment strategies for a jump–diffusion financial market without cash

This paper considers an optimal reinsurance and investment strategies for an insurer under mean–variance criterion within a game theoretic framework. Specially, it is assumed that the surplus process is governed by a Cramér–Lundberg model, and apart from purchasing reinsurance, the insurer is allowed to invest in a financial market with multiple assets that all can be risky, whose price processes are modeled by the jump–diffusion process. Due to the market without cash, the method of separating the variables is not viable any more. We turn to an alternative approach to solve the extended Hamilton–Jacobi–Bellman equation, and closed-form expressions of the optimal strategies and value function are not only derived but also proved to be uniqueness. Moreover, some special cases of our model are provided and several numerical analyses for our results are presented as well. Under this criterion, different from existing literature, we find that (i) the value function is not linear but quadratic with respect to the current wealth; (ii) the optimal reinsurance and investment strategies depend on the wealth process; (iii) the parameters of risky assets(insurance market) have impacts on the optimal reinsurance(investment) policy; (iv) the safety loading of the insurer affects the optimal strategies.     

Optimal portfolio choice in the presence of domestic systemic risk: empirical evidence from stock markets

In this paper, we empirically investigate the consequences of domestic systemic risk for stock market investors. To tackle this issue, we consider two different investment strategies. One strategy is to be “crisis-conscious”, i.e., taking the possibility of systemic events into account, and the other one is to be “crisis-ignorant” and thus disregarding systemic risk. We compare the optimal portfolio choices and investment results of these strategies in an historical simulation, using almost three decades of historical stock price data. Our main findings are as follows: the crisis-conscious investor tends to choose less extreme portfolio weights for individual stocks than the ignorant investor. The overall risky investment is, however, of similar size for both. By ignoring the possibility of systemic events, the crisis-ignorant strategy performs significantly worse from the viewpoint of expected return as well as expected utility.     

Age-dependent investing: Optimal funding and investment strategies in defined contribution pension plans when members are rational life cycle financial planners

A defined contribution pension plan allows consumption to be redistributed from the plan member's working life to retirement in a manner that is consistent with the member's personal preferences. The plan's optimal funding and investment strategies therefore depend on the desired profile of consumption over the lifetime of the member. We investigate these strategies under the assumption that the member is a rational life cycle financial planner and has an Epstein–Zin utility function, which allows a separation between risk aversion and the elasticity of intertemporal substitution. We also take into account the member's human capital during the accumulation phase of the plan and we allow the annuitisation decision to be endogenously determined during the decumulation phase.We show that the optimal funding strategy involves a contribution rate that is not constant over the life of the plan but is age-dependent and reflects the trade-off between the desire for current versus future consumption, the desire for stable consumption over time, the member's attitude to risk, and changes in the level of human capital over the life cycle. We also show that the optimal investment strategy during the accumulation phase of the plan is ‘stochastic lifestyling’, with an initial high weight in equity-type investments and a gradual switch into bond-type investments as the retirement date approaches in a way that depends on the realised outcomes for the stochastic processes driving the state variables. The optimal investment strategy during the decumulation phase of the plan is to exchange the bonds held at retirement for life annuities and then to gradually sell the remaining equities and buy more annuities, i.e., a strategy known as ‘phased annuitisation’.     

How much should an investor trust the startup entrepreneur? A network model

Trust is an important determinant of start-up financing. In a simple agent-based model it is determined what the best trusting strategy is for a collective of investors and whether it is rational for an individual investor to deviate from this collective optimum. Trust depends on a measure of social distance and is the precondition for investment. Trust increases and decreases based on whether an investor is satisfied with the interest payments received from an entrepreneur. If an investor is dissatisfied, he terminates the relation with the entrepreneur. For assessing the quality of their own investments, investors communicate with other investors in a network-like structure. I find that, as a collective, it is best for investors to compare their returns critically in order to identify unproductive entrepreneurs, but to be tolerant regarding existing links to entrepreneurs in order not to terminate profitable relations because of minor productivity drops. However, it is optimal for an individual investor to deviate from this strategy and to be less easily disappointed, but to decrease trust in larger steps. In a sense, an individual investor can free ride on the others’ critical assessment. If all investors behave according to this latter strategy, too many unproductive firms remain in the market and the average investor’s return is lower than in the collective optimum.     

Irreversible investment and R&D spillovers in a dynamic duopoly

Investments in new production processes usually involve a significant amount of R&D, generating spillovers that lowers the second comer's investment cost. We show that these spillovers substantially affect the equilibrium of the dynamic game. Even for low spillover values, the leader delays her investment until the stochastic fundamental has gone past the level such that the follower's optimal strategy is to invest as soon as he attains the spillover. This bears several interesting implications. First, because the follower invests as he benefits from the spillover, in equilibrium the average time delay between the two investments is short, as it should be expected. Second, in case of a major innovation, an optimal public policy requires an intervention in favor of the investment activity; an increase in uncertainty - delaying the equilibrium - calls for higher subsidization rates. Third, numerical simulations show that the spillover reduces the difference between the leader's and the follower's maximum value functions. Accordingly, our model can help generate realistic market betas.     

Eastern European Economic Integration and Foreign Direct Investment

Economic transition in Eastern Europe should generate market growth. In addition, current discussions on economic integration and the development of a free-trade area in Eastern Europe will improve market accessibility. These two forces will significantly affect the strategies by which external firms will choose to supply markets in Eastern Europe. This paper examines the ways in which supply strategy is likely to change. We show that both market growth and improved market accessibility will lead the external firms to switch from exporting to foreign direct investment. However, market growth is likely to lead to dispersed investment in the growing economies, whereas increased market accessibility, by establishing an integrated regional bloc in Eastern Europe, is more likely to lead to concentrated investment plus infra-regional exports to the remainder of the regional bloc. The switch from exporting to local production through foreign direct investment will favor consumers through lowered prices but will harm national producers by depressing profit margins.     

The choice between greenfield investment and cross-border acquisition: A real option approach

The purpose of this study is to formalize the choice of market entry strategy for an individual multinational enterprise (MNE) from a dynamic perspective. It is argued that incorporating a suitable treatment of irreversibility, uncertainty and flexibility related to a MNEs investment decision gives further insights to the choice of cross-border acquisitions to greenfield investment as the preferred entry mode. In most cases, the initial entry strategy serves as a platform allowing the firm to make subsequent investments to exploit host-country advantages and capabilities. We allow for this by taking a two-step expansion strategy explicitly into account. The evolutionary process of the value of the foreign direct investment includes two stochastic elements as well as the timing that triggers the transition from export to foreign direct investment. The results suggest that uncertainty and future investment opportunities play an important role when it comes to transit from export to the first phase of the foreign direct investment commitment as well as have an impact on the choice of entry strategy.     

Effectiveness of Augmented Dollar-Cost Averaging

Dollar-Cost Averaging investment strategy has been widely criticized by academics for decades. This article proposes an Augmented Dollar-Cost Averaging (ADCA) strategy that conditions investment strategy to the prevailing market environment. The ADCA investment strategy is more aggressive if the economy is expanding and more conservative if the economy is contracting. Changes in market volatility, unemployment rate and capacity utilization were used to determine whether the economy was expanding or contracting. Using the Sharpe ratio, coupled with first-order and second-order stochastic dominance criteria, this study shows the risk-reducing benefits of ADCA in the U.S. stock market between 1967 and 2018.