Mean-variance versus utility maximization revisited: The case of constant relative risk aversion

We examine if mean-variance (M-V) is a good proxy for portfolios based on the Constant Relative Risk Aversion (CRRA) utility function. M-V portfolios are considered good proxies for portfolios from several utility functions which is why they are routinely used in the portfolio theory literature as the benchmark. Our results clearly show this is not the case. Low risk CRRA portfolios are in many cases very different to M-V portfolios, especially with respect to downside risk. If a risk-free asset is available, in many cases, no M-V portfolio is an adequate proxy for CRRA portfolios. The implications of our findings are that: i) M-V portfolios are a poor proxy for investors with CRRA preferences, ii) CRRA portfolios are more suited to investors who care about downside risk than M-V portfolios, and iii) the efficacy of M-V to proxy for utility maximization should be examined more thoroughly.     

Pricing the US residential asset through the rent flow: A cross-sectional study

The paper explores how the standard consumption-CAPM fares in pricing housing returns and regional rental income streams in a cross-section of regions. In particular, we estimate the Euler equations associated with the gross housing returns inclusive of price appreciations and rents jointly for several metropolitan areas of the US. The representative agent has a Constant Relative Risk Aversion (CRRA) utility. The rent growth is allowed to depend on the business cycle. When biannual data from 1978 to 2007 is used, the parameter estimates are reasonable, and the model is not rejected. Large standard errors indicate uninformative estimates. The implied price rent ratio time series averages are similar to the data; however the model misses the boom-bust pattern in the prices. The model significantly understates the average and the variance of the price appreciations. Results are robust to allowing housing consumption directly in the utility function or using the Epstein–Zin–Weil utility.     

Welfare effects of information and rationality in portfolio decisions under parameter uncertainty

We analyse and quantify, in a financial market with parameter uncertainty and for a Constant Relative Risk Aversion investor, the utility effects of two different boundedly rational (i.e. sub-optimal) investment strategies (namely, myopic and unconditional strategies) and compare them with each other and with the utility effect of full information. We show that effects are mainly caused by full information and predictability, being the effect of learning marginal. We also investigate the saver's decision regarding whether to manage her/his portfolio personally (DIY investor) or hire, against the payment of a management fee, a professional investor and find that delegation is mainly motivated by the belief that professional advisors are, depending on investment horizon and risk aversion, either better informed (‘insiders’) or more capable of gathering and processing information, rather than possessing the ability to learn from financial data. In particular, for very short investment horizons, delegation is primarily, if not exclusively, motivated by the beliefs that professional investors are better informed.     

Portfolio optimization with a defaultable security

In this paper we derive a closed-form solution for a representative investor who optimally allocates her wealth among the following securities: a credit-risky asset, a default-free bank account, and a stock. Although the inclusion of a credit-related financial product in the portfolio selection is more realistic, no closed-form solutions to date are given in the literature when a recovery value is considered in the event of a default. While most authors have assumed some recovery scheme in their initial model set up, they do not address the portfolio problem with a recovery when a default actually occurs. Given the tractability of the recovery of market value, we solved the optimal portfolio problem for the representative investor whose utility function is a Constant Relative Risk Aversion utility function. We find that the investor will allocate larger fraction of wealth to the defaultable security as long as the default-event risk is priced. These results are very intuitive and reasonable since it indicates that if the default risk premium is not priced properly the investor purchases less defaultable securities.     

Why stocks may disappoint

We provide a formal treatment of both static and dynamic portfolio choice using the Disappointment Aversion preferences of Gul (1991. Econometrica 59(3), 667–686), which imply asymmetric aversion to gains versus losses. Our dynamic formulation nests the standard CRRA asset allocation problem as a special case. Using realistic data generating processes, we find reasonable equity portfolio allocations for disappointment averse investors with utility functions exhibiting low curvature. Moderate variation in parameters can robustly generate substantial cross-sectional variation in portfolio holdings, including optimal non-participation in the stock market.     

Concavity of utility,concavity of welfare,and redistribution of income

The marginal social value of income redistribution is understood to depend on both the concavity of individuals’ utility functions and the concavity of the social welfare function. In the pertinent literatures, notably on optimal income taxation and on normative inequality measurement, it seems to be accepted that the role of these two sources of concavity is symmetric with regard to the social concern about inequality in the distribution of income. Direct examination of the question, however, reveals that this is not the case. Concavity of utility has a simple, direct effect on the marginal social value of redistribution, as might be expected, whereas concavity of the social welfare function has a more subtle influence, one that in some cases may not be very significant. The implications of this difference are examined for some standard forms of utility and welfare functions, including particular versions that appear in the optimal income taxation literature.     

Takeover Immunity, Takeovers, and the Market for Nonexecutive Directors

We develop and test two competing hypotheses that relate the market for nonexecutive directors to the level of external monitoring mechanism of the firms they serve. The Reward for Discretion Hypothesis posits that directors are valued more when they display discretion concerning their choice of antitakeover provision (ATP) levels rather than follow a rule. Alternatively, the CEO Risk Aversion Hypothesis implies that CEOs seek directors with inclination for uniform and high ATP levels. We examine how changes in ATP levels and approval of value creating/destroying acquisitions affect the careers of nonexecutive directors. Our results, based on data from about 3,000 listed US companies during 1994-2003, support the Reward for Discretion Hypothesis.     

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.     

Gender-based and couple-based taxation

In this paper, I explore the optimal taxation of singles and couples in an economy with bargaining couples. The government is concerned with the redistribution of income from individuals with high utility to individuals with low utility, recognizing that some individuals live in couple households where resources are unevenly distributed. I analyze how redistributive linear income taxes, which depend on either gender or household composition (or both) impact the distribution of utility within and across households. An interesting implication arising from the interaction between the model elements is that even though between-group lump-sum transfers always favor women, when the bargaining power of men is high, women are subject to a higher tax rate; this in contrast to previous analyses of gender-based taxation. My quantitative analysis demonstrates that the welfare effects of gender-based taxation are sizable and even larger when taxes depend on the composition of the household.     

Optimal Income Taxation and the Ability Distribution: Implications for Migration Equilibria

As recently argued by Diamond (1998), one of the key factors explaining the progressivity of an optimal non-linear income tax is the distribution of productivity among workers. Migration is one source of changes in the productivity distribution. How changes in the populations ability distribution affect optimal income tax schedules has received little attention. Changing the distribution generally affects both the objective function and the government budget constraint. We first consider the comparative statics of the fraction of highly-skilled workers with maximin and maximax welfare functions (so that only the second effect is present) and a quasi-linear utility function. We also present some results for a utilitarian social welfare function.We then study the interaction between mobility and redistributive taxation. We consider mobility by either the skilled or unskilled population under majority voting where governments take the population as fixed. If individuals choose to relocate independently, having identical ability distributions is always a stable equilibrium when the unskilled are the mobile group. However, this is not always the case when the skilled are mobile. If groups of individuals can choose where to locate, having identical ability distributions across regions is only an equilibrium when the mobile type has an overall majority.     

Investment decisions when utility depends on wealth and other attributes

The problem of optimal investment under a multivariate utility function allows for an investor to obtain utility not only from wealth, but other (possibly correlated) attributes. In this paper we implement multivariate mixtures of exponential (mixex) utility to address this problem. These utility functions allow for stochastic risk aversions to differing states of the world. We derive some new results for certainty equivalence in this context. By specifying different distributions for stochastic risk aversions, we are able to derive many known, plus several new utility functions, including models of conditional certainty equivalence and multivariate generalisations of HARA utility, which we call dependent HARA utility. Focusing on the case of asset returns and attributes being multivariate normal, we optimise the asset portfolio, and find that the optimal portfolio consists of the Markowitz portfolio and hedging portfolios. We provide an empirical illustration for an investor with a mixex utility function of wealth and sentiment.     

Using journal entries to teach partnership tax: An illustrative case

The use of journal entries to teach partnership taxation concepts provides students with a visual tool that liberates them from the memorization of formulas that has long been a staple in partnership tax education. Employing journal entries as our pedagogy, we present a case designed to be a comprehensive project for a stand-alone graduate partnership taxation course. We also provide guidance for how individual components within the case can be assigned, which could be particularly useful to instructors of business entity tax courses. Our case provides a resource that will assist instructors in teaching and students in understanding (1) the book accounting requirements, and (2) the interrelationship between the tax and book reporting requirements. Graduate tax students who completed this case in its entirety agree that the case meets its stated learning objectives, and that journal entries are an effective tool for analyzing partnership tax transactions and make learning partnership taxation easier.     

Multivariate risk aversion and uninsurable risks: Theory and applications

The objective of this paper is to develop conditions for global multivariate comparative risk aversion in the presence of uninsurable, or background, risks, and thus generalize Kihlstrom and Mirman [1974] and Karni [1979,1989]. We analyze von Neumann-Morgenstern (VNM) utility functionsas well as smooth preference functionals which are nonlinear in distribution but locally linear in probabilities. In each case we provide an economic application which illustrates how our theorems can be used. We analyze a risk sharing, a portfolio choice, and a labor supply problem for VNM utility functions, and the optimal allocation of effort to risky technologies in the presence of a random supply (or quality) of a public good for nonlinear preference functionals. We consider thecase where the random variables are mean-independent as well as the case where they are independent. In the labor supply application for VNM utility functions, we show that if the two risks are independent, the comparative statics effect of greater risk aversion on labor supply in the presence of a background non-wage income risk is determined by a monotonic relationship between labor supply and the wage rate under certainty. That is, we extend the applicability of the Diamond-Stiglitz [1974]-Kihlstrom-Mirman [1974]single-crossing property to the case where an independent background risk is present.     

Prospect and Markowitz stochastic dominance

Levy and Wiener (J Risk Uncertain 16(2), 147–163, 1998), Levy and Levy (Manage Sci 48(10), 1334–1349, 2002; Rev Fin Stud 17(4), 1015–1041, 2004) develop the prospect and Markowitz stochastic dominance theory with S-shaped and reverse S-shaped utility functions for investors. In this paper, we extend their work on prospect stochastic dominance theory (PSD) and Markowitz stochastic dominance theory (MSD) to the first three orders and link the corresponding S-shaped and reverse S-shaped utility functions to the first three orders. We also provide experiments to illustrate each case of the MSD and PSD to the first three orders and demonstrate that the higher order MSD and PSD cannot be replaced by the lower order MSD and PSD. Furthermore, we formulate the following PSD and MSD properties: hierarchy exists in both PSD and MSD relationships; arbitrage opportunities exist in the first orders of both PSD and MSD; and for any two prospects under certain conditions, their third order MSD preference will be ‘the opposite of’ or ‘the same as’ their counterpart third order PSD preference. By extending the work of Levy and Wiener and Levy and Levy, we provide investors with more tools to identify the first and third order PSD and MSD prospects and thus they could make wiser choices on their investment decision.     

Cross-border shopping and the Atkinson–Stiglitz theorem

We introduce cross-border shopping and indirect tax competition into a model of optimal taxation. The Atkinson–Stiglitz result that indirect taxation cannot improve the efficiency of information-constrained tax-transfer policies, and that indirect taxes should not be differentiated across goods, is shown to hold in this case even if countries are asymmetric. However, if the tax system must contain indirect taxation, differentiated indirect tax rates arise in the equilibrium and restricting differentiated indirect taxation can be welfare-increasing.     

Alternative utility functions: review,analysis and comparison

The paper reviews the development of von Neumann and Morgenstern (vNM) utility theory. Kahneman and Tversky’s (KT’s) prospect theory is introduced. The vNM utility function is compared and contrasted with KT’s value function. We prove the uniqueness of two popular utility functions. First, we show that all power utility functions possess constant RRA. And, we show that all exponential utility functions have constant ARA. The paper concludes by discussing applications, strengths and weaknesses of various utility functions.     

基于计算实验金融方法的决策偏好比较研究

风险决策偏好表征着个体在面对不确定条件或具有风险时的决策态度,不同的偏好特征以效用函数为载体,外在地表现为个体具体所运用的投资策略。风险决策机制的深入理解以及基于不同决策偏好的策略比较分析对投资者的投资决策具有重要意义。通过运用计算实验金融方法对传统决策偏好以及前景理论进行多角度的比较分析,研究发现基于前景理论构造的投资策略相比传统决策偏好具有较大的优势,对于投资者本身来说是一个最佳的策略选择。     

Complexity and Progressivity in Income Tax Design: Deductions for Work-Related Expenses

We analyze optimal income taxes with deductions for work-related or consumptive goods. We consider two cases. In the first case (called a complex tax system) the tax authorities can exactly distinguish between consumptive and work-related expenditures. In the second case (called a simple tax system) this distinction is not exact. Assuming additively separable utility functions, we show that work-related expenditures should be fully deductible in the first case while deduction rates should be less than 100 percent in the second case. Under further simplifying assumptions, we also show that the simple system can be characterized by higher tax burdens on low income earners and less redistribution.     

Reforming Business Taxation: Lessons from Italy?

We carefully review the recent Italian reform of business taxation, compare it with other international experiences and theoretical proposals, and calculate its effects on the cost of capital and on the effective average corporate tax rate. We argue that the Italian reform is an original attempt to find a compromise between two conflicting aims, both of which are unavoidable in an open economy: the first is to reduce the average rate of taxation on profits, and the second is to reduce the financial and real distortions produced by corporate taxation. In assessing the initial evidence in the Italian case, we argue that too much weight has been given to the latter objective, and that further reductions in average taxation on profits may be needed.     

Rent taxation and its intertemporal welfare effects in a small open economy

Previous literature concludes that replacing wage taxation by taxes on a fixed factor or its rents benefits future generations. However, the effects of such steady-state gains on the transition generations have been left open. In this paper, we show that taxation of rents may also increase utility of the current generation provided tax revenues are earmarked to reduce wage taxes. In particular, a shift in the tax mix may yield an intergenerational Pareto-improvement when the initially prevailing tax mix is sufficiently skewed toward wage taxation.