The optimal consumption function in a Brownian model of accumulation Part A: The consumption function as solution of a boundary value problem

We consider a neo-classical model of optimal economic growth with c.r.r.a. utility in which the traditional deterministic trends representing population growth, technological progress, depreciation and impatience are replaced by Brownian motions with drift. When transformed to ‘intensive’ units, this is equivalent to a stochastic model of optimal saving with diminishing returns to capital. For the intensive model, we give sufficient conditions for optimality of a consumption plan (open-loop control) comprising a finite welfare condition, a martingale condition for shadow prices and a transversality condition as t→∞. We then replace these by conditions for optimality of a plan generated by a consumption function (closed-loop control), i.e. a function expressing log-consumption as a time-invariant, deterministic function of log-capital . Making use of the exponential martingale formula we replace the martingale condition by a non-linear, non-autonomous second-order o.d.e. which an optimal consumption function must satisfy; this has the form , where . Economic considerations suggest certain limiting values which and should satisfy as , thus defining a two-point boundary value problem (b.v.p.) — or rather, a family of problems, depending on the values of parameters. We prove two theorems showing that a consumption function which solves the appropriate b.v.p. generates an optimal plan. Proofs that a unique solution of each b.v.p. exists are given in a separate paper (Part B).     

Shadow costs of incomplete information and short sales in the valuation of the firm and its assets

This paper presents a simple framework for the valuation of compound options within shadow costs of incomplete information and short sales. The shadow cost includes two components. The first component is the product of pure information cost due to imperfect knowledge and heterogeneous expectations. The second component represents the additional cost caused by the short-selling constraint. Information costs are linked to Merton's (1987. Journal of Finance 42, 510) model of capital market equilibrium with incomplete information, CAPMI. This model is extended by Wu et al. (1996. Review of Quantitative Finance and Accounting, 7, 136) who propose an incomplete-information capital market equilibrium with heterogeneous expectations and short sale restrictions, GCAPM. This model is used in our paper to provide for the first time in the literature analytic solutions for derivatives in the presence of both shadow costs of incomplete information and short sales.When deriving the compound call option formula, we consider a call option on a stock, which is itself an option on the assets of the firm. Our methodology incorporates shadow costs of incomplete information and short sales on the firm's assets as well as the effects of leverage in the capital structure. The formula can be useful in the valuation of several corporate liabilities in the presence of information uncertainty and short sales constraints about the firm and its cash flows. Our analysis can be used for the valuation of several real options.     

The consumption–investment decision of a prospect theory household: A two-period model

This study extends the literature on portfolio choice under prospect theory preferences by introducing a two-period life cycle model, where the sufficiently loss averse household decides on optimal consumption and investment in a portfolio with one risk-free and one risky asset. The optimal solution depends primarily on whether the household’s present value of the consumption reference levels is below, equal to, or above the present value of its endowment income. Reference levels below the endowment income are associated with the self-enhancement motive. In this case, the household avoids relative losses in consumption in any present or future state of nature (good or bad). As a result the degree of loss aversion does not directly affect optimal consumption and risk taking activity. Reference levels equal to the endowment income are associated with the belonging motive. An example would be a household comparing to others that belong to the same social class. In this case the household’s optimal consumption is the reference consumption and the household will not invest in the risky asset. Finally, reference levels above the endowment income are associated with the self-improvement motive (or high aspirations). For such high reference levels, households cannot avoid experiencing a relative loss in consumption, either now or in the future. As a result, loss aversion directly affects consumption and risky investment.     

ESTIMATION OF CENSORED PANEL‐DATA MODELS WITH SLOPE HETEROGENEITY

This paper considers estimation of censored panel‐data models with individual‐specific slope heterogeneity. The slope heterogeneity may be random (random slopes model) or related to covariates (correlated random slopes model). Maximum likelihood and censored least‐absolute deviations estimators are proposed for both models. The estimators are simple to implement and, in the case of maximum likelihood, lead to straightforward estimation of partial effects. The rescaled bootstrap suggested by Andrews (Econometrica 2000; 68 : 399–405) is used to deal with the possibility of variance parameters being equal to zero. The methodology is applied to an empirical study of Dutch household portfolio choice, where the outcome variable (portfolio share in safe assets) has corner solutions at zero and one. As predicted by economic theory, there is strong evidence of correlated random slopes for the age profiles, indicating a heterogeneous age profile of portfolio adjustment that varies significantly with other household characteristics. Copyright © 2013 John Wiley & Sons, Ltd.     

随机工资下DC型企业年金的最优资产配置策略——基于鞅方法求解

研究了当工资为一个随机过程时,缴费确定型(DC)企业年金如何对股票、国债以及银行存款进行最优资产配置的问题。假设企业年金的投资目标为最终财富的期望效用函数最大化,利用鞅方法给出了此优化问题的解析解。结果表明,企业年金的最优投资策略由三部分组成:Merton投机策略、工资的收入效应投机策略以及工资的随机效应对冲策略。     

Asset allocation over the life cycle: How much do taxes matter?

We study the welfare effect of tax-optimizing portfolio decisions in a life cycle model with unspanned labor income and realization-based capital gain taxation. For realistic parameterizations of our model, certainty equivalent welfare gains from fully tax-optimized portfolio decisions are less than 2% of present financial wealth and lifetime income compared to a heuristic portfolio policy ignoring the taxation of profits (capital gains, interest and dividend payments). Compared to a heuristic portfolio policy that only ignores the realization-based feature of capital gain taxation and instead assumes mark-to-market taxation, these gains are less than 0.5%. That is, our work provides a justification for ignoring taxes in life cycle portfolio choice problems – a wide-spread assumption in that literature. However, if capital gains are forgiven at death (as in the U.S.), investors with strong bequest motives face substantial welfare costs when not tax-optimizing their portfolio decisions towards the end of the life cycle.     

A closed-form solution for the continuous-time consumption model with endogenous labor income

In this paper, we study the consumption, labor supply, and portfolio decisions of an infinitely lived individual who receives a certain wage rate and income from investment into a risky asset and a risk-free bond. Uncertainty about labor income arises endogenously, because labor supply evolves randomly over time in response to changes in financial wealth. We derive closed-form solutions for optimal consumption, labor supply and investment strategy. We find that deferring the retirement age stimulates optimal consumption over time and discourages optimal labor supply during the working life. We also find explicitly that optimal portfolio allocation becomes more ‘conservative’ when the individual approaches his prescribed retirement age. The effects of risk-aversion coefficients on optimal decisions are examined.     

Intertemporal recursive utility and an equilibrium asset pricing model in the presence of Lévy jumps

This paper presents an equilibrium formulation of asset pricing in an environment of mixed Poisson–Brownian information with recursive utility. The optimal portfolio choice problem is studied together with a derivation of Euler equation as necessary condition for optimality. It is further shown that the price processes governed by the Euler equation, together with the market clearing conditions, constitute the equilibrium price processes. Closed form formulas are derived for European call options and for other derivative securities in a particular parameterization of the economy. The derived option pricing formula contain many existing models as special cases, and is potentially useful in explaining the moneyness biasedness associated with Black–Scholes model.     

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.     

Numeraire portfolios and utility-based price systems under proportional transaction costs

In a discrete-time incomplete financial market with proportional transaction costs and with independent and bounded returns, we prove the existence of a consistent price system that can be written as the expectation of the discounted claim under the real-world probability measure P and not just under a martingale measure. In fact, the claim is then discounted by some specific dynamic portfolio called the numeraire portfolio as in the classical case of markets without transaction costs. For that specific numeraire, P will be a martingale measure. Naturally, the concept of a numeraire portfolio has here to be adapted to the concept of consistent price systems for markets with transaction costs. Moreover, again as in the classical case, the numeraire portfolio can be chosen as log-optimal portfolio. The same analysis works for power utility functions. However, then a change of measure is necessary. This paper applies methods from stochastic dynamic programming to finance.     

<Emphasis Type="Italic">Notes and Comments:</Emphasis> The numeraire portfolio in financial markets modeled by a multi-dimensional jump diffusion process

In continuous time, we study a financial market which is free of arbitrage opportunities but incomplete under the physical probability measure P. Thus one has several choices of equivalent martingale measures. In the present paper, the (unique) martingale measure P ^* is studied which is defined by the concept of the numeraire portfolio. The choice of P ^* can be justified by a change of numeraire in place of a change of measure. Mathematics Subject Classification (2000): 90A09, 91B28, 91B62, 93E20, 62P05 Journal of Economic Literature Classification: G10, G12, G13     

Coupled projects,core imputations,and the CAPM

Projects, private or public, that share input factors or output requirements had better be construed as members of a portfolio. Present risk, the capital asset pricing model may facilitate valuation of each member. Chief results of that model are derived and generalized here as core solutions to a transferable-utility production game. Shadow prices define stochastic discount factors that determine values of individual projects. Variance aversion largely affects such prices whence optimal allocations.     

Adaptive market hypothesis: The story of the stock markets and COVID-19 pandemic

Since the level of markets’ information efficiency is key to profiteering by strategic players, Shocks; such as the COVID-19 pandemic, can play a role in the nature of markets’ information efficiency. The martingale difference and conditional heteroscedasticity tests are used to evaluate the Adaptive form of market efficiency for four (4) major stock market indexes in the top four affected economies during the COVID-19 pandemic (USA, Brazil, India, and Russia). Generally, based on the martingale difference spectral test, there is no evidence of a substantial change in the levels of market efficiency for the US and Brazilian stock markets in the short, medium, and long term. However, in the long term, the Indian stock markets became more information inefficient after the coronavirus outbreak while the Russian stock markets become more information efficient. Intuitively, these affect the forecastability and predictability of these markets’ prices and/or returns. Thereby, informing the strategic and trading actions of stock investors (including arbitrageurs) towards profit optimization, portfolio asset selection, portfolio asset adjustment, etc. Similar policy implications are further discussed.     

The pricing accuracy of alternative equity valuation models: Scandinavian evidence

In many decision contexts, there is a need for benchmark equity valuations, based on simplified modeling and publicly available information. Prior research on U.S. data however shows that the accuracy of such valuation models can be low and sensitive to the choice of model specifications and value driver predictions. In this paper, we test the applicability and pricing accuracy of three fundamental valuation (dividend discount, residual income, and abnormal earnings growth) models, all based on forecasts of company dividends, earnings, and/or equity book values. Extending prior research, we apply these models to Scandinavian firms with accounting data from the period 2005–2014, explicitly testing two approaches for the prediction of the value drivers—exogenously forecasted numbers versus projected historical numbers. Given access to the forecasted value drivers, the dividend discount model comes out as the most accurate valuation model. In particular, this holds in a comparison between the most parsimonious model specifications. The residual income valuation model generates the best pricing accuracy given the prediction of value drivers based on historical financial numbers. Notably, we observe pricing errors that in general are lower than what has been reported in prior U.S.‐based research for the dividend discount and the residual income valuation models. The pricing accuracy of the abnormal earnings growth models is surprisingly weak in the Scandinavian setting. However, these models improve somewhat after a couple of complexity adjustments, in particular with value driver predictions based on the projected history setting.     

Labor supply flexibility and portfolio choice in a life cycle model

This paper examines the effect of the labor-leisure choice on portfolio and consumption decisions over an individual's life cycle. The model incorporates the fact that individuals may have considerable flexibility in varying their work effort (including their choice of when to retire). Given this flexibility, the individual simultaneously determines optimal levels of current consumption, labor effort, and an optimal financial investment strategy at each point in his life cycle. We show that labor and investment choices are intimately related. The ability to vary labor supply ex post induces the individual to assume greater risks in his investment portfolio ex ante.     

Household wealth accumulation and portfolio choices in Korea

This paper constructs a quantitative lifecycle model with uninsurable labor income and housing return risk to investigate how Korean households make saving and portfolio decisions. The model not only incorporates the special roles housing plays in the portfolio of households: collateral, a source of service flows, as well as a source of potential capital gains or losses, but also adds to existing models of wealth accumulation some unique institutional features present in Korea, namely the rental system (‘chonsae’) and the lack of a mortgage system. When the model is calibrated to match the Korean economy, several key features of the data are better able to be reproduced. The paper also analyzes the role of institutional features by comparing several alternative housing market arrangements to assess their impact on wealth accumulation, portfolio choices, and homeownership. A 10 percentage points reduction in down-payment requirement is associated with approximately 1 percentage point increase in the aggregate homeownership ratio in Korea. Lower down-payment also increases the fraction of aggregate wealth held in housing assets but lowers aggregate net worth with mixed demographic implications.     

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.     

Communication of Private Information and the Valuation of Initial Public Offerings in Singapore

This study examines a sample of 108 initial public offerings in Singapore between 1987 and 1993, and documents the effects of four channels of entrepreneurial communication, that is, retained ownership, audited report, auditor choice and underwriter choice on the valuation of new issues. Our results indicate that retained ownership and book value of equity are significantly and positively associated with the valuation of initial public offerings in Singapore. Underwriter choice and auditor choice are not significant in explaining the valuation of initial public offerings. Issues listed on the Main Board are valued higher than those on Sesdaq (Stock Exchange of Singapore Dealing and Automated Quotation). Firms choosing the auction system are valued higher than those choosing the fixed system.
This paper provides evidence on the valuation of new issues in an emerging market in the Asia-Pacific region. The results are of interest to investors, investment bankers and companies seeking a listing on the Singapore Stock Exchange. We provide some insights on how new issues in the Singapore market are valued.     

Value-Driving Activities in Euro-Zone Banks

We develop and test accounting-based valuation models for commercial banks. We extend Begley et al.'s framework (2006) and propose a valuation model where goodwill is generated by virtually all commercial and investment banking activities. Key features of our model are: the development of a relation between future cash flows from fee income and the bank value that depends on lending, borrowing and off-balance sheet business; and the inclusion of proprietary investment and trading as value-driving activities. Empirical tests on a sample of Euro-zone banks from 1998 to 2006 provide the following evidence. Unrealised expected cash flows from fee income are the most important source of unrecorded goodwill. This is consistent with the increasing importance of revenue from the sale of financial services to banks' income. The contribution of fee income to goodwill is higher for banks with large deposits and new loans. Equity securities are a source of unrecorded goodwill, but the introduction of fair value accounting, with the adoption of the International Financial Reporting Standards (IFRS), reduces their valuation role. Yet equity securities remain positively associated with unrecorded goodwill after IFRS adoption, suggesting that the fair value standards do not fully capture market expectations about future cash flows of investment assets.     

Choice of Accounting Method for Valuation of Investment Securities: Evidence from Hong Kong Firms

This study examines whether Hong Kong managers choose “benchmark” or “alternative” valuation method for investment securities, after the Hong Kong SSAP 24 became effective starting with fiscal‐year ending December 31, 1999. Tests are conducted on a sample of 292 firms, out of which 155 Hong Kong firms reported unrealized gains and losses and 128 firms that did not report holding gains/losses, but reported investment securities. The findings indicate that firms with strong relative performance, i.e. current year's EPS higher than that of the last year, chose the alternative valuation method when the investment securities had holding gains and recognized the unrealized holding gains in the equity section of the balance sheet. This finding is consistent with the Cookie Jar hypothesis because these holding gains would be used in the income statement in future periods, when needed. With regard to firms with strong relative performance and holding losses, the findings indicate that the benchmark valuation was used. The losses were reported in the income statement to the extent that they did not reduce the EPS below that of the last year. This finding is consistent with the Income Smoothing Hypothesis, because the use of benchmark valuation reduced EPS of the current year to bring it in line with that of the last year. Evidence on firms with weak economic performance and holding gains or losses provided weak support to the Income Smoothing Hypothesis and Big Bath Hypothesis. Additionally, the results indicate that the firms with high debt‐equity ratio preferred the benchmark method and recorded securities at cost. This treatment provided managers with an opportunity to liquidate or reclassify the securities in future periods and use the accrued gains, when needed. The findings are inconclusive with regard to the impact of bonus plan on the choice of valuation method.