Time to wealth goals in capital accumulation

This paper considers the problem of investment of capital in risky assets in a dynamic capital market in continuous time. The model controls risk, and in particular the risk associated with errors in the estimation of asset returns. The framework for investment risk is a geometric Brownian motion model for asset prices, with random rates of return. The information filtration process and the capital allocation decisions are considered separately. The filtration is based on a Bayesian model for asset prices, and an (empirical) Bayes estimator for current price dynamics is developed from the price history. Given the conditional price dynamics, investors allocate wealth to achieve their financial goals efficiently over time. The price updating and wealth reallocations occur when control limits on the wealth process are attained. A Bayesian fractional Kelly strategy is optimal at each rebalancing, assuming that the risky assets are jointly lognormal distributed. The strategy minimizes the expected time to the upper wealth limit while maintaining a high probability of reaching that goal before falling to a lower wealth limit. The fractional Kelly strategy is a blend of the log-optimal portfolio and cash and is equivalently represented by a negative power utility function, under the multivariate lognormal distribution assumption. By rebalancing when control limits are reached, the wealth goals approach provides greater control over downside risk and upside growth. The wealth goals approach with random rebalancing times is compared to the expected utility approach with fixed rebalancing times in an asset allocation problem involving stocks, bonds, and cash.     

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.     

Investment in financial literacy and saving decisions

We present an intertemporal consumption model of investment in financial literacy. Consumers benefit from such investment because financial literacy allows them to increase the returns on wealth. Since literacy depreciates over time and has a cost in terms of current consumption, the model delivers an optimal investment in literacy. Furthermore, literacy and wealth are determined jointly, and are positively correlated over the life-cycle. The model drives our empirical approach to the analysis of the effect of financial literacy on wealth and saving and indicates that the stock of financial literacy early in life is a valid instrument in the regression of wealth on financial literacy. Using microeconomic and aggregate data, we find strong support for the model’s predictions.     

Optimal Investment Strategy to Minimize the Probability of Lifetime Ruin

Abstract

I study the problem of how individuals should invest their wealth in a risky financial market to minimize the probability that they outlive their wealth, also known as the probability of lifetime ruin. Specifically, I determine the optimal investment strategy of an individual who targets a given rate of consumption and seeks to minimize the probability of lifetime ruin. Two forms of the consumption function are considered: (1) The individual consumes at a constant (real) dollar rate, and (2) the individual consumes a constant proportion of his or her wealth. The first is arguably more realistic, but the second has a close connection with optimal consumption in Merton’s model of optimal consumption and investment under power utility.

For constant force of mortality, I determine (a) the probability that individuals outlive their wealth if they follow the optimal investment strategy; (b) the corresponding optimal investment rule that tells individuals how much money to invest in the risky asset for a given wealth level; (c) comparative statics for the functions in (a) and (b); (d) the distribution of the time of lifetime ruin, given that ruin occurs; and (e) the distribution of bequest, given that ruin does not occur. I also include numerical examples to illustrate how the formulas developed in this paper might be applied.     

Why is Convertible Debt Subordinated? An Investment‐Based Agency Theory

This paper offers an agency‐based explanation for the junior priority status of convertible bonds. Using a simple economic model, I show that when convertible and straight debt have equal priority, shareholders can prefer value‐decreasing projects, which results in wealth transfers from bondholders to shareholders; and I prove that this problem is solved when convertible debt is subordinated. Empirical evidence supports the theory. I find that firms with greater potential for investment‐based agency conflicts are more likely to issue subordinated convertible debt, and firms with senior convertible debt are more likely to deviate from the optimal investment policy.     

Anticipated growth and business cycles in matching models

In a business cycle model that incorporates a standard matching framework, employment increases in response to news shocks, even though the wealth effect associated with the increase in expected productivity reduces labor force participation. The reason is that the matching friction induces entrepreneurs to increase investment in new projects and vacancies early. If there is underinvestment in new projects in the competitive equilibrium, then the efficiency gains associated with an increase in employment make it possible that consumption, employment, output, as well as the investment in new and existing projects jointly increase long before the actual increase in productivity materializes. If there is no underinvestment, then investment in existing projects decreases, but total investment, consumption, employment, and output still jointly increase.     

Dynamic asset–liability management in a Markov market with stochastic cash flows

This paper provides a general model to investigate an asset–liability management (ALM) problem in a Markov regime-switching market in a multi-period mean–variance (M–V) framework. Emphasis is placed on the stochastic cash flows in both wealth and liability dynamic processes, and the optimal investment and liquidity management strategies in achieving the M–V bi-objective of terminal surplus are evaluated. In this model, not only the asset returns and liability returns, but also the cash flows depend on the stochastic market states, which are assumed to follow a discrete-time Markov chain. Adopting the dynamic programming approach, the matrix theory and the Lagrange dual principle, we obtain closed-form expressions for the efficient investment strategy. Our proposed model is examined through empirical studies of a defined contribution pension fund. In-sample results show that, given the same risk level, an ALM investor (a) starting in a bear market can expect a higher return compared to beginning in a bull market and (b) has a lower expected return when there are major cash flow problems. The effects of the investment horizon and state-switching probability on the efficient frontier are also discussed. Out-of-sample analyses show the dynamic optimal liquidity management process. An ALM investor using our model can achieve his or her surplus objective in advance and with a minimum variance close to zero.     

Reconciling conflicting evidence on the elasticity of intertemporal substitution: A macroeconomic perspective

In this paper we reconcile two opposing views about the elasticity of intertemporal substitution (EIS). Empirical studies using aggregate consumption data typically find the EIS to be close to zero, whereas calibrated models designed to match growth and fluctuations facts typically require it to be close to one. This contradiction is resolved when two kinds of heterogeneity are acknowledged: one, the majority of households do not participate in stock markets; and two, the EIS increases with wealth. We introduce these two features into a standard real business cycle model. First, limited participation creates substantial wealth inequality as in the U.S. data. Consequently, the properties of aggregates directly linked to wealth (e.g., investment and output) are mainly determined by the (high-EIS) stockholders. Since consumption is much more evenly distributed than is wealth, estimation from aggregate consumption uncovers the low EIS of the majority (i.e., the poor).     

A Reexamination of Housing Price and Household Consumption in China: The Dual Role of Housing Consumption and Housing Investment

It is important to investigate the correlation between housing price and household consumption to gain an understanding of the behavior of the economy and effectively handle the consequences of economic development. In the last two decades, the accumulation of housing wealth by Chinese households has not been effectively transmitted to their final consumption. We discovered that the sustained increase in household wealth and housing-ownership rate in China has been accompanied by a decrease in consumption rate. We also identified a negative correlation between housing price and household consumption for both the homeowners who own one housing unit and those who own two units of housing. We investigated this phenomenon in China both theoretically and empirically by capturing the dual nature of housing as a consumption good and an investment vehicle. We found that the demand for second housing units is motivated by increasing housing consumption demand rather than pure investment needs. To explain the mechanisms that drive household-consumption behavior, we also explored the effects on household consumption of China’s educational system, marriage market and ageing society, as well as future housing-market uncertainty. The implications of government intervention in the housing market are discussed.     

Technological innovation and real investment booms and busts

We investigate why new, high-risk technologies can attract excessive and often unprofitable investment. We develop an equilibrium model in which rational, risk-averse agents overinvest in a risky technology, possibly to the point that its expected return is negative. Overinvestment results from relative wealth concerns which arise endogenously from the imperfect tradability of future endowments. Competition over future consumption leads to an indirect utility for wealth with “keeping up with the Joneses” properties that can induce herding. Because overinvestment increases with the risk of the technology, our model can explain why new, risky technological innovations may promote investment bubbles.     

Correspondence between lifetime minimum wealth and utility of consumption

We establish when the two problems of minimizing a function of lifetime minimum wealth and of maximizing utility of lifetime consumption result in the same optimal investment strategy on a given open interval O in wealth space. To answer this question, we equate the two investment strategies and show that if the individual consumes at the same rate in both problems—the consumption rate is a control in the problem of maximizing utility—then the investment strategies are equal only when the consumption function is linear in wealth on O, a rather surprising result. It then follows that the corresponding investment strategy is also linear in wealth and the implied utility function exhibits hyperbolic absolute risk aversion.      

Accelerated investment effect of risky debt

In this paper we examine a new effect of risky debt on a firm’s investment strategy. We call this effect “accelerated investment”. It stems from a potential loss of investment option in the event of default. The possibility of default reduces the value of the option to wait and provides equity holders with an incentive to speed up investment. As a result, in the absence of wealth expropriation by a levered firm’s debt holders, its shareholders exercise their investment option earlier than the shareholders of an otherwise identical all-equity firm. This result is at odds with the generally accepted intuition that in the absence of potential wealth transfers and taxes the shareholders of a levered firm would follow the same investment policy as that of an unlevered firm. In addition to providing various illustrations of the accelerated investment effect, we relate its magnitude to the presence of competition for investment opportunities.     

论地方政府“土地财政”对居民消费的影响——基于全国地级市面板数据的估计

基于跨期消费与投资组合模型研究了"土地财政"对于居民消费的影响机理,并利用我国2004～2010年267个地级市面板数据进行实证检验。研究发现:首先,"土地财政"通过影响居民实际收入以及推高房价共同抑制了居民消费,并且随着"土地财政"依赖程度的增加,居民将相应地增大房产部分在家庭财富配置的比重;其次我国的"房地产财富效应"不显著,但是居民住房面积的增加有助于促进居民消费;最后,提高信贷利率和改善公共服务水平都将有助于提振居民消费。因此,减少地方政府对于"土地财政"依赖、建立居民合理分享土地增值收益机制以及弥补政府保障性住房的职能缺位是提振居民消费的关键。     

Revisiting the consumption-real exchange rate anomaly in a model with non-traded goods

This paper shows that the assumption used in many two-country business cycle models that all non-traded goods are nondurable consumption goods magnifies the severity of the consumption-real exchange rate anomaly, which is the discrepancy between the high correlation between relative consumption and the real exchange rate predicted by most models and the low correlation observed empirically. This assumption hampers the ability to generate wealth effects necessary for the economies to deviate away from full risk-sharing. Using an alternative setup in which non-traded goods can also be investment goods improves the ability of the model to generate wealth effects, and therefore to overcome the anomaly.     

Dynamic portfolio strategy by loss-averse fund managers facing performance-induced fund flows

In a continuous-time framework, we establish an optimal dynamic portfolio strategy for a loss-averse fund manager facing performance-induced fund flows. Using the martingale approach, we derive closed-form solutions to both the optimal terminal value and optimal dynamic strategy of the fund under management. The model shows that the loss-averse manager strives to earn high returns in good market conditions at the risk of losing all investments at the terminal date in bad market conditions. The prospect of higher fund inflows induced by superior performance motivates fund managers to take more aggressive investment strategies, increasing the fund's risk exposure, whereas the prospect of fund outflows due to underperformance has no impact on the fund manager's investment decision. While the prospect of higher fund inflows increases dynamic optimal wealth as well as optimal terminal wealth in good market conditions, in bad market conditions, it reduces dynamic optimal wealth and results in a higher chance of a complete loss at the terminal date. Finally, a manager with a higher degree of loss aversion tends to take a conservative investment strategy with a lower risk exposure especially in bad market conditions, leading to a lower dynamic and terminal wealth in good market conditions and also a lower chance of a complete loss in bad market conditions.     

The spirit of capitalism among the income classes

This paper tests the consumption-based capital asset model within the context of the spirit of capitalism. The spirit of capitalism asserts that consumers gain utility not just from consumption of goods and services, but also from the social status obtained from wealth. We examine two asset pricing models developed by Bakshi and Chen (1996) that employ wealth in the utility function, for households sorted by income quintiles. In the first model, households obtain utility from both consumption and the social status that comes from their own wealth. In the second model, households gain utility from both consumption and the social status obtained from their own wealth relative to the wealth of other peer households. Our results indicate that both models are inconsistent with the data regardless of income. However, using cointegration methods as a diagnostic tool, we find that the data are “loosely” consistent with the spirit of capitalism, at least for the upper income quintiles.     

Time‐Varying Risk–Return Trade‐off in the Stock Market

We uncover a strong comovement of the stock market risk–return trade‐off with the consumption–wealth ratio (CAY). The finding reflects time‐varying investment opportunities rather than countercyclical aggregate relative risk aversion. Specifically, the partial risk–return trade‐off is positive and constant when we control for CAY as a proxy for investment opportunities. Moreover, conditional market variance scaled by CAY is negatively priced in the cross‐section of stock returns. Our results are consistent with a limited stock market participation model, in which shareholders require an illiquidity premium that increases with CAY, in addition to the risk premium that is proportional to conditional market variance.     

Asset pricing in production economies with extrapolative expectations

Introducing extrapolative bias into a standard production-based model with recursive preferences reconciles salient stylized facts about business cycles (low consumption volatility, high investment volatility relative to output) and financial markets (high equity premium, volatile stock returns, low and smooth risk-free rate) with plausible levels of risk aversion and intertemporal elasticity of substitution. Furthermore, the model captures return predictability based upon dividend yield, Q, and investment. Intuitively, extrapolative bias increases the variation in the wealth–consumption ratio, which is heavily priced under recursive preferences; adjustment costs decrease the covariance between marginal utility and asset returns. Empirical support for key implications of the model is also provided.     

Visibility Bias in the Transmission of Consumption Beliefs and Undersaving

We model visibility bias in the social transmission of consumption behavior. When consumption is more salient than nonconsumption, people perceive that others are consuming heavily, and infer that future prospects are favorable. This increases aggregate consumption in a positive feedback loop. A distinctive implication is that disclosure policy interventions can ameliorate undersaving. In contrast with wealth-signaling models, information asymmetry about wealth reduces overconsumption. The model predicts that saving is influenced by social connectedness, observation biases, and demographic structure, and provides new insight into savings rates. These predictions are distinct from other common models of consumption distortions.     

住房财富对中国城镇家庭消费的影响

在构建以国内大循环为主体,国内国际双循环相互促进的新发展格局下,把握扩大内需这一战略基点,激发居民消费潜力,是推动经济高质量发展的关键之一。住房已经成为中国家庭财富的重要组成部分,一方面可通过财富效应促进家庭消费,另一方面也可能由于“房奴效应”降低家庭消费。因此,住房财富对家庭消费的影响方向并不确定。本文基于2013-2019年中国家庭金融调查数据,研究了住房财富对家庭消费的影响,并检验了住房财富影响家庭消费的可能渠道。研究发现,住房财富对城镇家庭消费有显著促进作用,并显著改善了家庭消费结构,住房资产具有财富效应。进一步研究发现,住房财富能够缓解流动性约束,从而提高家庭消费水平。异质性分析表明,住房财富对不同类型的消费具有不同的促进作用,不同地区和拥有住房数量的差别均会对住房财富产生不同影响。根据本文研究,在控制风险的前提下,可发挥既有住房财富对平滑家庭消费的积极作用,促进家庭消费增长,改善家庭消费结构,进一步推进家庭消费升级。