Progressive Taxation, Tax Exemption, and Irreversible Investment under Uncertainty

We analyze the impact of progressive taxation on irreversible investment under uncertainty. We show that if tax exemption is lower than sunk cost, higher tax rate will decelerate optimal investment by increasing the optimal investment threshold, while if tax exemption exceeds sunk cost, three different regimes arise. For “small” volatilities the optimal investment threshold is a positive function of volatility, but independent of tax rate. For “medium” volatilities it is independent of both tax rate and volatility. Finally, for “high” volatilities the optimal investment threshold depends positively on volatility, but negatively on tax rate so that we have “tax paradox”.     

FORECASTING GLOBAL EQUITY INDICES USING LARGE BAYESIAN VARS

This paper proposes a large Bayesian Vector Autoregressive (BVAR) model with common stochastic volatility to forecast global equity indices. Using a monthly dataset on global stock indices, the BVAR model controls for co‐movement commonly observed in global stock markets. Moreover, the time‐varying specification of the covariance structure accounts for sudden shifts in the level of volatility. In an out‐of‐sample forecasting application we show that the BVAR model with stochastic volatility significantly outperforms the random walk both in terms of point as well as density predictions. The BVAR model without stochastic volatility, on the other hand, shows some merits relative to the random walk for forecast horizons greater than six months ahead. In a portfolio allocation exercise we moreover provide evidence that it is possible to use the forecasts obtained from our model with common stochastic volatility to set up simple investment strategies. Our results indicate that these simple investment schemes outperform a naive buy‐and‐hold strategy.     

The sovereign property of foreign reserve investment in China: A CVaR approach

This paper investigates the role of foreign exchange reserve investment to hedge overall macroeconomic risks. Different from usual micro profit-maximizing purpose, the investment with macro objective is unique in the field of foreign reserve investment. We propose a framework of mean-variance-CVaR (conditional value at risk) model to capture the features of such investment and calculate the optimal allocation of foreign reserves in China. We use Cornish–Fisher method to calculate CVaR and adopt quasi-Newton algorithm to solve the optimization problem. Two scenarios are compared in the paper: the usual micro profit-maximizing portfolio and the sovereign portfolio hedging macro risks. We find that hedging the overall macro risks and lower the overall volatility of the economy through foreign reserve investment is possible under certain risk constraints.     

Foreign equity option pricing under stochastic volatility model with double jumps

This paper considers the challenging problem advocated by Huang and Hung (2005), that is to incorporate the stochastic volatility into the foreign equity option pricing. Foreign equity options (quanto options) are contingent claims where the payoff is determined by an equity in one currency but the actual payoff is done in another currency. Huang and Hung (2005) priced foreign equity options under the Lévy processes. In Huang and Hung's paper, they considered jumps in the foreign asset prices and exchange rates and assumed the volatility as constant. However, many studies showed that constant volatility and jumps in returns are incapable of fully capturing the empirical features of equity returns or option prices. In this paper, the stochastic volatility with simultaneous jumps in prices and volatility is proposed to model foreign asset prices and exchange rates. The foreign equity option pricing formula is given by using the Fourier inverse transformation. The numerical results show that the use of stochastic volatility with simultaneous jumps in prices and volatility proposed to model foreign asset prices and exchange rates is necessary and this approach can help us to capture more accurately the foreign equity option prices.     

DYNAMIC ASSET ALLOCATION AND CONSUMPTION CHOICE IN INCOMPLETE MARKETS*

We study the optimal investment and consumption problem of a CRRA investor when the drift and volatility of the stock are driven by a correlated factor. The myopic and non‐myopic components of the optimal portfolio process are characterised in terms of the market price of traded and non‐traded risk of the minimax martingale measure. We find that the optimal policies depend crucially on the nature of the agent, aggressive versus conservative, and the market incompleteness, improving versus deteriorating investment opportunities. Furthermore, we show that the original problem cannot be decomposed into a pure consumption and a pure terminal wealth problem, unless the market is complete.     

Producing energy in a stochastic environment: Switching from non-renewable to renewable resources

In this paper, we study the determinants of switching from non-renewable natural resource inputs to renewable resource inputs in energy production. We assume that the stocks of both natural resources are stochastic, and that the adoption of renewable resources is costly and irreversible. Our formulation gives raise to an optimal stopping/switching problem that cannot be solved analytically, then we turn to numerical simulations. Our results suggest that the optimal switching time depends not only on the uncertainty parameters, but also on energy demand, costs, and the relative productivity of the resources.     

Competitive investing equilibrium under a procurement mechanism

This paper proposes a procurement mechanism for a research and development (R&D) project, in which the stochastic nature of R&D is incorporated, and the potential agents needed to invest prior to the agent are selected. The incentive contract aims to attract the investment of potential agents through a sharing rate. By establishing the stopping time game, an optimal investing strategy for potential agents is derived. Furthermore, the investment equilibria are discussed, and the conditions under which the equilibrium represents preemption or simultaneous investment are presented.     

Real estate investment: Market volatility and optimal holding period under risk aversion

This paper deals with real estate portfolio optimization when investors are risk averse. In this framework, we examine an important decision making problem, namely the determination of the optimal time to sell a diversified real estate portfolio. The optimization problem corresponds to the maximization of a concave utility function defined on both the free cash flows and the terminal value of the portfolio. We determine several types of optimal times to sell and analyze their properties. We extend previous results, established for the quasi linear utility case, where investors are risk neutral. We consider four cases. In the first one, the investor knows the probability distribution of the real estate index. In the second one, the investor is perfectly informed about the real estate market dynamics. In the third case, the investor uses an intertemporal optimization approach which looks like an American option problem. Finally, the buy-and-hold strategy is considered. For these four cases, we analyze in particular how the solutions depend on the market volatility and we compare them with those of the quasi linear case. We show that the introduction of risk aversion allows to better account for the real estate market volatility. We also introduce the notion of compensating variation to better measure the impacts of both the risk aversion and the volatility.     

A new generalized volatility proxy via the stochastic volatility model

This article proposes power transformation of absolute returns as a new proxy of latent volatility in the stochastic model. We generalize absolute returns as a proxy for volatility in that we place no restriction on the power of absolute returns. An empirical investigation on the bias, mean square error and relative bias is carried out for the proposed proxy. Simulation results show that the new estimator exhibiting negligible bias appears to be more efficient than the unbiased estimator with high variance.     

Asset allocation under stochastic interest rate with regime switching

We investigate an optimal asset allocation problem in a Markovian regime-switching financial market with stochastic interest rate. The market has three investment opportunities, namely, a bank account, a share and a zero-coupon bond, where stochastic movements of the short rate and the share price are governed by a Markovian regime-switching Vasicek model and a Markovian regime-switching Geometric Brownian motion, respectively. We discuss the optimal asset allocation problem using the dynamic programming approach for stochastic optimal control and derive a regime-switching Hamilton–Jacobi–Bellman (HJB) equation. Particular attention is paid to the exponential utility case. Numerical and sensitivity analysis are provided for this case. The numerical results reveal that regime-switches described by a two-state Markov chain have significant impacts on the optimal investment strategies in the share and the bond. Furthermore, the market prices of risk in both the bond and share markets are crucial factors in determining the optimal investment strategies.     

The structural transformation between manufacturing and services and the decline in the US GDP volatility

I construct a two-sector growth model to study the effect of the structural transformation between manufacturing and services on the decline in GDP volatility in the US. In the model, a change in the relative size of the two sectors affects the transmission mechanism that relates sectoral TFP shocks to endogenous variables. I calibrate the model to the US and show that, for given stochastic sectoral TFP processes in manufacturing and services, structural change generates a decline in the volatility of both aggregate TFP and GDP, in the volatility of each broad component of GDP (manufacturing consumption, services consumption and investment) and in the volatility of labor. Numerical results suggest that the structural transformation can account for 28% of the reduction in the US GDP volatility between the periods 1960–1983 and 1984–2005.     

Optimal accumulation in a small open economy with technological uncertainty

Summary. This paper analyzes the optimal allocation problem of a small trading country facing an uncertain technology. It is involved in production of many commodities. Differentiability cannot be guaranteed, hence, the Ramsey-Euler condition of optimality needs to be modified. From the optimality criterion, we derive a pair of conditions, which does not require differentiability. If “enough” uncertainty is allowed, the sequence of the distribution functions of investment expenditure converges uniformly to a unique invariant measure. In addition to the weak convergence of the stochastic process of investment expenditure we also have the sequences of the stochastic process of investment expenditure converging weakly. Received: September 8, 1994; revised version: September 25, 1997     

Restoring Wetlands Through Wetlands Mitigation Banks

This paper offers the first economic analysis of wetlands mitigation banks. The banks are a new alternative for restoration of wetlands by developers before receiving regulatory approval for future development of wetlands in the same watershed. A stochastic optimal control model is developed which incorporates ecological uncertainty of wetlands restoration. The model helps in examining the decisions of how much to invest in a wetlands mitigation bank. The model is calibrated with data from California bioeconomic parameters. Numerical simulation of the model provides a sensitivity analysis of how model parameters of restoration costs, stochastic biological growth, interest rate, and the market value of credits affect the trajectory of investment and the optimal stopping state of wetlands quality when the investment ends. The analysis reveals that restoration of the whole site will occur when there is a reduction in restoration costs, an increase in biological uncertainty or an increase in the value of wetlands credits. Continued restoration is harder to justify with a higher interest rate.     

Optimal risk adoption: a real options approach

Summary. This study develops a real options approach for analyzing the optimal risk adoption policy in an environment where the adoption means a switch from one stochastic flow representation into another. We establish that increased volatility does not necessarily decelerate investment, as predicted by the standard literature on real options, once the underlying volatility of the state variable is made endogenous. We prove that for a decision maker with a convex (concave) objective function, increased post-adoption volatility increases (decreases) the expected cumulative present value of the post-adoption profit flow, which consequently decreases (increases) the option value of waiting and, therefore, accelerates (decelerates) current investment.Received: 12 October 2001, Revised: 4 December 2002, JEL Classification Numbers: O32, G30, D92, C61. Correspondence to: Luis H.R. AlvarezConstructive comments from an anonymous referee are acknowledged. The financial support from the Foundation for the Promotion of the Actuarial Profession (Aktuaaritoiminnan Kehittämissäätiö) to Luis H. R. Alvarez is gratefully acknowledged. Both authors are grateful for the financial support from The Yrjö Jahnsson Foundation.     

Empirical Evidence of the Leverage Effect in a Stochastic Volatility Model: A Realized Volatility Approach

Increasing attention has been focused on the analysis of the realized volatility, which can be treated as a proxy for the true volatility. In this paper, we study the potential use of the realized volatility as a proxy in a stochastic volatility model estimation. We estimate the leveraged stochastic volatility model using the realized volatility computed from five popular methods across six sampling-frequency transaction data (from 1-min to 60- min) based on the trust region method. Availability of the realized volatility allows us to estimate the model parameters via the MLE and thus avoids computational challenge in the high dimensional integration. Six stock indices are considered in the empirical investigation. We discover some consistent findings and interesting patterns from the empirical results. In general, the significant leverage effect is consistently detected at each sampling frequency and the volatility persistence becomes weaker at the lower sampling frequency.     

ANALYTICAL EVALUATION OF VOLATILITY FORECASTS*

Estimation and forecasting for realistic continuous‐time stochastic volatility models is hampered by the lack of closed‐form expressions for the likelihood. In response, Andersen, Bollerslev, Diebold, and Labys (Econometrica, 71 (2003), 579–625) advocate forecasting integrated volatility via reduced‐form models for the realized volatility, constructed by summing high‐frequency squared returns. Building on the eigenfunction stochastic volatility models, we present analytical expressions for the forecast efficiency associated with this reduced‐form approach as a function of sampling frequency. For popular models like GARCH, multifactor affine, and lognormal diffusions, the reduced form procedures perform remarkably well relative to the optimal (infeasible) forecasts.     

Asset prices and economic fluctuations: The implications of stochastic volatility

This paper investigates whether the multi-factor stochastic volatility of stock returns is related to economic fluctuations and affects asset prices. We address these issues in a dynamic Fama-French three-factor volatility model framework. Consistent with the ICAPM with stochastic volatility (Campbell et al., 2017), we find that the conditional volatility of the size and value factors is significantly related to economic uncertainty. These volatilities are also significant pricing factors. The out-of-sample forecasting analysis further reveals that the conditional volatility can predict stock returns and deliver economic gain in asset allocation. Our analysis sharpens the understanding on the link between the stock market and economic fundamentals.     

Asymmetry, realised volatility and stock return risk estimates

In this paper we estimate minimum capital risk requirements for short and long positions with three investment horizons, using the traditional GARCH model and two other GARCH-type models that incorporate the possibility of asymmetric responses of volatility to price changes. We also address the problem of the extremely high estimated persistence of the GARCH model to generate observed volatility patterns by including realised volatility as an explanatory variable into the model??s variance equation. The results suggest that the inclusion of realised volatility improves the GARCH forecastability as well as its ability to calculate accurate minimum capital risk requirements and makes it quite competitive when compared with asymmetric conditional heteroscedastic models such as the GJR and the EGARCH.     

保险公司不动产最优投资策略研究*

本文研究了保险公司投资不动产时的最优投资策略问题。本文假设保险公司的风险过程为经典Cramer Lundeberg模型。保险公司可把资金投资于现金市场和两个风险市场，分别为债券、股票和不动产。在卖空、借贷限制下，基于均值—方差模型，应用辅助随机二次线性问题求解方法，得到最优投资策略和有效边界。研究结果显示，不动产最优投资量不仅与初始资本金存在非简单线性关系，还与不动产的市场溢价水平、未预期冲击存在一系列复杂关系。     

短期经济波动如何影响长期增长趋势?

短期经济波动如何影响长期经济平均增长趋势已成为一个新的研究热点。本文研究我国省际数据发现,波动性对长期增长趋势有显著影响:1978年前,波动性与平均增长呈负相关的特征在多数省份出现;1978年后,两者关系主要表现为正相关。本文通过建立内生随机增长模型,研究波动与增长之间的内在关联,提出了实际波动与增长关系的一种合理解释。模型的基本思想是:人力资本形成过程分为自然形成和主观形成,教育投入等决定主观形成过程的因素的多少是决定波动性如何影响长期经济增长方向的关键。当教育投入较高,以致主观过程占优时,波动性对长期增长趋势有正效应;反之,当自然过程占优时,波动性对平均增长有负效应。模型结论与建国后的发展历史相印证:1978年前,生产水平低,教育投入少,人力资本形成中干中学比例占优,因而波动性同增长呈负相关;1978年恢复高考后,教育正常化,生产发展,教育投入增加,因而波动性与增长逐渐呈现正相关。