Focusing on volatility information instead of portfolio weights as an aid to investor decisions

When faced with the challenge of forming a portfolio containing a risky and a risk-free asset, investors tend to apply the same portfolio weights independently of the volatility of the risky asset. This “percentage heuristic” can lead to different levels of portfolio risk when the same investor is presented with a more or a less risky asset. Using four experiments, we show that asking investors to choose the return distribution for their portfolio while keeping the exact portfolio weights unknown leads to greater similarity in levels of portfolio volatility (across different levels of risk of the risky asset) than asking investors to choose this distribution while additionally facing the portfolio weights. Higher consistency in risk taking is obtained both between and within test subjects.     

Asset prices and business cycles with costly external finance

This paper asks whether the asset pricing fluctuations induced by the presence of costly external finance are empirically plausible. To accomplish this, we incorporate costly external finance into a dynamic stochastic general equilibrium model and explore its implications for the properties of the returns on key financial assets, such as stocks, bonds and risky loans. We find that the mean and volatility of the equity premium, although small, are significantly higher than those in comparable adjustment cost models. However, we also show that these results require a procyclical financing premium, a property that seems at odds with the data.     

Uncertainty in the public debt market and stochastic long-run growth

In a continuous time model, a representative household has to allocate its investment and consumption in an optimal manner under conditions of uncertainty. In the present study it is hypothesized that there are two types of assets: a risk-free and a risky asset. The risk-free asset is assumed to be the physical capital, while at the same time uncertainty is allowed to result from the exogenous random variations in the public debt market, rendering in this way government bonds to act as the risky asset. In the endogenous growth framework with productive public investment, the expected long-run growth rate, the dynamic path of consumption as well as the optimal allocation of investment between a risky and a riskless asset, are analytically derived. This kind of treatment allows us to create a locus for the long-run growth over the various levels of uncertainty. The outcome of the analysis is that a rise in uncertainty impacts negatively upon the long-run growth rate. In order to empirically assess the relationship between growth and uncertainty, we lay our emphasis on the US economy for the period 1957:1 to 2008:4. Within the framework of a bivariate BEKK–GARCH(1,1)-M model a significant negative relationship between uncertainty and economic growth has been established.     

马尔可夫调制模型下交换期权的定价

在这篇文章中,假定市场经济状态由一个两状态马尔可夫链描述,风险资产满足一个两状态的马尔可夫调制过程。当市场处于高波动状态时,风险资产的价格满足跳扩散过程;当市场处于稳定状态时,风险资产的价格满足几何布朗运动.通过测度变换的技术,得到了交换期权的定价公式。最后,利用蒙特卡洛方法给出了期权价值的数值结果。     

Euler equation errors

The standard, representative agent, consumption-based asset pricing theory based on CRRA utility fails to explain the average returns of risky assets. When evaluated on cross-sections of stock returns, the model generates economically large unconditional Euler equation errors. Unlike the equity premium puzzle, these large Euler equation errors cannot be resolved with high values of risk aversion. To explain why the standard model fails, we need to develop alternative models that can rationalize its large pricing errors. We evaluate whether four newer theories at the vanguard of consumption-based asset pricing can explain the large Euler equation errors of the standard consumption-based model. In each case, we find that the alternative theory counterfactually implies that the standard model has negligible Euler equation errors. We show that the models miss on this dimension because they mischaracterize the joint behavior of consumption and asset returns in recessions, when aggregate consumption is falling. By contrast, a simple model in which aggregate consumption growth and stockholder consumption growth are highly correlated most of the time, but have low or negative correlation in severe recessions, produces violations of the standard model's Euler equations and departures from joint lognormality that are remarkably similar to those found in the data.     

THE IRREDUCIBLE ROLE OF DERIVED MARGINAL UTILITY IN DYNAMIC STOCHASTIC PROGRAMMING

Abstract. Using the important case of multi-period investing between a safe asset with a low mean return and an equity basket with a higher total return but a riskier one, this analysis demonstrates that the relevant stochastic programming involves irreducibly recursive variational relations. The "direct" Lagrange-Chow procedure is related to the derivatives of the Bellman "indirect"'algorithms and shown to require essentially the same computations save only for standard integrations or taking of first derivatives. To demonstrate that the comparison is unchanged when a vector of control variables must be optimized in a many-period stochastic scenario, the problem is solved for a rentier to both decide how much to save in each period and how much to put of each period's investment into risky securities.     

Endogenous uncertainty and market volatility

We advance the theory that the distribution of beliefs in the market is the most important propagation mechanism of economic volatility. Our model is based on the theory of Rational Beliefs (RB) and Rational Belief Equilibrium (RBE) developed by Kurz (1994, 1997). We argue that the diverse market puzzles which are examined, such as the equity premium puzzle, are all driven by the structure of market expectations. In support of our view, we present an RBE model with which we study financial markets. The model is able to simulate the correct order of magnitude of: (i) the long term mean and standard deviation of the price\dividend ratio; (ii) the long term mean and standard deviation of the risky rate of return on equities; (iii) the long term mean and standard deviation of the riskless rate; (iv) the long term mean equity premium. In addition, the model predicts (v) the GARCH property of risky asset returns; (vi) the observed pattern of the predictability of long returns on assets, and (vii) the Forward Discount Bias in foreign exchange markets. The common economic explanation for these phenomena is the existence of heterogenous agents with diverse but correlated beliefs such that some agents are optimistic and some pessimistic about future capital gains. The model has a unique parameterization under which the model makes all the above predictions simultaneously. The parameterization requires the optimists to be in the majority but the rationality of belief conditions of the RBE require the pessimists to have a higher intensity level. In simple terms, the large equity premium and the low equilibrium riskless rate are the result of the fact that at any moment of time there are agents who hold extreme pessimistic beliefs and they have a relatively stronger impact on the market. The paper also studies the effect of correlation of beliefs among investors. It shows that the main effect of such correlation is on the dynamic patterns of asset prices and returns and is hence important for studying such phenomena as stochastic volatility. Received: May 16, 2000; revised version: November 15, 2000     

Rational inattention,long-run consumption risk,and portfolio choice

This paper explores how the introduction of rational inattention (RI) – that agents process information subject to finite channel capacity – affects optimal consumption and investment decisions in an otherwise standard intertemporal model of portfolio choice. We first explicitly derive optimal consumption and portfolio rules under RI and then show that introducing RI reduces the optimal share of savings invested in the risky asset because inattentive investors face greater long-run consumption risk. We also show that the investment horizon matters for portfolio allocation in the presence of RI, even if investment opportunities are constant and the utility function of investors is constant relative risk aversion. Second, after aggregating across investors, we show that introducing RI can better explain the observed joint dynamics of aggregate consumption and the equity return. Finally, we show that RI increases the implied equity premium because investors under RI face greater long-run consumption risk and thus require higher compensation in equilibrium.     

CAN FINANCING CONSTRAINTS EXPLAIN THE ASSET PRICING PUZZLES IN PRODUCTION ECONOMIES?*

General Equilibrium asset pricing models have a difficult time simultaneously delivering a sizable equity premium, a low and counter cyclical real risk free rate, and cyclical variation in return volatility. To explain these stylized facts, this article introduces occasionally binding financing constraints that impede producers’ ability to invest. The financial frictions drive a wedge between the marginal rate of substitution and firms’ internal stochastic discount factors so that the shadow value of capital is not tied to the average price of capital. The model delivers higher and more volatile asset returns during recessions as well as a counter cyclical equity premium.     

Growth Optimal Investment Strategy: The Impact of Reallocation Frequency and Heavy Tails

The strategy to maximize the long‐term growth rate of final wealth (maximum expected log strategy, maximum geometric mean strategy, Kelly criterion) is based on probability theoretic underpinnings and has asymptotic optimality properties. This article reviews the allocation of wealth in a two‐asset economy with one risky asset and a risk‐free asset. It is also shown that the optimal fraction to be invested in the risky asset (i) depends on the length of the basic return period and (ii) is lower for heavy‐tailed log returns than for light‐tailed log returns.     

Estimating a continuous time portfolio selection model: An application with UK data

An empirical assessment of a continuous time portfolio selection model is studied for the UK economy between 1970 and 1996. The estimates obtained from this study are both statistically significant and consistent with the model's predictions. The estimate of risk aversion parameter refers to low risk aversion which is consistent with the optimal risky asset holding parameter. Furthermore, the estimated parameters of the asset pricing relationship are also found to be consistent with the historical values of the stock prices. First version received: February 1998/final version received: March 1999     

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.     

Asset price volatility and government revenue

This paper investigates the effect of commercial, residential property and equity price volatility on the variability of cyclically adjusted government revenue. We find significant evidence that asset price volatility increases the variability of government revenue. A 1% increase in equity price volatility increases government revenue variability by 0.37–0.44%. An increase in residential property price volatility increases revenue volatility by about 0.15–0.22%, whereas this effect diminishes to 0.11% in case of commercial property price. This evidence reflects the automatic increase of government revenue variability due to asset price movements and supports arguments in favour of adjusting fiscal variables for both business cycle and asset price changes. However, we also find evidence that equity price variability increases revenue variability even when government revenue is adjusted for both economic and asset price cycles, indicating the presence of more complicated dynamics between fiscal variables and asset price changes.     

Equity risk premium and time horizon: What do the U.S. secular data say?

We consider a representative investor whose wealth is made up of the equity market portfolio and the riskless asset, and who maximizes the expected utility of his/her future wealth for a given horizon. The solution of this program shows that the equilibrium value of the equity risk premium – the latter being measured by the difference between the expected equity portfolio return and the risk-free interest rate – is given by the product of the price of risk by the expected variance of stock returns. When returns are predictable, these two magnitudes are both time-varying and horizon-dependent. In accordance with this theoretical framework, our paper presents an econometric model of the equity risk premia for two traditional horizons: the one-period-ahead horizon (i.e. the ‘short-term’ premium) and the infinite-time horizon (i.e. the ‘long-term’ premium). Using annual US secular data from 1871 to 2008, and representing the expected returns by mixing the three traditional adaptive, extrapolative and regressive processes, large disparities in the dynamics of the two premia are evidenced. Concerning the determination of the equilibrium values of the two premia, the expected variances depend on the past values of the centered squared returns while the prices of risk (unobservable variables) are estimated according to the Kalman filter methodology, which enables us to capture the influence of hidden variables and of non-directly measurable psychological effects. A spread of interest rates adds to this determination. Possibly due to risky arbitrage and transaction costs, the results show that observed premia gradually converge towards their equilibrium values, this process being described by an error correction model. Overall, our model provides a rather satisfactory representation of ‘short-term’ and ‘long-term’ premia.     

Collateral rehypothecation,safe asset scarcity,and unconventional monetary policy

We build a mark-to-market model where commercial banks can enlarge their balance sheets, repledging the available collateral several times to exchange liquidity through the interbank market. In bad times, the fall of risky asset price disrupts the length of the repledging chain due to the increase of the haircut and the decrease of external assets' value. In such a scenario, the central bank can intervene implementing unconventional monetary policies by purchasing a fraction of the banking system's external assets, both safe treasury bonds, and risky asset-backed securities, to inject liquidity. Our results show that a quantitative easing policy that purchases only safe assets is highly ineffective in restoring the intermediation activity to the pre-crisis level due to its inability to sustain the risky asset price and the repledging chain of collateral. Instead, focusing on risky assets only, the monetary authority can sustain risky asset prices, avoiding the freezing of the money market.     

考虑基准资产的动态投资组合选取

职业基金经理的目标经常是希望自己的投资组合以稳定的表现能够超越所某一基准资产或组合。因此本文给出一个考虑基准资产的动态均值——方差投资组合选取模型。假设状态之间的转移遵循马氏过程,给定状态转移矩阵,可以得到对风险资产最优投入的解析表达式。此表达式表明对风险资产的投入由三项构成,前两项是不考虑基准资产时对风险资产的投入,最后一项与基准资产有关;在基准资产上的权重由基准资产收益的大小来决定,与积极投资组合管理者的风险厌恶程度无关;随着风险厌恶程度的增加,管理者会减少在风险资产上的投入。数值分析显示考虑基准资产的投资组合是一个积极的投资组合。     

Strategic Information Acquisition in Capital Markets*

A simple model of an asset market is presented, where agents are asymmetrically informed and hence information is transmitted through the price system. Prior to the trading period, a group of traders is given the opportunity to decide in a collusive arrangement whether they want to undertake a (costless) analysis which yields information about the future dividends of a risky asset. It will be shown that the fully rational and risk-averse insiders can do better without the information, if the dividend volatility of the risky asset is sufficiently low.
JEL Classification Numbers: D82, G14.     

Equity market information and credit risk signaling: A quantile cointegrating regression approach

Investigating linkages between credit and equity markets, we consider daily aggregate U.S. CDS spreads as well as well-chosen equity market and implied volatility indexes over ten years. We describe such robust (to spurious correlation) relationship with the quantile cointegrating regression approach. Such approach handles extreme quantiles/CDS values and their behavior with respect to the equity market's influence. Heteroskedastic patterns such as time-varying variance, but also autocorrelation, skewness and leptokurtosis are captured. Thus, the sensitivity of aggregate CDS spreads to equity market price and volatility channels is accurately measured across quantiles and spreads. Such quantile-dependent sensitivity exhibits asymmetric responses to equity market shocks. A sub-period analysis investigates potential regime shifts in estimated quantile cointegrating regressions. Quantile cointegrating coefficients vary over time and quantiles, and exhibit different magnitudes across sub-periods and spreads. Therefore, the relationship is unstable over time. We also propose a scenario analysis and risk signaling application for credit risk management prospects. Under specific risk levels, credit risky situations are described conditional on the equity market's information over time, and related expected aggregate CDS spreads are computed. Estimated conditional quantiles/CDS spreads act as credit alert triggers.     

基于风险基金的资本资产定价模型

本文提出并证明了基于风险基金的CAPM模型。基于风险基金的CAPM模型描述了资产的收益与风险之间的线性关系 ,其中资产的风险定义为资产收益率与风险基金收益率的协方差除以风险基金收益率的方差。作为应用例子 ,本文使用基于风险基金的CAPM模型证明了著名的CCAPM模型。     

The Influence of Different Investment Horizons on Risk Behavior

For longer investment periods, investment consultants usually recommend a larger proportion of risky assets for investor portfolios. We examine the effect of different investment horizons on investors' risk behavior. We are interested both in participants' risk perceptions and in their asset allocation behavior. We find significant underestimations of long-term risks, which lead to a higher proportion of risky assets in the long-term portfolios. Our data show that the belief in mean reversion is a potential explanation for this behavior.