On the equivalence of the static and dynamic asset allocation problems

A classic dynamic asset allocation problem optimizes the expected final-time utility of wealth, for an individual who can invest in a risky stock and a risk-free bond, trading continuously in time. Recently, several authors considered the corresponding static asset allocation problem in which the individual cannot trade but can invest in options as well as the underlying. The optimal static strategy can never do better than the optimal dynamic one. Surprisingly, however, for some market models the two approaches are equivalent. When this happens the static strategy is clearly preferable, since it avoids any impact of market frictions. This paper examines the question: when, exactly, are the static and dynamic approaches equivalent? We give an easily tested necessary and sufficient condition, and many non-trivial examples. Our analysis assumes that the stock follows a scalar diffusion process, and uses the completeness of the resulting market model. A simple special case is when the drift and volatility depend only on time; then the two approaches are equivalent precisely if (μ (t)? r)/σ²(t) is constant. This is not the Sharpe ratio or the market price of risk, but rather a nondimensional ratio of excess return to squared volatility that arises naturally in portfolio optimization problems.     

Stochastic regularization for the mean-variance allocation scheme

Despite being based on sound principles, the original Markovitz portfolio allocation theory cannot produce sound allocations, and restrictions or modifications need to be imposed from outside the theory in order to obtain meaningful portfolios. This is unsatisfactory, and the reasons for this failure are discussed, in particular, the unavoidable small eigenvalues of the covariance. Within the original principles of risk minimization and return maximization, several modifications of the original theory are introduced. First, the strategic and tactical time horizons are separated. A base long-term allocation is chosen at the strategic time horizon, while the portfolio is optimized at the tactical time horizon using information from the price histories. Second, the tactical portfolio is financed by the strategic one, and a funding operator is introduced. The corresponding optimal allocation (without constraints) has one free parameter fixing the leverage. Third, the transaction costs are taken into account. This includes the current re-allocation cost, but crucially the expected costs of the next reallocation. This last term depends on the sensitivity of the allocation with respect to the covariance, and the expectation introduces another dependency on the (inverse) covariance. The new term regularizes the original minimization problem by modifying the lower part of the spectrum of the covariance, leading to meaningful portfolios. Without constraints, the final Lagrangian can be minimized analytically, with a solution that has a structure similar to the original Markovitz solution, but with the inverse covariance regularized by the expected transaction costs.     

Conditions Ensuring the Decomposition of Asset Demand for All Risk-Averse Investors

Abstract

The paper explores how the demand for a risky asset can be decomposed into an investment effect and a hedging effect by all risk-averse investors. This question has been shown to be complex when considered outside of the mean-variance framework. Dependence among returns on the risky assets is restricted to quadrant dependence and it is found that the demand for one risky asset can be decomposed into an investment component based on the risk premium offered by the asset and a hedging component used against the fluctuations in the return on the other risky asset. The paper also discusses how the class of quadrant-dependent distributions is related to that of two-fund separating distributions. This contribution opens up the search for broader distributional hypotheses suitable to asset demand models. Examples are discussed.     

Buy-and-hold mean-variance portfolios with a random exit strategy

We show how buy-and-hold investors can move from horizon uncertainty to profit opportunity. The analysis is conducted under a risk-averse framework rather than the standard Markowitz formulation in the case of i.i.d. asset processes. We make this practical achievement by considering a threshold stopping rule as the strategy to determine when to exit the market. The resulting investment horizon is random and can be correlated with the market. Under this setting, we first provide an analytical approximation to optimal weights, and then identify a class of reference variables associated with the stopping rule that leads to ex-ante improvements in portfolio allocation, vis-a-vis the fixed exit time alternative. The latter conclusion is based on a generalization of the Sharpe ratio, adjusted for horizon uncertainty. The obtained investment suggestion is simple and can be implemented empirically.     

What is the impact of wealth shocks on asset allocation?

I test the assumption of constant relative risk aversion using U.S. macroeconomic data and analyse the role of wealth shocks in generating transitory changes in asset portfolio composition. I show that the risky asset share exhibits cyclical behavior and it is significantly (and positively) affected by unexpected variation in wealth. Therefore, the empirical evidence suggests that risk aversion is counter-cyclical. I also find that the portfolio share of housing wealth falls when the agent is faced with a positive wealth shock, i.e. housing is a hedge against unfavorable wealth fluctuations. Finally, considering a variety of wealth definitions, the results show that: (i) wealth effects are stronger for direct holdings of risky assets than for indirect holdings, which highlights that investors do not typically trade some assets such as pension or mutual funds; (ii) although significant, wealth effects on asset allocation are mainly temporary as agents quickly rebalance the asset portfolio composition (i.e. there is weak evidence of inertia or slow adjustment in asset allocation); and (iii) changes in expected returns partially explain the variation in risky asset allocation.     

Country and industry concentration and the performance of international mutual funds

We examine the relation between country and industry portfolio concentration and performance using a data set of international equity mutual funds. When sorted by concentration measures, funds in the most concentrated quintile outperform those in the most diversified quintile by 0.16% and 0.30% monthly in country and industry dimensions, respectively. Further analysis shows that the superior performance of concentrated funds is largely driven by industry rather than country concentration, suggesting the existence of global industry private information. Finally, we show that industry-concentrated funds rotate top-holding industries less frequently than their diversified counterparts, and that the industries these funds purchase subsequently outperform the industries they sell.     

The creation of wealth

The paper is concerned with the existence of a consumption sequence that implies wealth to grow at a given rate. It is shown that under reasonable assumptions such a sequence exists and can be determined by solving a fixed-point problem.     

Asset allocation in markets with contagion: The interplay between volatilities,jump intensities,and correlations

We study the impact of financial contagion on the dynamic asset allocation problem of a CRRA investor facing an incomplete market with two risky assets. We apply a Markov chain regime-switching framework with state-dependent jump intensities, diffusion volatilities and diffusion correlations. The key model feature that a switch to the bad contagion regime is triggered by a loss in one of the risky assets allows for the implementation of a hedging demand against contagion risk. Moreover, a state-dependent diffusion correlation combined with heterogeneity in jump intensities and volatilities can, e.g., generate a flight to quality effect upon a systemic jump.     

Optimizing a portfolio of mean-reverting assets with transaction costs via a feedforward neural network

Optimizing a portfolio of mean-reverting assets under transaction costs and a finite horizon is severely constrained by the curse of high dimensionality. To overcome the exponential barrier, we develop an efficient, scalable algorithm by employing a feedforward neural network. A novel concept is to apply HJB equations as an advanced start for the neural network. Empirical tests with several practical examples, including a portfolio of 48 correlated pair trades over 50 time steps, show the advantages of the approach in a high-dimensional setting. We conjecture that other financial optimization problems are amenable to similar approaches.     

Monotonicity in asset returns: New tests with applications to the term structure,the CAPM,and portfolio sorts

Many theories in finance imply monotonic patterns in expected returns and other financial variables. The liquidity preference hypothesis predicts higher expected returns for bonds with longer times to maturity; the Capital Asset Pricing Model (CAPM) implies higher expected returns for stocks with higher betas; and standard asset pricing models imply that the pricing kernel is declining in market returns. The full set of implications of monotonicity is generally not exploited in empirical work, however. This paper proposes new and simple ways to test for monotonicity in financial variables and compares the proposed tests with extant alternatives such as t-tests, Bonferroni bounds, and multivariate inequality tests through empirical applications and simulations.     

我国货币替代的实证研究

货币替代是开放经济条件下特有的货币现象,对我国宏观经济的影响也随着经济金融体系的开放而不断加深。通过建立货币替代的理论模型对我国的货币替代程度及其影响因素之间的关系作了动态分析,结果表明人民币汇率波动对货币替代影响最为突出,名义有效汇率的频繁波动会造成货币替代乃至货币需求的不稳定,我国的利率管制使得国内外货币收益率的相对变化并未在货币替代过程中呈现显著作用。     

Long-term U.S. infrastructure returns and portfolio selection

Our understanding of the long-term return behavior and portfolio characteristics of public infrastructure investments is limited by a relatively short history of empirical data. We re-construct U.S. listed infrastructure index returns by mapping their monthly performance to received systematic and industry risk factors from 1927 through 2010. Our findings reveal that the infrastructure returns in recent years may understate the tail-risk that investors could experience over the long-term, however, this tail-risk is commensurate with holding a broad portfolio of U.S. stocks. For mean-variance and mean-CVaR investors, we report the benefits of holding public infrastructure assets in investment portfolios.     

Optimal mean-reversion strategy in the presence of bid-ask spread and delays in capital allocations

A portfolio optimization problem for an investor who trades T-bills and a mean-reverting stock in the presence of proportional and convex transaction costs is considered. The proportional transaction cost represents a bid-ask spread, while the convex transaction cost is used to model delays in capital allocations. I utilize the historical bid-ask spread in US stock market and assume that the stock reverts on yearly basis, while an investor follows monthly changes in the stock price. It is found that proportional transaction cost has a relatively weak effect on the expected return and the Sharpe ratio of the investor's portfolio. Meantime, the presence of delays in capital allocations has a dramatic impact on the expected return and the Sharpe ratio of the investor's portfolio. I also find the robust optimal strategy in the presence of model uncertainty and show that the latter increases the effective risk aversion of the investor and makes her view the stock as more risky.     

次贷危机后中国外汇储备资产的风险及优化配置北大核心

次贷危机爆发后,国际金融市场动荡,中国巨额外汇储备资产面临着严重亏损风险。本文首先分析了我国外汇储备以美国国债为主而隐含的信用风险、汇率风险、流动性风险以及投资收益损失风险。长期来看,要逐步减持美元资产,优化外汇储备资产配置。然后,本文从金融资产和非金融资产两个角度对中国外汇储备的资产优化配置问题进行了研究。     

Identifying reference companies using the book-to-market ratio: a minimum spanning tree approach

There is substantial evidence to suggest that the book-to-market (BM) ratio is an important factor in explaining stock market returns. Its role has proved difficult to isolate, however, due to statistical problems in its construction and to its observational equivalence to a number of risk and behavioural explanations. In addition, now widely recognised complex behaviour in financial markets has called into question modelling approaches that are limited in their ability to uncover relationships that are possibly masked during financial crises, for example. As one response, our research explores the value of a newly applied technique which examines the topological properties of minimum spanning trees as applied to both the BM ratio and market returns. Our intention is to identify and report investment signals as determined by the BM ratio and to assess the relationships of these signals to returns outcomes. The approach enables highly nonlinear behaviour to be addressed and the relationships we set out to capture to be reported in novel ways. We motivate and evidence a previously unreported role for BM as an investment signal which is effective over varying stock market conditions, including the financial crisis that began in 2008.     

Investment strategies in the long run with proportional transaction costs and a HARA utility function

We consider an agent who invests in a stock and a money market in order to maximize the asymptotic behaviour of expected utility of the portfolio market price in the presence of proportional transaction costs. The assumption that the portfolio market price is a geometric Brownian motion and the restriction to a utility function with hyperbolic absolute risk aversion (HARA) enable us to evaluate interval investment strategies. It is shown that the optimal interval strategy is also optimal among a wide family of strategies and that it is optimal also in a time changed model in the case of logarithmic utility.     

中国城镇家庭的资产配置与消费行为:理论与证据

根据流动性资产和非流动性资产的配置组合,家庭可以分为P-HtM(贫穷月光族)、W-HtM(富裕月光族)、P-nHtM(贫穷非月光族)和W-nHtM(富裕非月光族)四类,他们表现出各自不同的消费特征。利用中国家庭金融调查2011年至2017年四轮数据,我们发现中国城镇家庭中四种类型的占比分别为6.8%、36.7%、6.6%和49.9%;在消费—收入弹性上,P-HtM和W-HtM家庭显著高于W-nHtM家庭,而P-nHtM家庭显著低于W-nHtM家庭;在暂时性收入冲击的边际消费倾向上,P-HtM和W-HtM家庭大于W-nHtM家庭,而P-nHtM家庭小于W-nHtM家庭。这些发现意味着,若要取得更好的消费刺激效果,需要更加精准的消费刺激政策。     

The 4% strategy revisited: a pre-commitment mean-variance optimal approach to wealth management

In contrast to single-period mean-variance (MV) portfolio allocation, multi-period MV optimal portfolio allocation can be modified slightly to be effectively a down-side risk measure. With this in mind, we consider multi-period MV optimal portfolio allocation in the presence of periodic withdrawals. The investment portfolio can be allocated between a risk-free investment and a risky asset, the price of which is assumed to follow a jump diffusion process. We consider two wealth management applications: optimal de-accumulation rates for a defined contribution pension plan and sustainable withdrawal rates for an endowment. Several numerical illustrations are provided, with some interesting implications. In the pension de-accumulation context, Bengen (1994)’s [J. Financial Planning, 1994, 7, 171–180], historical analysis indicated that a retiree could safely withdraw 4% of her initial retirement savings annually (in real terms), provided that her portfolio maintained an even balance between diversified equities and U.S. Treasury bonds. Our analysis does support 4% as a sustainable withdrawal rate in the pension de-accumulation context (and a somewhat lower rate for an endowment), but only if the investor follows an MV optimal portfolio allocation, not a fixed proportion strategy. Compared with a constant proportion strategy, the MV optimal policy achieves the same expected wealth at the end of the investment horizon, while significantly reducing the standard deviation of wealth and the probability of shortfall. We also explore the effects of suppressing jumps so as to have a pure diffusion process, but assuming a correspondingly larger volatility for the latter process. Surprisingly, it turns out that the MV optimal strategy is more effective when there are large downward jumps compared to having a high volatility diffusion process. Finally, tests based on historical data demonstrate that the MV optimal policy is quite robust to uncertainty about parameter estimates.     

On statistical inference on the mean-variance efficient set

A proof of the asymptotic distribution of the estimated mean-variance frontier is given. A Bayesian prediction interval is derived for the capital asset pricing model. Numerical illustrations show that the prediction intervals for the CAPM are smaller than those for the constant mean model, if the fit of the CAPM is better than that of the constant mean model.     

Rare events and annuity market participation

We investigate whether a rare event (like the default of the annuity provider) can explain the annuity market participation puzzle. High risk aversion is needed to change behavior in the presence of such a disastrous shock but higher risk aversion also makes annuities more valuable. Therefore, these rare events are unlikely candidates to explain the low take-up of voluntary annuities: the conclusion is robust to disentangling risk aversion from intertemporal substitution and to allowing portfolio investment in a stock market index.