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.     

Investment Policy Implications of the Capital Asset Pricing Model

The results of previous generalized Security Market Line (SML) tests of the Mean Variance (MV) and Linear Risk Tolerance (LRT) Capital Asset Pricing Models indicate that the models are empirically identical. A very widely accepted, but technically incorrect, explanation for the results is that with normal return distributions all expected utility maximizing riskaverse investors will pick MV portfolios. The paper shows that the generalized SML tests cannot distinguish between the MV model and a much wider variety of power utility LRT models than has previously been entertained. On the other hand, with approximately normal, or real world, return distributions the investment policies of the various models are shown to be different from each other, and from the MV policy in particular. To the extent the results of the portfolio selection calculations are robust, the results of, and implications drawn from, the tests of the macro pricing relations are not based on firm micro foundations.     

Optimal asset allocation under linear loss aversion

We study the asset allocation of a linear loss-averse (LA) investor and compare it to the more traditional mean-variance (MV) and conditional value-at-risk (CVaR) investors. First we derive conditions under which the LA problem is equivalent to the MV and CVaR problems and solve analytically the two-asset problem of the LA investor for a risk-free and a risky asset. Then we run simulation experiments to study properties of the optimal LA and MV portfolios under more realistic assumptions. We find that under asymmetric dependence LA portfolios outperform MV portfolios, provided investors are sufficiently loss-averse and dependence is large. Finally, using 13 EU and US assets, we implement the trading strategy of a linear LA investor who reallocates his/her portfolio on a monthly basis. We find that LA portfolios clearly outperform MV and CVaR portfolios and that incorporating a dynamic update of the LA parameters significantly improves the performance of LA portfolios.     

Stochastic dominance and portfolio analysis

The principle of stochastic dominance is used to characterize the optimal efficient sets when the distributions of the random prospects belong to a family. Most of the well-known distributions are considered. In each case, the optimal efficient sets are characterized by easily verifiable conditions on the parameters of the distributions. These optimal efficient sets are then compared with the corresponding mean-variance (MV) efficient set. It is often found that the optimal efficient sets are proper subsets of the MV efficient set. Thus, the MV criterion is a proper efficiency criterion, but the MV efficient set can be excessively large compared to the optimal efficient set.     

The Estimation of Systematic Risk under Differentiated Risk Aversion: A Mean-Extended Gini Approach

This paper examines a mean-Gini model of systematic risk estimation that resolves some econometric problems with mean-variance beta estimation and allows for heterogeneous risk aversion across investors. Using the mean-extended Gini (MEG) model, we estimate systematic risks for different degrees of risk aversion. MEG betas are shown to be instrumental variable estimators that provide econometric solutions to biases generated by the estimation of mean-variance (MV) betas. When security returns are not normally distributed, MEG betas are proved to differ from MV betas. We design an econometric test that assesses whether these differences are significant. As an application using daily returns, we estimate MEG and MV betas for U.S. securities.     

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.     

The Dynamic Relations between Market Returns and Two Types of Risk with Business Cycles

We examine the dynamic relations among market returns, market (MV), and idiosyncratic (IV) around business cycles. Compared to the conventional view, which treats MV and IV separately, we first find that excess return on the market anticipates negative MV and IV, suggesting market return's role as an economic indicator, with the relation stronger in recessions. Second, IV helps predict positive MV, mainly in early part of recessions, suggesting a dynamic evolution from IV to MV. Third, MV helps predict negative IV, suggesting MV may substitute IV to some extent.     

THE MEAN‐GINI EFFICIENT PORTFOLIO FRONTIER

A main advantage of the mean‐variance (MV) portfolio frontier is its simplicity and ease of derivation. A major shortcoming, however, lies in its familiar restrictions, such as the quadraticity of preferences or the normality of distributions. As a workable alternative to MV, we present the mean‐Gini (MG) efficient portfolio frontier. Using an optimization algorithm, we compute MG and mean‐extended Gini (MEG) efficient frontiers and compare the results with the MV frontier. MEG allows for the explicit introduction of risk aversion in building the efficient frontier. For U.S. classes of assets, MG and MEG efficient portfolios constructed using Ibbotson (2000) monthly returns appear to be more diversified than MV portfolios. When short sales are allowed, distinct investor risk aversions lead to different patterns of portfolio diversification, a result that is less obvious when short sales are foreclosed. Furthermore, we derive analytically the MG efficient portfolio frontier by restricting asset distributions. The MG frontier derivation is identical in structure to that of the MV efficient frontier derivation. The penalty paid for simplifying the search for the MG efficient frontier is the loss of some information about the distribution of assets.     

Board of directors' responsiveness to shareholders: Evidence from shareholder proposals

In recent years boards have become significantly more likely to implement non-binding, majority-vote (MV) shareholder proposals. Using a sample of 620 MV proposals between 1997 and 2004, we find that shareholder pressure (e.g., the voting outcome and the influence of the proponent) and the type of proposals are the main determinants of the implementation decision, while traditional governance indicators do not seem to affect the decision. We then examine the labor market consequences of the implementation decision for outside directors and find that directors implementing MV shareholder proposals experience a one-fifth reduction in the likelihood of losing their board seat as well as other directorships.     

The effect of pre-emptive right amendments on shareholder wealth

Pre-emptive rights allow existing shareholders to purchase a new offering of shares before the general public. This paper investigates the effect on shareholder wealth of removing pre-emptive rights from corporate charters. Two hypotheses are constrasted: (1) Shareholder wealth maximization suggests that management uses this extra degree of freedom to pick the least cost method for raising new equity; hence, the amendment increases shareholder wealth. (2) Management welfare maximization holds that management will use the passage of the amendment to maximize their own welfare, sometimes to the detriment of shareholders; hence, the amendment decreases shareholder wealth. The evidence indicates that the amendment decreases shareholder wealth.     

Consumption, (dis)aggregate wealth,and asset returns

In this work, I show, from the consumer's budget constraint, that the residuals of the trend relationship among consumption, financial wealth, housing wealth and labor income (summarized by the variable cday) should predict better U.S. and U.K. quarterly stock market returns than a variable like cay from Lettau and Ludvigson (2001), which considers aggregate wealth instead.I find that the superior forecasting power of cday is due to: (i) its ability to track the changes in the composition of asset wealth; and (ii) the faster rate of convergence of the coefficients to the “long-run equilibrium” parameters.In addition, the results suggest that, while financial wealth shocks are mainly transitory, fluctuations in housing wealth are very persistent. Moreover, they highlight that expectations about future returns are “synchronized” across countries.     

MARKET EXPECTATIONS AND THE VALUATION EFFECTS OF EQUITY ISSUANCE

We examine how the wealth effects of equity offers are influenced by investors' expectation of the equity type (public or private) to be issued. Firms deviating to the public market may be issuing when information asymmetry or agency costs are high, and their wealth effects are more negative than for firms that are anticipated to issue equity publicly. Firms deviating to the private market, however, may signal firm undervaluation or monitoring benefits and experience more positive wealth effects than firms that are expected to issue equity privately. For the private issues, public market accessibility appears to influence the wealth effects.     

Initial Public Offering Underpricing: The Issuer's View—A Comment

I consider the underpricing of initial public offerings (IPOs) and the wealth transfers implicit in that underpricing. I find that initial returns properly measure the “issue cost” effect of underpricing as a fraction of offer size, as in Ritter (1987) . I present a measure of the wealth effect of underpricing per share retained. In general, the wealth effects on existing shareholders depend on the extent to which they participate in the offering. From the perspective of issuer's wealth, I find that Dawson's (1987) measure is appropriate only in the special case in which all of the prior owners'; shares are sold in the IPO.     

信贷增长如何影响中国的收入和财富不平等

本文基于中国家庭追踪调查(CFPS)数据考察了信贷增长对中国家庭收入和财富不平等的影响。整体而言，信贷增长可以缩小家庭收入不平等，主要作用机制是信贷增长通过提高中低收入群体的劳动收入和单位时薪以缩小劳动收入不平等。同时，文献中所发现的信贷增长可能恶化收入不平等的机制——扩大家庭间非货币金融资产差距，在我国表现并不明显，原因在于中国家庭的非货币金融资产比例较低，这一点对于高收入家庭也不例外，且大部分家庭难以从金融资产交易中获利。信贷增长带来了各个收入组的房屋价值上涨，但高收入家庭房产价值上涨的幅度高于中低收入家庭，因此房价上涨扩大了不同收入家庭所持有的房产价值差异。考虑到家庭调查数据往往对高收入家庭的收入和财产覆盖不完整，上述结论可能低估了信贷增长对极少数高收入家庭收入和资产的影响。本文有助于更好地理解我国信贷增长对收入分配问题的影响，为相关政策制定提供了一定启示。     

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。     

Reduction of estimation risk in optimal portfolio choice using redundant constraints

It is well known that when the moments of the distribution governing returns are estimated from sample data, the out-of-sample performance of the optimal solution of a mean–variance (MV) portfolio problem deteriorates as a consequence of the so-called “estimation risk”. In this document we provide a theoretical analysis of the effects caused by redundant constraints on the out-of-sample performance of optimal MV portfolios. In particular, we show that the out-of-sample performance of the plug-in estimator of the optimal MV portfolio can be improved by adding any set of redundant linear constraints. We also illustrate our findings when risky assets are equally correlated and identically distributed. In this specific case, we report an emerging trade-off between diversification and estimation risk and that the allocation of estimation risk across portfolios forming the optimal solution changes dramatically in terms of number of assets and correlations.     

Golden Parachutes: Incentive Aligners,Management Entrenchers,or Takeover Bid Signals?

In this paper we investigate the effect of golden parachute (GP) adoptions on shareholder wealth. We control for the potential effect a GP adoption has on the probability that a firm will receive a takeover bid by investigating the wealth effects for firms that are in play when the GP is adopted. We find that announcements are wealth neutral when firms are in play and wealth increasing when firms are not in play when a GP is adopted. The results suggest that GPs have no influence on the success of a tender offer, refuting the hypotheses that they either align manager and shareholder interests or that they entrench inefficient managers. The difference in the results for in-play and not-in-play firms is consistent with the hypothesis that GPs signal an increased likelihood that a firm will receive a takeover bid.     

A new way of looking at the risk in defined benefit pension plans

The portability feature of a defined contribution (DC) pension greatly reduces the risk to the accumulation of pension wealth. Conversely, defined benefit (DB) pensions have a variety of default risks that decrease the expected value of DB pension wealth. This paper examines those risks. Accrual of DB pension wealth is characterized in terms of purchases of risky bonds. Changing jobs triggers default on these bonds. Simulations are presented to show the potential loss in pension wealth from default. In addition, a methodology used to price corporate bonds is applied to generate estimates of the implied risk premiums of DB pension bonds over comparable riskless bonds.     

Long-Term Disability Claims Rates and the Consumption-to-Wealth Ratio

A framework for linking long-term disability (LTD) claims rates to the macro-economy using the consumption-to-wealth ratio is developed from financial economic and option theories. Financial economic theory suggests that the consumption-to-wealth ratio reflects consumption smoothing and reveals expectations about future wealth. For individuals contemplating submitting an LTD claim, the expected payoff to exercising this insurance option is a function of their expectations about their future wealth. The lower (higher) their expectations about future wealth, the higher (lower) the expected payoff, and the higher (lower) claims rates are likely to be. Using cointegration analysis, we find that LTD claims rates and the consumption-to-wealth ratio are linked in a long-run equilibrium. When the consumption-to-wealth ratio is high (low), LTD claims rates are low (high).