An algebraic theory of portfolio allocation

Summary. Using group and majorization theory, we explore what can be established about allocation of funds among assets when asymmetries in the returns vector are carefully controlled. The key insight is that preferences over allocations can be partially ordered via majorized convex hulls that have been generated by a permutation group. Group transitivity suffices to ensure complete portfolio diversification. Point-wise stabilizer subgroups admit sectoral separability in fund allocations. We also bound the admissible allocation vector by a set of linear constraints the coefficients of which are determined by group operations on location and scale asymmetries in the rate of returns vector. For a distribution that is symmetric under a reflection group, the linear constraints may be further strengthened whenever there exists an hyperplane that separates convex sets. Received: May 15, 2001; revised version: March 20, 2002 RID="*" ID="*" Journal paper No. J-19797 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project No. 3463, and supported by Hatch Act and State of Iowa funds. Correspondence to: D. A. Hennessy     

A characterization of the distributions that imply mean—Variance utility functions

If there is a riskless asset, then the distribution of every portfolio is determined by its mean and variance if and only if the random returns are a linear transformation of a spherically distributed random vector. If there is no riskless asset, then the spherically distributed random vector is replaced by a random vector in which the last n ? 1 components are spherically distributed conditional on the first component, which has an arbitrary distribution. If the number of assets is infinite, then there must exist random variables m, v, y, where the distribution of y conditional on m and v is standard normal, such that every portfolio is distributed as some linear combination of m and vy. If there is a riskless asset, then m has zero variance. These distributions exhibit two-fund separability even if the utility function is not concave.     

Robustness of the market model

Summary The market model specifies that the random vector of returns on risky assets is an affine function of the return on the market portfolio plus a residual which has zero conditional expectation given the return on the market. The model is important because of its intimate relation to distributional two-fund separation and the CAPM equation. This paper shows that the market model is robust to small changes in the asset supplies only if the distribution of returns is spherically generated.     

The importance of fear: investor sentiment and stock market returns

The presence of investor sentiment pushes asset prices away from the equilibrium level justified by underlying fundamentals. While sentiment is not directly observable, identifying appropriate proxies and, quantifying the impact of sentiment on asset prices is an important topic. Asset prices that do not appropriately reflect fundamental values may result in inefficient allocation of capital – impacting portfolio allocation decisions and the cost of capital. Utilizing a number of sentiment proxies, over the period 1990–2015, we demonstrate a strong relationship between investor sentiment and stock returns that is consistent with theoretical explanations of sentiment. We determine that implied volatility index (VIX) is the preferred measure of sentiment in terms of improving model fit and adding explanatory power. Causality tests suggest that investor fear (VIX) drives returns across firm-size and value, and also across industry. We also illustrate that firms that are more subjective to value, or face limits to arbitrage, such as small-cap stocks, or those in the business equipment (technology) or telecoms industry, are most responsive to changes investor sentiment. Finally, we demonstrate that sentiment has a greater influence on market returns during recession, when sentiment is at its lowest ebb, and this is particularly true for those stocks most susceptible to speculative demand.     

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.     

Economies of scale in Norwegian electricity distribution: a quantile regression approach

In this article, we investigate scale economies in Norwegian electricity distribution companies using a quantile regression approach. To the best of our knowledge, this is the first attempt to apply this estimation technique when analysing scale economies. We estimate the cost elasticities of the two output components: network length and number of customers, to calculate returns to scale. Our results show large potential of scale economies, particularly for the smallest companies. We also find that returns to scale is increasing over time. These findings have important implications for policymakers when they are deciding the structure of the industry in the future.     

The effect of the tax reform act of 1986 on the location of assets in financial services firms

This paper examines the effects of the Tax Reform Act of 1986 on the international location decisions of U.S. financial services firms. The Act included rule changes that made it substantially more difficult for U.S. firms to defer U.S. taxes on overseas financial services income held in low-tax jurisdictions. We use information from the tax returns of U.S. corporations to examine how local taxes affect the allocation of financial assets held abroad by financial services firms. We find that, before the Act, the location of reported assets in financial subsidiaries was responsive to differences in host country tax rates across jurisdictions. However, after the Act, differences in host country tax rates no longer explain the distribution of assets held in financial services subsidiaries abroad. Our results suggest that the tightening of the anti-deferral provisions applicable to financial services companies has been successful in diminishing the effect of host country income taxes on asset location decisions.     

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.     

Tax Rate Variability and Public Spending as Sources of Indeterminacy

We consider a constant returns to scale, one sector economy with segmented asset markets of the Woodford type. We analyze the role of public spending, financed by labor income and consumption taxation, on the emergence of indeterminacy. We find that what is relevant for indeterminacy is the variability of the distortion introduced by government intervention. We show that the degree of public spending externalities in preferences affects the combinations between the tax rate and its variability under which indeterminacy occurs. Moreover, we find that consumption taxes can lead to local indeterminacy when asset markets are segmented.     

Rational functions: an alternative approach to asset pricing

This paper shows that asset prices are linear polynomials of various underlying explanatory factors and asset returns being ratios of these polynomials, are rational functions that do not add linearly when averaging. Hence, average returns should be modeled based on stock prices. However, continuous returns may be treated as approximately linear across time and modeled directly. Our new Rational Function (RF) models, empirically outperform the traditional asset pricing models like the Capital Asset Pricing Model (CAPM) and the Fama–French three and five-factor models for both average and continuous returns. Moreover, the RF theory also provides a model to estimate the asset volumes. The average change in asset volumes together with average returns provide the estimates for average change in market values of assets. Thus, the RF model approach can be used to select assets that provide either highest returns for profit maximization or highest change in market values for wealth maximization for given levels of risk.     

External Economies of Scale and Optimal Plant Location

This paper departs from earlier work on location theory by introducing external economies of scale into the Weber–Moses location model. It is shown that under Cournot–Nash competition, when external economies prevail, constant returns to scale at the firm level is not a sufficient condition for ensuring the invariance of the firm's optimal location with respect to a change in market demand, regardless of whether or not free entry is allowed. Moreover, when free entry is allowed and the production function exhibits decreasing returns to scale, but with very strong external economies, the optimal location moves towards or away from the market as demand increases according to whether the demand function is convex or concave. These results are different significantly from the conventional wisdom.     

An examination of the economic significance of stock return predictability in UK stock returns

We explore the out-of-sample performance of domestic UK asset allocation strategies that use forecasts of expected returns from a linear predictive regression and those that are implied by asset pricing models such as the capital asset pricing model (CAPM) or arbitrage pricing theory (APT). Our findings suggest that using forecasts of expected returns from the predictive regression generate significant benefits in out-of-sample performance. We find the performance of the strategies using expected return forecasts implied by the CAPM or APT is lower than the predictive regression strategy. However, with binding investment constraints, the performance of the APT matches that of the predictive regression.     

Are stocks desirable in tax-deferred accounts?

Existing literature suggests that, in order to maximize the tax benefit of retirement accounts, investors should follow a “pecking order” location rule of placing highly taxed assets (e.g., bonds) in a tax-deferred account and lightly taxed assets (e.g., stocks) in a taxable account. Empirical evidence, however, documents that a large number of investors violate this rule. In this paper, we show that such violations can be optimal for risk-averse investors who face portfolio constraints. In particular, while the strategy of placing bonds in the tax-deferred account maximizes the expected level of tax benefit, it may lead to volatile benefits under different realizations of stock returns. By holding a similar portfolio in both accounts, investors can achieve a more balanced growth in the two accounts, minimize the likelihood of violating the constraints in the future and hence “smooth” the volatility of the tax benefit. For some risk-averse investors, this smoothing motive can lead to the observed violation of the pecking order location rule. Our model predicts that such violations are more likely when future tax benefits are more volatile, which can occur, for example, when: (i) the tax rate differential across assets increases over time due either to tax law changes or to tax bracket changes for investors; (ii) asset returns are more volatile; and (iii) investors anticipate large future liquidity needs.     

Luck versus skill over time: time-varying performance in the cross-section of mutual fund returns

ABSTRACT

Using returns histories spanning January 1984 to October 2014 of 5785 actively managed US closed-end equity mutual funds, we address the ‘thorny problems’ highlighted by Fama and French (The Journal of Finance, 2010, vol. 65, p. 1925) that arise due to their resampling procedure. This prevents them from capturing time variation in the parameters of equilibrium asset pricing models. These problems are addressed by combining innovative procedures which allow for testing of multiple break dates on fund-specific parameters along with cross-section bootstraps that remain valid in the presence of time-varying parameters. We find that substantial proportion – 8% – of the estimated versions of the asset pricing model have significant changes in their parameters. The effects of this time variation on the cross-section distribution of the risk-adjusted performance measure are significant and substantially increase centiles of the right tail of this distribution when compared to those produced without time-varying parameters. Our evidence regarding the lack of actively managed US equity mutual funds that generate excess returns is significantly weaker than those of Fama and French but our results do not overturn their pessimistic conclusion regarding the lack of skilled managers. We do find, unlike Fama and French, that managers generating negative returns are just unlucky but have no skill.     

DEFINED CONTRIBUTION PLANS, DEFINED BENEFIT PLANS, AND THE ACCUMULATION OF RETIREMENT WEALTH

The private pension structure in the United States, once dominated by defined benefit (DB) plans, is currently divided between defined contribution (DC) and DB plans. Wealth accumulation in DC plans depends on a participant's contribution behavior and on financial market returns, while accumulation in DB plans is sensitive to a participant's labor market experience and to plan parameters. This paper simulates the distribution of retirement wealth under representative DB and DC plans. It uses data from the Health and Retirement Study (HRS) to explore how asset returns, earnings histories, and retirement plan characteristics contribute to the variation in retirement wealth outcomes. We simulate DC plan accumulation by randomly assigning individuals a share of wages that they and their employer contribute to the plan. We consider several possible asset allocation strategies, with asset returns drawn from the historical return distribution. Our DB plan simulations draw earnings histories from the HRS, and randomly assign each individual a pension plan drawn from a sample of large private and public defined benefit plans. The simulations yield distributions of both DC and DB wealth at retirement. Average retirement wealth accruals under current DC plans exceed average accruals under private sector DB plans, although DC plans are also more likely to generate very low retirement wealth outcomes. The comparison of current DC plans with more generous public sector DB plans is less definitive, because public sector DB plans are more generous on average than their private sector DB counterparts.     

The pricing of time-varying beta

We generalize an asset pricing model based on the Arbitrage Pricing Theory (APT) allowing beta to be time-varying. Making beta a random variable adds flexibility to the model because permits a non-linear relation between individual returns and the set of factors, and accounts for the effect of possible omitted variables. We integrate the conditional APT with a general linear stochastic process for beta. We analyze the behavior of the conditional expected return, the conditional variance and conditional covariance of individual asset returns as functions of the conditional moments of beta. On considering time-varying betas we introduce another source of uncertainty (risk) independent of the factors. We need to disentangle if this extra risk is systematic or non-systematic. To this end, we introduce a modified conditional APT model that rationalizes why the time variation of beta may represent extra systematic risk. For a sample of individual stocks, we test the hypothesis of time-varying beta and the feasibility of the modified conditional APT. We present a test for time-varying beta based on the conditional second moments of returns. We find that there is strong evidence against constancy of betas in favor of a random coefficient model, and that the time variation of beta is due to non-systematic behavior of the firms and investors should be able to diversify this risk away.     

Malmquist and Törnqvist productivity indexes: returns to scale and technical progress with imperfect competition

Caves, Christensen and Diewert proposed a method for estimating a theoretical productivity index for a firm using Törnqvist input and output indexes, augmented by exogenous estimates of local returns to scale. However, in order to implement their method, they assumed that the firm maximized revenue in each period, conditional on the observed input vector in each period, taking output prices as fixed. This assumption is not warranted when there are increasing returns to scale. Thus in the present paper, it is assumed that the firm solves a monopolistic profit maximization problem when there are increasing returns to scale and the results of Caves, Christensen and Diewert are modified in accordance with this assumption.     

Decentralized resource allocation and increasing returns

We study the possibility of designing a decentralized resource allocation mechanism that yields optimal solutions in economies with increasing returns. After a brief review of the mechanisms already designed to cope with nonconvexities, we find out that either they fail to provide efficient solutions in Koopmans' sense, or else they use extremely complex messages. The question arises whether it is possible to define a nonwasteful and privacy-preserving mechanism over a class of environments with increasing returns using finite-dimensional vectors as messages. We show that the answer is no.     

Investment horizon effect on asset allocation between value and growth strategies

How does the optimal risk exposure of assets change as their investment horizons increase? Does this impact investment portfolio decision-making, in particular, optimal asset allocation between value and growth strategies over various investment horizons? This paper adopts a new approach to address these questions by examining portfolio allocation between value and growth stocks over various investment horizons. This new approach is based on wavelet analysis, which decomposes the returns of a particular investment strategy across multiple investment horizons. The key empirical results show that the success of pursuing the value strategy (short-selling growth stocks and going long on value stocks) is impacted by the approach used to classify value and growth stock returns. We explore two common alternatives: Fama-French versus Standard & Poor's (S&P) 500/Barra portfolios. The results using Fama-French portfolios show that as the investment horizon increases, the optimal mean allocation of investors tilts heavily away from growth stocks, particularly for lower and moderate levels of risk aversion. Interestingly, for S&P 500/Barra portfolios the allocation weights between value and growth do not vary much.     

上市公司大股东控制下的资本配置行为研究——基于控制权收益视角的实证分析

基于控制权收益①驱动公司资本配置行为的理论阐释,结合我国上市公司特有的股权结构及其导致的控制权分配格局,文章从固定资产投资和股权投资两个方面,对形成我国上市公司控制权收益的资本配置行为进行了实证研究。研究结果表明:(1)控制权收益水平与资本配置规模显著正相关;(2)控制权收益水平越高,则增加等量控制权收益所需的资本配置规模就越大;(3)较固定资产投资而言,通过股权并购方式取得控制权收益的代价较低,但控制性股东占有被并购公司控制权收益的比例也较低;(4)上市公司资本配置行为在形成控制权收益的同时并没有通过提高公司业绩而增加控制权的共享收益,资本配置决策在很大程度上是大股东控制下的自利行为。