The effect of limited information and estimation risk on optimal portfolio diversification

This paper analyzes the optimal portfolio choice problem when security returns have a joint multivariate normal distribution with unknown parameters. For the case of limited, but sufficient (sample plus prior) information, we show that for a general family of conjugate priors, the optimal portfolio choice is obtained by the use of a mean-variance analysis that differs from traditional mean-variance analysis due to estimation risk. We also consider two illustrative cases of insufficient sample information and minimal prior information and show that in these cases it is asymptotically optimal for an investor to limit diversification to a subset of the securities. These theoretical results corroborate observed investor behavior in capital markets.     

International exchange risk and asset substitutability

This paper estimates subsitutability/complementarity relations among financial assets denominated in foreign currencies. Utilizing a representative investor and a flexible functional form methodology, a mean-variance utility function was estimated and used to determine expected return and variance elasticities between assets in the world portfolio. The hypothesis that international assets are perfect substitutes was rejected. It was also found that relative changes in variance tended to have a bigger impact on asset demand than did relative changes in expected returns. Substituability/complementarity relationships were not strong except in specific cases where strong relationships were expected a priori.     

Time diversification and security preferences: A stochastic dominance analysis

We use stochastic dominance to test whether investor should prefer riskier securities as the investment horizon lengthens. Return distributions for stocks, bonds, and U.S. Treasury bills are generated for holding periods of one to 25 years by simulation. For each holding period, stochastic dominance tests are run to establish preferences between the alternative security classes. Contrary to previous mean-variance based studies, we find no evidence that high-risk securities (stocks) dominate low-risk securities (bonds, Treasury bills) as the investment horizon lengthens. However, we do find that corporate bonds systematically dominate government bonds.     

Estimating Portfolio and Consumption Choice: A Conditional Euler Equations Approach

This paper develops a nonparametric approach to examine how portfolio and consumption choice depends on variables that forecast time-varying investment opportunities. I estimate single-period and multiperiod portfolio and consumption rules of an investor with constant relative risk aversion and a one-month to 20-year horizon. The investor allocates wealth to the NYSE index and a 30-day Treasury bill. I find that the portfolio choice varies significantly with the dividend yield, default premium, term premium, and lagged excess return. Furthermore, the optimal decisions depend on the investor's horizon and rebalancing frequency.     

Islamic and conventional portfolios optimization under investor sentiment states: Bayesian vs Markowitz portfolio analysis

This paper investigates the portfolio optimization under investor’s sentiment states of Hidden Markov model and over a different time horizon during the period 2004–2016. To compare the efficient portfolios of the Islamic and the conventional stock indexes, we have employed two approaches: the Bayesian and Markowitz mean-variance. Our findings reveal that the Bayesian efficient frontier of Islamic and conventional stock portfolios is affected by the investor’s sentiment state and the time horizon. Our findings also indicate that the investor’s sentiment regimes change the Islamic and the conventional optimal diversified portfolios.Moreover, the results show that the potential diversification benefits seem to be more important when using the Bayesian approach than when applying the Markowitz approach. This finding is valid for the bearish, depressed, bullish and calm states in Islamic stock markets. However, the diversification of potential portfolios is significant only for the bullish and the bubble states in the conventional financial markets.The findings of the study provided additional evidence for investors to exploit googling investor sentiment states to evaluate the portfolio performance and make an optimal portfolio allocation.     

Is Mean-Variance Analysis Vacuous: Or was Beta Still Born?

We show in any economy trading options, with investors havingmean-variance preferences, that there are arbitrage opportunitiesresulting from negative prices for out of the money call options.The theoretical implication of this inconsistency is that mean-varianceanalysis is vacuous. The practical implications of this inconsistencyare investigated by developing an option pricing model for aCAPM type economy. It is observed that negative call pricesbegin to appear at strikes that are two standard deviationsout of the money. Such out-of-the money options often trade.For near money options, the CAPM option pricing model is shownto permit estimation of the mean return on the underlying asset,its volatility and the length of the planning horizon. The model is estimated on S&P 500 futures options data coveringthe period January 1992–September 1994. It is found thatthe mean rate of return though positive, is poorly identified.The estimates for the volatility are stable and average 11%,while those for the planning horizon average 0.95. The hypothesisthat the planning horizon is a year can not be rejected. Theone parameter Black–Scholes model also marginally outperformsthe three parameter CAPM model with average percentage errorsbeing respectively, 3.74% and 4.5%. This out performance ofthe Black–Scholes model is taken as evidence consistentwith the mean-variance analysis being vacuous in a practicalsense as well.     

Mean-Gini,Portfolio Theory,and the Pricing of Risky Assets

This paper presents the mean-Gini (MG) approach to analyze risky prospects and construct optimum portfolios. The proposed method has the simplicity of a mean-variance model and the main features of stochastic dominance efficiency. Since mean-Gini is consistent with investor behavior under uncertainty for a wide class of probability distributions, Gini's mean difference is shown to be more adequate than the variance for evaluating the variability of a prospect. The MG approach is then applied to capital markets and the security valuation theorem is derived as a general relationship between average return and risk. This is further extended to include a degree of risk aversion that can be estimated from capital market data. The analysis is concluded with the concentration ratio to allow for the classification of different securities with respect to their relative riskiness.     

Evaluating the effectiveness of monetary reforms

Using a monthly model of the economy, containing a detailed financial sector, various monetary reforms are evaluated in a stochastic setting. The setting is stochastic because parameters must be estimated from finite data sets and because unexplained residuals exist. The objective function is a single-period, simple quadratic function in income. The problem then reduces to finding the opportunity locus (mean-variance curve) corresponding to each reform; the more effective the reform the more favorable the mean-variance tradeoff. The general finding is that most of the reforms considered are effective, but their impact is not very significant.     

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 the sensitivity of mean-variance-efficient portfolios to changes in asset means: some analytical and computational results

This paper investigates the sensitivity of mean-variance(MV)-efficientportfolios to changes in the means of individual assets. Whenonly a budget constraint is imposed on the investment problem,the analytical results indicate that an MV-efficient portfolio'sweights, mean, and variance can be extremely sensitive to changesin asset means. When nonnegativity constraints are also imposedon the problem, the computational results confirm that a positivelyweighted MV-efficient portfolio's weights are extremely sensitiveto changes in asset means, but the portfolio's returns are not.A surprisingly small increase in the mean of just one assetdrives half the securities from the portfolio. Yet the portfolio'sexpected return and standard deviation are virtually unchanged.     

Portfolio selection based on the mean–VaR efficient frontier

Value-at-Risk (VaR) has become one of the standard measures for assessing risk not only in the financial industry but also for asset allocations of individual investors. The traditional mean–variance framework for portfolio selection should, however, be revised when the investor's concern is the VaR instead of the standard deviation. This is especially true when asset returns are not normal. In this paper, we incorporate VaR in portfolio selection, and we propose a mean–VaR efficient frontier. Due to the two-objective optimization problem that is associated with the mean–VaR framework, an evolutionary multi-objective approach is required to construct the mean–VaR efficient frontier. Specifically, we consider the elitist non-dominated sorting Genetic Algorithm (NSGA-II). From our empirical analysis, we conclude that the risk-averse investor might inefficiently allocate his/her wealth if his/her decision is based on the mean–variance framework.     

Are Stocks Really Less Volatile in the Long Run?

According to conventional wisdom, annualized volatility of stock returns is lower over long horizons than over short horizons, due to mean reversion induced by return predictability. In contrast, we find that stocks are substantially more volatile over long horizons from an investor's perspective. This perspective recognizes that parameters are uncertain, even with two centuries of data, and that observable predictors imperfectly deliver the conditional expected return. Mean reversion contributes strongly to reducing long‐horizon variance but is more than offset by various uncertainties faced by the investor. The same uncertainties reduce desired stock allocations of long‐horizon investors contemplating target‐date funds.     

On the Optimal Hedge of a Nontraded Cash Position

In this paper, we focus on the optimal demand for futures contracts by an investor with a logarithmic utility function who attempts to hedge a nontraded cash position. When the analysis is conducted in the “cash-commodity-price” space, we show that the value function associated with the Bernoulli investor program is not additively separable, thus suggesting that this investor hedges against shifts in the opportunity set as represented by the commodity price. By establishing the equivalence between the cash formulation of the problem and the wealth formulation, we are able to analyze the problem in the “wealth-commodity-price” space. In this space, we show the additive separability of the value function when the futures settlement price process is perfectly locally correlated with the commodity price process. The demand for futures in this instance is composed of (a) a mean-variance term and (b) a minimum-variance component that is a classic feature of models with nontraded assets. Since the first-best (nonmyopic) optimum is attained, however, the deviation from a mean-variance demand should not be interpreted as the expression of a nonmyopic behavior but rather as an attempt to restore a first-best optimum. On the other hand, when the correlation between the futures price and the underlying commodity price is imperfect, in general, the value function does not separate additively, the first-best solution cannot be attained, and the optimal futures trading strategy involves a hedging term against shifts in the opportunity set.     

The Role of Learning in Dynamic Portfolio Decisions

This paper analyzes the effect of uncertainty about the mean return on the risky asset on the portfolio decisions of an investor who has a long investment horizon. Building on the earlier work of Detemple (1986), Dothan and Feldman (1986), and Gennotte (1986), it is shown that the possibility of future learning about the mean return on the risky asset induces the investor to take a larger or smaller position in the risky asset than she would if there were no learning, the direction of the effect depending on whether the investor is more or less risk tolerant than the logarithmic investor whose portfolio decisions are unaffected by the possibility of future learning. Numerical calculations show that uncertainty about the mean return on the market portfolio has a significant effect on the portfolio decision of an investor with a 20 year horizon if her assessment of the market risk premium is based solely on the Ibbotson and Sinquefield (1995) data.     

Predictability and diversification benefits of investing in commodity and currency futures

We re-examine diversification benefits of investing in commodities and currencies by considering a risk-averse investor with mean-variance preferences who exploits the possibility of predictable time variation in asset return means, variances, and covariances. We implement unconditional and conditional efficient portfolio strategies designed to exploit this predictability, together with more traditional and/or ad hoc ones yet hitherto relatively unexplored in this context (including the equally weighted, fixed weight, volatility timing, and reward-to-risk timing strategies). We find that, for all portfolio strategies, commodities and currencies do not improve the investment opportunity set of the investor with an existing portfolio of stocks, bonds and T-bills, and an investment horizon of one month. Our findings, which reverse the conclusions of previous studies that focus on static portfolio strategies, are robust across several performance metrics.     

Portfolio selection with skewness: A multiple-objective approach

In the presence of skewness, the portfolio selection entails considering competing and conflicting objectives, such as maximizing both its expected returns and skewness, and minimizing its risk for decreasing absolute risk-aversion investors. Since it is unlikely that a portfolio can solve the multiple-objectives problem simultaneously, a portfolio selection must depend on the investor's preference among objectives. This article shows that investor preference can be incorporated into a polynomial goal programming problem from which a portfolio selection with skewness is determined. An inefficient mean-variance portfolio may be optimal in the mean-variance-skewness content. The features of applying polynomial goal programming in portfolio selection are 1) the existence of an optimal solution, 2) the flexibility of the incorporation of investor preference, and 3) the relative simplicity of computational requirements.     

Modeling risk in arbitrage strategies using finite mixtures§

We revisit the problem of calculating the exact distribution of optimal investments in a mean variance world under multivariate normality. The context we consider is where problems in optimisation are addressed through the use of Monte-Carlo simulation. Our findings give clear insight as to when Monte-Carlo simulation will, and will not work. Whilst a number of authors have considered aspects of this exact problem before, we extend the problem by considering the problem of an investor who wishes to maximise quadratic utility defined in terms of alpha and tracking errors. The results derived allow some exact and numerical analysis. Furthermore, they allow us to also derive results for the more traditional non-benchmarked portfolio problem.     

Short‐Horizon Return Predictability in International Equity Markets

This study measures the degree of short‐horizon return predictability of 50 international equity markets and examines how its variation is related to the indicators of equity market development. Two multiple‐horizon variance ratio tests are employed to measure the degree of return predictability. We find evidence that return predictability is negatively correlated with publicly available indicators of equity market development. Our cross‐sectional regression analysis shows that the per capita gross domestic product, market turnover, investor protection, and absence of short‐selling restrictions are correlated with cross‐market variations in return predictability.     

我国投资者情绪与股票收益实证研究

根据投资者情绪是股票价格形成重要影响因素这一研究观点,围绕投资者情绪是否构成系统性风险及其对不同类型股票的差异化影响,运用我国股市交易数据进行的实证研究结果表明,投资者情绪不构成股市的系统性风险,但对不同市值的股票有着差异化的影响,随着股票的"投机性"增加,投资者情绪对其影响也增大.此外,投资者情绪会削弱股票收益与其波动的正相关性,且对于"投机性"越高的股票,这一影响也越大.