Portfolio selection with mental accounts and delegation

Das et al. (2010) develop an elegant framework where an investor selects portfolios within mental accounts but ends up holding an aggregate portfolio on the mean-variance frontier. This investor directly allocates the wealth in each account among available assets. In practice, however, investors often delegate the task of allocating wealth among assets to portfolio managers who seek to beat certain benchmarks. Accordingly, we extend their framework to the case where the investor allocates the wealth in each account among portfolio managers. Our contribution is threefold. First, we provide an analytical characterization of the existence and composition of the optimal portfolios within accounts and the aggregate portfolio. Second, we present conditions under which such portfolios are not on the mean-variance frontier, and conditions under which they are. Third, we show that the aforementioned analytical characterization is also applicable within the framework of Das et al. and thus improves upon their numerical approach.     

Portfolio selections under mean-variance preference with multiple priors for means and variances

We study portfolio selections under mean-variance preference with multiple priors for means and variances. We introduce two types of multiple priors, the priors for means and the priors for variances of risky asset returns. As our framework, in the absence of a risk-free asset, the global minimum-variance portfolio is optimal when the investor is extremely ambiguity averse with respect to means, and the equally weighted portfolio is optimal when the investor is extremely ambiguity averse with respect to variances.     

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.     

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.     

International portfolio selection and efficiency analysis

In the risk-return tradeoff, the traditional mean-variance analysis has been widely used for studies of international portfolio efficiency and diversification. Without prior knowledge about either the parametric structure of assets' return distributions or the form of investors' preference functions, the variance may no longer serve as a suitable risk proxy. This article examines international portfolio efficiency and diversification effects through mean-variance and various distribution-free (or less restrictive) risk-return measures. We show empirically that the mean-variance model is appropriate for large or well-diversified portfolios, but may provide biased results for single assets and less diversified portfolios. While stochastic dominance stands as theoretically the most appropriate method of international portfolio selection and efficiency analysis, the lack of optimal search algorithms reduces its practical usefulness. Very little gain is obtained by using the Gini-mean-difference risk measure as compared to the semivariance measure. The semivariance measure is a powerful and convenient discriminator of risky prospects, while stochastic dominance can serve as a benchmark to justify portfolio efficiency.     

Portfolio choice and equilibrium in capital markets with safety-first investors

This paper develops optimal portfolio choice and market equilibrium when investors behave according to a generalized lexicographic safety-first rule. We show that the mutual fund separation property holds for the optimal portfolio choice of a risk-averse safety-first investor. We also derive an explicit valuation formula for the equilibrium value of assets. The valuation formula reduces to the well-known two-parameter capital asset pricing model (CAPM) when investors approximate the tail of the portfolio distribution using Tchebychev's inequality or when the assets have normal or stable Paretian distributions. This shows the robustness of the CAPM to safety-first investors under traditional distributional assumptions. In addition, we indicate how additional information about the portfolio distribution can be incorporated to the safety-first valuation formula to obtain alternative empirically testable models.     

Liquidity and conditional portfolio choice: A nonparametric investigation

This paper studies the relation between liquidity and optimal portfolio allocations. Given that the portfolio problem of a constant relative risk aversion investor does not have a closed-form solution, we use a nonparametric approach to estimate the optimal allocations. Using a sample of NYSE stocks from 1963–2000, we find that the optimal portfolio weight in small stocks is strongly increasing in liquidity at short daily and weekly horizons. This result is consistent for three different measures of liquidity: price impact, dollar volume, and turnover. However, liquidity does not influence the optimal portfolio choice for large stocks, nor for longer monthly investment horizons.     

Risk-neutral investors do not acquire information

Give a risk-neutral investor the choice to acquire a costly signal prior to asset market equilibrium. She refuses to pay for the signal under general conditions. The reason is that a risk-neutral investor is indifferent between a risky asset or a safe bond in optimum and expects the same return to her portfolio ex ante, whether or not she acquires information. Risk neutrality thus implies the absence of costly information from asset price in competitive asset markets.     

International diversification and Microfinance

International commercial banks, institutional investors, and private investors have become increasingly interested in financing microfinance institutions (MFIs). This paper investigates whether adding microfinance funds to a portfolio of risky international assets yields diversification gains. By using mean-variance spanning tests with short-sale constraints, we find that investing in microfinance may be attractive for investors seeking a better risk-return profile. Specifically, the analysis suggests that investing in MFIs from Latin America, or microfinance and rural banks yields more efficient portfolios. In contrast, adding MFIs from Africa or microfinance NGOs to a portfolio of international assets is not beneficial for a mean-variance investor.     

Forecasting aggregate stock market volatility with industry volatilities: The role of spillover index

In this paper, we aim to improve the predictability of aggregate stock market volatility with industry volatilities. The empirical results show that individual industry volatilities can provide useful predictive information, while the predictive contribution is limited. We further consider the spillover index between industry volatilities and find it displays strong predictive power for stock market volatility. Based on the portfolio exercise, we find that a mean-variance investor can achieve sizeable economic gains by using volatility forecasts of the spillover index. In addition, we conduct three extended analyses and further demonstrate the superior performance of the spillover index. Also, our results show robustness to a series of alternative settings. Finally, we investigate why the spillover index performs better and answer what information it contains. The results show that the spillover index can reflect and explain investor sentiments that are related to stock market volatility.     

How suboptimal are linear sharing rules?

The objective of this paper is to analyze criteria for portfolio choice when two investors are forced to invest in a common portfolio and share the proceeds by a linear sharing rule. A similar situation with many investors is typical for defined contribution pension schemes. The restriction implies two sources of suboptimal investment decisions as seen from each of the two investors individually. One is the suboptimal choice of portfolio, the other is the forced linear sharing rule. We measure the combined consequence for each investor by their respective loss in wealth equivalent. We show that significant losses can arise when investors are diverse in their risk attitude. We also show that an investor with a low degree of risk aversion, like the logarithmic or the square root investor, often applied in portfolio choice models, can either inflict or be subject to severe losses when being forced to participate in such a common investment pool.     

OPTIMAL PORTFOLIO SELECTION WITH A SHORTFALL PROBABILITY CONSTRAINT: EVIDENCE FROM ALTERNATIVE DISTRIBUTION FUNCTIONS

We propose a new approach to optimal portfolio selection in a downside risk framework that allocates assets by maximizing expected return subject to a shortfall probability constraint, reflecting the typical desire of a risk-averse investor to limit the maximum likely loss. Our empirical results indicate that the loss-averse portfolio outperforms the widely used mean-variance approach based on the cumulative cash values, geometric mean returns, and average risk-adjusted returns. We also evaluate the relative performance of the loss-averse portfolio with normal, symmetric thin-tailed, symmetric fat-tailed, and skewed fat-tailed return distributions in terms of average return, risk, and average risk-adjusted return.     

Dynamic optimal portfolio choice in a jump-diffusion model with investment constraints

We consider the dynamic portfolio choice problem in a jump-diffusion model, where an investor may face constraints on her portfolio weights: for instance, no-short-selling constraints. It is a daunting task to use standard numerical methods to solve a constrained portfolio choice problem, especially when there is a large number of state variables. By suitably embedding the constrained problem in an appropriate family of unconstrained ones, we provide some equivalent optimality conditions for the indirect value function and optimal portfolio weights. These results simplify and help to solve the constrained optimal portfolio choice problem in jump-diffusion models. Finally, we apply our theoretical results to several examples, to examine the impact of no-short-selling and/or no-borrowing constraints on the performance of optimal portfolio strategies.     

An Empirical Analysis on Log-Utility Asset Management

In this paper, we empirically verify the optimal portfolio schemes for the log-utility investor under incomplete information which converge to the optimal portfolio maximizing the expected log-utility under complete information. That is, our main interest lies in examining whether these schemes really attain the above desired properties, in the NYSE/AMEX stock market. With these properties regarded as performance measures, our empirical research is executed through a sensitivity analysis with transaction costs. Moreover, we show the interesting character of the U.S. stock market exhibited through the analysis.     

Benefits of international diversification with investment constraints: An over-time perspective

This paper investigates the benefits and asset allocation of the optimal international diversification for the U.S.A. investor while considering various portfolio constraints. Although the global financial market is becoming more integrated, the findings suggest that adding lower and upper weighting bounds reduces, but does not completely eliminate, the potential economic value of international investment. The addition of investment constraints makes asset allocation more feasible and decreases the volatility in portfolio return. The time-variation in the optimal asset allocation implies that fund managers should rebalance international portfolios dynamically. The out-of-sample test suggests that the Markowitz model with constraints realizes trivial improvement in mean-variance efficiency but still demonstrates significant reduction in risk.     

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.     

SINGLE-PERIOD MEAN-VARIANCE IN A MULTIPERIOD CONTEXT

It is not readily apparent that the single-period mean and variance are sufficient to specify the investor choice problem when the investor horizon is greater than one period. It is pointed out that the standard justifications for use of single-period mean-variance analysis are inconsistent with the assumptions usually made in the multiperiod problem. It is argued, however, that if the investor horizon is long enough, the single-period mean and variance will be approximately sufficient. The argument is much less restrictive than the standard justifications for the use of single-period mean-variance analysis. The predictions of this alternative justification are empirically tested and found to be quite accurate for the time frames found in the literature.     

The Effect of Shortfall as a Risk Measure for Portfolios with Hedge Funds

Abstract:  Current research suggests that the large downside risk in hedge fund returns disqualifies the variance as an appropriate risk measure. For example, one can easily construct portfolios with nonlinear pay-offs that have both a high Sharpe ratio and a high downside risk. This paper examines the consequences of shortfall-based risk measures in the context of portfolio optimization. In contrast to popular belief, we show that negative skewness for optimal mean-shortfall portfolios can be much greater than for mean-variance portfolios. Using empirical hedge fund return data we show that the optimal mean-shortfall portfolio substantially reduces the probability of small shortfalls at the expense of an increased extreme crash probability. We explain this by proving analytically under what conditions short-put payoffs are optimal for a mean-shortfall investor. Finally, we show that quadratic shortfall or semivariance is less prone to these problems. This suggests that the precise choice of the downside risk measure is highly relevant for optimal portfolio construction under loss averse preferences.     

Learning about Predictability: The Effects of Parameter Uncertainty on Dynamic Asset Allocation

This paper examines the effects of uncertainty about the stock return predictability on optimal dynamic portfolio choice in a continuous time setting for a long-horizon investor. Uncertainty about the predictive relation affects the optimal portfolio choice through dynamic learning, and leads to a state-dependent relation between the optimal portfolio choice and the investment horizon. There is substantial market timing in the optimal hedge demands, which is caused by stochastic covariance between stock return and dynamic learning. The opportunity cost of ignoring predictability or learning is found to be quite substantial.     

The 1/n Pension Investment Puzzle

Abstract

This paper examines the so-called 1/n investment puzzle that has been observed in defined contribution plans whereby some participants divide their contributions equally among the available asset classes. It has been argued that this is a very naive strategy since it contradicts the fundamental tenets of modern portfolio theory. We use simple arguments to show that this behavior is perhaps less naive than it at first appears. It is well known that the optimal portfolio weights in a mean-variance setting are extremely sensitive to estimation errors, especially those in the expected returns. We show that when we account for estimation error, the 1/n rule has some advantages in terms of robustness; we demonstrate this with numerical experiments. This rule can provide a risk-averse investor with protection against very bad outcomes.