Optimal asset allocation for a large number of investment opportunities

This paper introduces a stock‐picking algorithm that can be used to perform an optimal asset allocation for a large number of investment opportunities. The allocation scheme is based upon the idea of causal risk. Instead of referring to the volatility of the assets time series, the stock‐picking algorithm determines the risk exposure of the portfolio by concerning the non‐forecastability of the assets. The underlying expected return forecasts are based on time‐delay recurrent error correction neural networks, which utilize the last model error as an auxiliary input to evaluate their own misspecification. We demonstrate the profitability of our stock‐picking approach by constructing portfolios from 68 different assets of the German stock market. It turns out that our approach is superior to a preset benchmark portfolio. Copyright © 2005 John Wiley & Sons, Ltd.     

Long‐Run Consumption Risk and Asset Allocation under Recursive Utility and Rational Inattention

We study the portfolio decision of a household with limited information‐processing capacity (rational inattention [RI]) in a setting with recursive utility. We find that RI combined with a preference for early resolution of uncertainty could lead to a significant drop in the share of portfolios held in risky assets, even when the departure from the standard expected utility setting with full‐information rational expectations is small. In addition, we show that the equilibrium equity premium increases with the degree of inattention because inattentive investors with recursive utility face greater long‐run risk and thus require higher compensation in equilibrium.     

Time Diversification,Safety-First and Risk

The purpose of this article is to demonstrate the effect of investment time horizon on the choice of risky assets in a portfolio when the investor in question is optimizing a Safety-First (downside risk-aversion) utility function. It is shown, under standard assumptions, that although shortfall risk decreases exponentially with investment time horizon, the portfolio asset allocation proportions remain invariant. In fact, in some instances, the optimal allocation will not even depend on the drift of the underlying assets. Thus, we extend the classical results of Samuelson and Merton, derived under conventional utility assumptions, to an individual optimizing an A.D. Roy Safety-First objective; a discontinuous utility function that has been extolled as conforming to observed investor behaviour. A numerical example is provided.     

Accounting information,disclosure, and expected utility: Do investors really abhor uncertainty?

Investors are said to “abhor uncertainty,” but if there were no uncertainty they could earn only the risk‐free rate. A fundamental result in the analytical accounting literature shows that investors buying into a CARA‐normal CAPM market pay lower asset prices, gain higher ex‐ante expected returns, and obtain higher expected utility, when the market payoff has higher variance. New investors obtain similar “welfare” gains from risk under a log/power utility CAPM. These results do not imply that investors “abhor information.” To realize investors' ex‐ante expectations, the subjective probability distributions representing market expectations must be accurate. Greater payoff risk can add to investors' expected utility, but higher ex‐post(realized) utility comes from better information and more accurate ex‐ante expectations. An important implication for accounting is that greater disclosure can have the simultaneous effects of (i) exposing more fully or perceptibly firms' payoff uncertainty, thereby increasing new investors' expected utility, and (ii) improving market estimates of firms' payoff parameters (means, variances, covariances), thereby giving investors a better chance of realizing their expectations. Paradoxically, better information can be valuable to new investors by exposing more fully and more accurately the risk in firms' business operations and results–new investors maximizing expected utility want both more risk and better information.     

Portfolio optimization under a generalized hyperbolic skewed t distribution and exponential utility

In this paper, we show that if asset returns follow a generalized hyperbolic skewed t distribution, the investor has an exponential utility function and a riskless asset is available, the optimal portfolio weights can be found either in closed form or using a successive approximation scheme. We also derive lower bounds for the certainty equivalent return generated by the optimal portfolios. Finally, we present a study of the performance of mean–variance analysis and Taylor’s series expected utility expansion (up to the fourth moment) to compute optimal portfolios in this framework.     

Time to wealth goals in capital accumulation

This paper considers the problem of investment of capital in risky assets in a dynamic capital market in continuous time. The model controls risk, and in particular the risk associated with errors in the estimation of asset returns. The framework for investment risk is a geometric Brownian motion model for asset prices, with random rates of return. The information filtration process and the capital allocation decisions are considered separately. The filtration is based on a Bayesian model for asset prices, and an (empirical) Bayes estimator for current price dynamics is developed from the price history. Given the conditional price dynamics, investors allocate wealth to achieve their financial goals efficiently over time. The price updating and wealth reallocations occur when control limits on the wealth process are attained. A Bayesian fractional Kelly strategy is optimal at each rebalancing, assuming that the risky assets are jointly lognormal distributed. The strategy minimizes the expected time to the upper wealth limit while maintaining a high probability of reaching that goal before falling to a lower wealth limit. The fractional Kelly strategy is a blend of the log-optimal portfolio and cash and is equivalently represented by a negative power utility function, under the multivariate lognormal distribution assumption. By rebalancing when control limits are reached, the wealth goals approach provides greater control over downside risk and upside growth. The wealth goals approach with random rebalancing times is compared to the expected utility approach with fixed rebalancing times in an asset allocation problem involving stocks, bonds, and cash.     

KNOW YOUR CLIENT! INVESTOR PROFILE AND TAILOR‐MADE ASSET ALLOCATION RECOMMENDATIONS

We study how the investor profile influences the asset allocation recommendations of professional advisors. We find the investor's perceived risk attitude influences more the mix of risky assets, whereas the socioeconomic variables influence more the cash percentage. The recommendations are consistent with a diversification behavior driven by actual asset correlations. These findings support the utility of investor advisory that may help enhance the risk and return trade‐off. The main drawback of the recommendations may consist in the degree of customization that is limited by the small number of investor characteristics actually influencing the asset allocation.     

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.     

The safety first expected utility model: Experimental evidence and economic implications

Roy’s [Roy, A., 1952. Safety first and the holding of assets. Econometrica 20 (3), 431–449] safety first criterion advocates the minimization of the probability of outcomes below a certain “disaster” level. This paper examines safety first theoretically and experimentally. We find that safety first plays a crucial role in decision-making, inducing choices that cannot be explained by, and even contradict, risk-aversion, Prospect Theory, and loss-aversion in general. Yet, safety first alone cannot explain individual choice. Therefore, we propose an expected utility – safety first (EU–SF) model where decisions are made based on a weighted average of the safety first criterion and standard expected utility maximization. We experimentally estimate these relative weights, and discuss their economic implications.     

Increasing return response to changes in risk

Risk aversion theory is based on an individual's choice among risky assets with expected utility in its foundation. It is about investor behavior (i.e., investor choice), under normal circumstances, toward assets with various levels of risk. A positive and marginally diminishing relationship between risk and return exists. This study is about investor behavior related to their response (not choice) to risk. We present an argument and supporting evidence that investors’ return response to risk is increasing with the level of risk. Thus, investor behavior is subject to change and the level of risk is a determinant of such change. We also explain the negative time‐series correlation between risk and return.     

Risk allocation under liquidity constraints

Risk allocation games are cooperative games that are used to attribute the risk of a financial entity to its divisions. In this paper, we extend the literature on risk allocation games by incorporating liquidity considerations. A liquidity policy specifies state-dependent liquidity requirements that a portfolio should obey. To comply with the liquidity policy, a financial entity may have to liquidate part of its assets, which is costly.The definition of a risk allocation game under liquidity constraints is not straightforward, since the presence of a liquidity policy leads to externalities. We argue that the standard worst case approach should not be used here and present an alternative definition. We show that the resulting class of transferable utility games coincides with the class of totally balanced games. It follows from our results that also when taking liquidity considerations into account there is always a stable way to allocate risk.     

Investment Horizon Effects

Abstract:   Boudry and Gray (2003) have documented that the optimal buy‐and‐hold demand for Australian stocks is not necessarily increasing in the investment horizon when returns are predictable. Such finding is in contrast with Barberis (2000) who shows that positive monotonic horizon effects predominate for US stocks. Using a closed‐form approximation to the asset allocation problem, this paper relates the return dynamics to the investor's portfolio choice for different investment horizons. In the special case of a single risky asset, it is shown that return predictability under stationarity may induce both positive and negative horizon effects in the optimal allocation to the risky asset. The paper extends previous empirical results by solving for the optimal portfolio when two risky assets with predictable returns are available for investment.     

Dynamic preferences for popular investment strategies in pension funds

In this paper, we characterize dynamic investment strategies that are consistent with the expected utility setting and more generally with the forward utility setting. Two popular dynamic strategies in the pension funds industry are used to illustrate our results: a constant proportion portfolio insurance (CPPI) strategy and a life-cycle strategy. For the CPPI strategy, we are able to infer preferences of the pension fund’s manager from her investment strategy, and to exhibit the specific expected utility maximization that makes this strategy optimal at any given time horizon. In the Black–Scholes market with deterministic parameters, we are able to show that traditional life-cycle funds are not optimal to any expected utility maximizers. We also prove that a CPPI strategy is optimal for a fund manager with HARA utility function, while an investor with a SAHARA utility function will choose a time-decreasing allocation to risky assets in the same spirit as the life-cycle funds strategy. Finally, we suggest how to modify these strategies if the financial market follows a more general diffusion process than in the Black–Scholes market.     

风险资产配置与货币政策规则——黏性价格均衡下的宏观资产配置模型初探

本文将一个基于动态新凯恩斯理论的连续时间黏性价格一般均衡模型与随机动态资产配置模型相结合,进而研究基于内生宏观经济动态和货币政策规则进行资产配置的问题。在最优配置策略下,投资者相对风险偏好随无风险名义利率的增大而单调减小,而随通胀率的变化呈“U”型,说明投资者在通胀偏离稳态幅度较大时配置风险资产的相对意愿较高。此外,本文也给出了使用该模型讨论投资者最大化跨期效用对经济反作用这一宏观审慎问题的方式。     

Mitigating Estimation Risk in Asset Allocation: Diagonal Models Versus 1/N Diversification

Recent literature suggests that optimal asset‐allocation models struggle to consistently outperform the 1/N naïve diversification strategy, which highlights estimation‐risk concerns. We propose a dichotomous classification of asset‐allocation models based on which elements of the inverse covariance matrix that a model uses: diagonal only versus full matrix. We argue that parsimonious diagonal‐only strategies, which use limited information such as volatility or idiosyncratic volatility, are likely to offer a good tradeoff between incorporating limited information while mitigating estimation risk. Evaluating five sets of portfolios over 1926–2012, we find that 1/N is generally not optimal when compared with these diagonal strategies.     

Moral hazard,hold‐up,and the optimal allocation of control rights

I examine the optimal allocation of control rights in a model with manager moral hazard, where the manager and investor may hold up each other ex post. The control allocation determines both the likelihood of hold‐up and the agents’ renegotiation payoffs. In equilibrium, only two control allocations are optimal: either exclusive investor control or a contingent control allocation that allows the manager to remain in control if, and only if, interim performance is good. Thus, my model explains why it may be optimal to link control to the firm’s performance such that managers retain control only following good performance.     

Portfolio credit-risk optimization

This paper evaluates several alternative formulations for minimizing the credit risk of a portfolio of financial contracts with different counterparties. Credit risk optimization is challenging because the portfolio loss distribution is typically unavailable in closed form. This makes it difficult to accurately compute Value-at-Risk (VaR) and expected shortfall (ES) at the extreme quantiles that are of practical interest to financial institutions. Our formulations all exploit the conditional independence of counterparties under a structural credit risk model. We consider various approximations to the conditional portfolio loss distribution and formulate VaR and ES minimization problems for each case. We use two realistic credit portfolios to assess the in- and out-of-sample performance for the resulting VaR- and ES-optimized portfolios, as well as for those which we obtain by minimizing the variance or the second moment of the portfolio losses. We find that a Normal approximation to the conditional loss distribution performs best from a practical standpoint.     

Large deviations estimation of the windfall and shortfall probabilities for optimal diversified portfolios

Many investors believe that they can effectively reduce risk by, among other ways, holding large combinations of investment assets. The purpose of this paper is to develop asymptotic approximations of the windfall and shortfall probabilities for an optimal portfolio of risky assets as the number of the assets becomes sufficiently large. We start by providing some heuristics to motivate our problem, then proceed to prove general large deviations theorems. We also present specific results with an application to the multivariate normal case. Both a theoretical analysis of the method and an empirical application justify the diversification tenet of the allocation strategies that many hedge funds and pension funds tend to adopt nowadays.     

Liquidity and capital under uncertainty and changing market sentiment: A simple analysis

This study introduces a general approach to investigate resource allocation and asset prices in an economy with uncertainty and shifts in market sentiment. The approach presents a number of key features: first, it proposes a choice-theoretic model that determines the utility that the agents derive from holding assets with different liquidity. Second, it incorporates a variable (endogenously-determined) cost structure of asset liquidation, which reflects the (in)efficiencies of the financial infrastructure and changes in market moods. Third, it also incorporates a model of expectations formation under uncertainty and changing market sentiment. While rich in structure, the approach offers a simple analytical framework to investigate resource allocation decision and asset price dynamics under various sources of uncertainty, and to explore the micro-economics of speculative bubbles and boom–bust sequences. The use of a possible market-specific prudential policy tool is discussed.