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In this paper using inverse statistics analysis, the effect of investment horizon on the efficiency of portfolio selection is examined. Inverse statistics analysis is a general tool also known as probability distribution of exit time that is used for detecting the distribution of the time in which a stochastic process exits from a zone. This analysis was used in Refs. 1 and 2 for studying the financial returns time series. This distribution provides an optimal investment horizon which determines the most likely horizon for gaining a specific return. Using samples of stocks from Tehran Stock Exchange (TSE) as an emerging market and S&P 500 as a developed market, effect of optimal investment horizon in asset allocation is assessed. It is found that taking into account the optimal investment horizon in TSE leads to more efficiency for large size portfolios while for stocks selected from S&P 500, regardless of portfolio size, this strategy does not only not produce more efficient portfolios, but also longer investment horizons provides more efficiency.

This paper provides an introduction to how, on the basis of concepts from fuzzy logic, a model of asset allocation can be constructed which can represent and aggregate all the relevant quantitative and qualitative features of an investment plan realistically and in this way attains comparatively good recommendations like an expert. All calculation steps are carried out in a transparent and reproducible manner. In order to clarify the approach and the advantages of the procedure, a pilot model is developed. This supports the advisor with the asset allocation, by first analysing the features of the investment goal and the market expectations and then evaluating the merits of several investment strategies as well as displaying the steps towards their evaluation in a comprehensible manner. Based on case studies, the results of the pilot model are compared with known good recommendations from an investigation of Stiftung Warentest on the quality of advice in banks.

The paper examines the optimal annuitization time and the optimal consumption/investment strategies for a retired individual subject to a constant force of mortality in an all-or-nothing framework. We allow for a different utility of consumption before and after annuitization. For a general family of preferences we characterize the value function and the optimal controls of the resulting combined stochastic control and optimal stopping problem. Assuming power utility functions we obtain explicit solutions. We show that if the individual evaluates the consumption flow and the annuity payments stream in the same way, then, depending on the parameters of the economy, the annuity is purchased at retirement or never. In the case when the individual is more risk averse in the annuity assessment, it is optimal to defer the annuitization until her wealth reaches a threshold, and such threshold depends on the parameters of the economy.

In this paper we derive sequential procedures for monitoring the structure of the tangency portfolio. A new measure of the distance between the estimated weights and the weights of the holding portfolio is suggested which is used in the derivation of the control schemes. The results are applied in a situation that is practically relevant.

This paper provides a detailed overview of the current research linking systemic risk, financial crises and contagion effects among assets on the one hand with asset allocation and asset pricing theory on the other hand. Based on the ample literature about definitions, measurement and properties of systemic risk, we derive some elementary ingredients for models of financial contagion and assess the current state of knowledge about asset allocation and asset pricing with explicit focus on systemic risk. The paper closes with a brief outlook on future research possibilities and some recommendations for the further development of capital market models incorporating financial contagion.

This paper demonstrates the simple incorporation of any shape of risk aversion into an asset allocation framework. Indeed, the relevant literature about risk aversion shows mixed evidence regarding the shape of this important but subjective variable. Our setting builds on, and can be compared with, the well-known constant relative risk aversion (CRRA) framework and mostly preserves the tractability of the affine-CRRA framework. Our numerical analysis exhibits some link between measures of risk aversions and empirical studies of asset allocation.

This paper explores dynamic mean-variance (MV) asset allocation over long horizons. This is equivalent to target-based investing with a quadratic loss penalty for deviations from the target level of terminal wealth. We provide a number of illustrative examples in a setting with a risky stock index and a risk-free asset. Our underlying model is very simple: the value of the risky index is assumed to follow a geometric Brownian motion diffusion process and the risk-free interest rate is specified to be constant. We impose realistic constraints on the leverage ratio and trading frequency. In many of our examples, the MV optimal strategy has a standard deviation of terminal wealth less than half that of a constant proportion strategy which has the same expected value of terminal wealth, while the probability of shortfall is reduced by a factor of two to three. We investigate the robustness of the model through resampling experiments using historical data dating back to 1926. These experiments also show much lower standard deviation and shortfall probability for the MV optimal strategy relative to a constant proportion strategy with approximately the same expected terminal wealth.

In this paper, we consider the estimation of the weights of tangent portfolios from the Bayesian point of view assuming normal conditional distributions of the logarithmic returns. For diffuse and conjugate priors for the mean vector and the covariance matrix, we derive stochastic representations for the posterior distributions of the weights of tangent portfolio and their linear combinations. Separately, we provide the mean and variance of the posterior distributions, which are of key importance for portfolio selection. The analytic results are evaluated within a simulation study, where the precision of coverage intervals is assessed.

Optimal stochastic control methods are used to examine decumulation strategies for a defined contribution (DC) plan retiree. An initial investment horizon of 15 years is considered, since the retiree will attain this age with high probability. The objective function reward measure is the expected sum of the withdrawals. The objective function tail risk measure is the expected linear shortfall with respect to a desired lower bound for wealth at 15 years. The lower bound wealth level is the amount which is required to fund a lifelong annuity 15 years after retirement, which generates the required minimum cash flows. This ameliorates longevity risk. The controls are the withdrawal amount each year, and the asset allocation strategy. Maximum and minimum withdrawal amounts are specified. Specifying a short initial decumulation horizon, results in the optimal strategy achieving: (i) median withdrawals at the maximum rate within 2–3 years of retirement (ii) terminal wealth larger than the desired lower bound at 15 years, with greater than $90\%$ probability and (iii) median terminal wealth at 15 years considerably larger than the desired lower bound. The controls are computed using a parametric model of historical stock and bond returns, and then tested in bootstrap resampled simulations using historical data. At the 15 year investment horizon, the retiree has the option of (i) continuing to self-manage the decumulation policy or (ii) purchasing an annuity.

We consider the practical investment consequences of implementing the two most popular formulations of the scalarization (or risk-aversion) parameter in the time-consistent dynamic mean–variance (MV) portfolio optimization problem. Specifically, we compare results using a scalarization parameter assumed to be (i) constant and (ii) inversely proportional to the investor’s wealth. Since the link between the scalarization parameter formulation and risk preferences is known to be nontrivial (even in the case where a constant scalarization parameter is used), the comparison is viewed from the perspective of an investor who is otherwise agnostic regarding the philosophical motivations underlying the different formulations and their relation to theoretical risk-aversion considerations, and instead simply wishes to compare investment outcomes of the different strategies. In order to consider the investment problem in a realistic setting, we extend some known results to allow for the case where the risky asset follows a jump-diffusion process, and examine multiple sets of plausible investment constraints that are applied simultaneously. We show that the investment strategies obtained using a scalarization parameter that is inversely proportional to wealth, which enjoys widespread popularity in the literature applying MV optimization in institutional settings, can exhibit some undesirable and impractical characteristics.

We determine a simple dynamic benchmark for asset allocation by solving an optimal stochastic control problem for outperforming the traditional constant proportion benchmark. An objective function based on a time averaged quadratic deviation from an elevated benchmark is proposed. We argue that this objective function combines the best features of tracking error and tracking difference. Assuming parametric models of the stock and bond processes, a closed form solution for the optimal control is obtained. The closed form optimal control is then clipped to prevent use of excessive leverage, and to prevent trading if insolvent. Monte Carlo computations using this clipped control are presented which show that for modest levels of outperformance (i.e. 80–170bps per year), this easily implementable strategy outperforms the traditional constant proportion benchmark with high probability. We advocate this clipped optimal strategy as a suitable benchmark for active asset allocation.

Supplementing the literature on information sharing between firms, the paper seeks to understand information sharing between hackers and how firms defend against increasingly sophisticated hackers. Each hacker seeks financial gain, mutually beneficial information exchange, and reputation gain. The two hackers’ attack and the firm’s defense are inverse U shaped in each other. A hacker shifts from attack to information sharing when attack is costly or the firm’s defense is cheap. The first hacker’s information sharing increases as both hackers focus increasingly on reputation gain. The two hackers largely increase their information sharing, with two exceptions. The second hacker’s attack is deterred by the first hacker’s reputation gain. The firm’s defense against the second hacker increases in the second hacker’s unit cost, decreases in the second hacker’s information sharing effectiveness and utilization of joint sharing, and also decreases in both hackers’ reputation gain. Policy and managerial implications are provided.

One firm defends proactively or retroactively against a first hacker, and thereafter against a second hacker, in four four-period games. The hackers share information for financial gain, mutual advantage, and reputation. The first hacker’s attack and information sharing are strategic substitutes. When the firm is proactive in period 1, the first hacker’s information sharing decreases as the second hacker’s attack cost increases. The deterring effort in eight corner solutions is proportional to the deterred player’s valuation and inverse proportional to the deterred player’s unit effort cost. When the first hacker exerts higher effort and shares more information, lower defense by the firm is sufficient to deter the second hacker. When the firm is deterred by the first hacker, the first hacker attacks less and shares more information than in the interior solution. For the first hacker and the firm, both players commonly prefer the disadvantaged player to move first. The exception is that the firm prefers to deter the first disadvantaged hacker when the two hackers benefit substantially from information sharing, reputation gain, or the second player is advantaged. The results contrast with the literature where the advantaged player commonly prefers to move first, with conflicting sequence preferences.

While indices, index tracking funds and ETFs have grown in popularity during then last ten years, there are many structural problems, tracking errors and biases inherent in index calculation methodologies and the legal/economic structure of ETFs, which raise actionable issues of "suitability" and "fraud" under US securities laws. This article contributes to the existing literature by: (a) introducing and characterizing the errors and biases inherent in "risk-adjusted" index-weighting methods and the associated adverse effects; (b) showing how these biases/effects reduce social welfare, and can facilitate harmful arbitrage activities; (c) introducing new theorems.

We study the dynamics of gains from sectoral versus geographic diversification and relate economic sources to changes in those gains. We estimate conditional correlations between returns on the US equity market and 16 equity markets and 10 local industries from other OECD countries and find that the average correlation across countries has increased in relation to that across industries. We also show that this process is accompanied by increased alignment in the industrial structures across countries and an increase in the average conditional correlation of aggregate production growth across countries relative to that of disaggregated production growth, especially among developed economies. Thus, the increased benefits of industry-level investing across developed markets are reflected in the real side of the global economy. However, country-level investing should remain the predominant asset allocation approach in emerging markets.

We derive allocation rules under isoelastic utility for a mixed jump-diffusion process in a two-asset portfolio selection problem with finite horizon in the presence of proportional transaction costs. We adopt a discrete-time formulation, let the number of periods go to infinity, and show that it converges efficiently to the continuous-time solution for the cases where this solution is known. We then apply this discretization to derive numerically the boundaries of the region of no transactions. Our discrete-time numerical approach outperforms alternative continuous-time approximations of the problem.

We derive allocation rules under isoelastic utility for a mixed jump-diffusion process in a two-asset portfolio selection problem with finite horizon in the presence of proportional transaction costs; we allow cash dividends on the risky asset. The allocation shifts toward the riskless asset relative to diffusion in varying degrees depending on parameter values. It is sensitive to the proportion of the jump component to total volatility, but also to the expected amplitude for a given proportion. The shift becomes small when the relative risk aversion increases, but it becomes major when the solvency constraint is active in the presence of jumps. We derive utility losses and risk premia due to jumps under realistic parameter values, and show that even when the no transaction region is very similar between pure diffusion and the mixed process the latter corresponds to lower utility because of higher portfolio restructuring costs.

With Private Funds having a new type of license for asset allocation practice in China, comprehensive asset allocation cross private equity and stock market has received more attention. However, most of the studies focus more on the stock market, and asset allocation models for private equity market that are mainly made based on experience. Thus, the joint allocation of assets crosses both markets making it a challenging research topic. This paper introduces the Black–Litterman model into the private equity market, realizing the transition from qualitative models to quantitative models. It lays a solid quantitative ground for the mixed asset allocation model in both the markets.

We argue that ambiguous correlation between asset payoffs plays an important role in the occurrence of “flight to quality”, which in some circumstances leads investors with incomplete information to portfolio under-diversification. In this paper, we consider a multi-asset economy with four types of investors who have heterogeneous beliefs on correlation coefficients, and in which ambiguity-averse traders make decisions in a maxmin expected utility framework. A unique general equilibrium presents in four scenarios according to the dispersion of asset quality. We define a measure to gauge the degree of portfolio under-diversification, with which we show that correlation ambiguity will drive less-informed investors to hold a nondiversified portfolio if the correlation coefficient is negative, while a positive correlation drives some less-informed investors to hold a fully diversified portfolio.

In this chapter, we first discuss utility theory and utility function in detail, then we show how asset allocation can be done in terms of the quadratic utility function. Based upon these concepts, we show Markowitz’s portfolio selection model can be executed by constrained maximization approach. Real world examples in terms of three securities are also demonstrated. In the Markowitz selection model, we consider that short sale is both allowed and not allowed.