Analytical solutions of optimal portfolio rebalancing

We study optimal portfolio rebalancing in a mean-variance type framework and present new analytical results for the general case of multiple risky assets. We first derive the equation of the no-trade region, and then provide analytical solutions and conditions for the optimal portfolio under several simplifying yet important models of asset covariance matrix: uncorrelated returns, same non-zero pairwise correlation, and a one-factor model. In some cases, the analytical conditions involve one or two parameters whose values are determined by combinatorial, rather than numerical, algorithms. Our results provide useful and interesting insights on portfolio rebalancing, and sharpen our understanding of the optimal portfolio.     

A conditional asset-pricing model with the optimal orthogonal portfolio

This paper employs a conditional asset-pricing model based on the optimal orthogonal portfolio approach to construct a factor portfolio that embodies all the latent factors important for pricing a given set of test assets. The advantage of this portfolio to the anomaly related mimicking portfolios is its ability to separate out the components of average return that are not related to the return covariation. The performance of this portfolio is evaluated against several conventional factors, using both cross-sectional and time-series regression approaches, as well as the Hansen and Jagannathan (1997) distance measure. Its strong out-of-sample results indicate that our suggested methodology may have important applications in risk management, portfolio selection and performance evaluation.     

When it comes to the crunch: Retail investor decision-making during periods of market volatility

Attitude to risk questionnaires are widely used by financial advisors to recommend investments of appropriate risk levels to their clients. Yet the usefulness of this instrument to gauge how investors will react when faced with extreme volatility in the values of their assets remains untested. Using realistic scenarios and based on a large-scale survey in the UK, in this study we examine how the investing public reacts to actual portfolio losses. We find that conventional risk tolerance measures are inadequate for determining whether investors would ‘sell out’ or hold their portfolios in such circumstances. On the other hand, we find that past experience, emotions and personality characteristics, including measures of financial self-efficacy and extraversion, are significant predictors of investor reactions to market crashes.     

Challenging the robustness of optimal portfolio investment with moving average-based strategies

The aim of this paper is to compare the performance of a theoretically optimal portfolio with that of a moving average-based strategy in the presence of parameter misspecification. The setting we consider is that of a stochastic asset price model where the trend follows an unobservable Ornstein–Uhlenbeck process. For both strategies, we provide the asymptotic expectation of the logarithmic return as a function of the model parameters. Then, numerical examples are given, showing that an investment strategy using a moving average crossover rule is more robust than the optimal strategy under parameter misspecification.     

Exploring the benefits of using stock characteristics in optimal portfolio strategies

I examine the benefits of using stock characteristics to model optimal portfolio weights in stock selection strategies using the characteristic portfolio approach of Brandt, Santa-Clara, and Valkanov. [2009. “Parametric Portfolio Policies: Exploiting Characteristics in the Cross-section of Equity Returns.” Review of Financial Studies 22: 3411–3447]. I find that there are significant out-of-sample performance benefits in using characteristics in stock selection strategies even after adjusting for trading costs, when investors can invest in the largest 350 UK stocks. Imposing short selling restrictions on the characteristic portfolio strategy leads to more consistent performance. The performance benefits are concentrated in the earlier part of the sample period and have disappeared in recent years. I find that there no performance benefits in using stock characteristics when using random subsets of the largest 350 stocks.     

The effect of estimation risk on optimal portfolio choice

This paper determines the effect of estimation risk on optimal portfolio choice under uncertainty. In most realistic problems, the parameters of return distributions are unknown and are estimated using available economic data. Traditional analysis neglects estimation risk by treating the estimated parameters as if they were the true parameters to determine the optimal choice under uncertainty. We show that for normally distributed returns and ‘non-informative’ or ‘invariant’ priors, the admissible set of portfolios taking the estimation uncertainty into account is identical to that given by traditional analysis. However, as a result of estimation risk, the optimal portfolio choice differs from that obtained by traditional analysis. For other plausible priors, the admissible set, and consequently the optimal choice, is shown to differ from that in traditional analysis.     

The optimal portfolio of start-up firms in venture capital finance

Venture capitalists (VCs) not only finance but also add value to start-up companies. Advising firms is time consuming and creates a trade-off between intensity of advice and portfolio size. We jointly determine the optimal number of portfolio companies and the intensity of managerial advice. Diminishing returns to advice per firm call for a larger portfolio. With progressively increasing managerial effort cost, however, a larger number crowds out advice to each individual firm. As they receive less support, entrepreneurs request a larger profit share, making further portfolio expansion eventually unprofitable. Comparative static analysis shows how optimal portfolio size responds to venture returns and other parameters.     

Reduction of estimation risk in optimal portfolio choice using redundant constraints

It is well known that when the moments of the distribution governing returns are estimated from sample data, the out-of-sample performance of the optimal solution of a mean–variance (MV) portfolio problem deteriorates as a consequence of the so-called “estimation risk”. In this document we provide a theoretical analysis of the effects caused by redundant constraints on the out-of-sample performance of optimal MV portfolios. In particular, we show that the out-of-sample performance of the plug-in estimator of the optimal MV portfolio can be improved by adding any set of redundant linear constraints. We also illustrate our findings when risky assets are equally correlated and identically distributed. In this specific case, we report an emerging trade-off between diversification and estimation risk and that the allocation of estimation risk across portfolios forming the optimal solution changes dramatically in terms of number of assets and correlations.     

保险公司资产组合与最优投资比例研究

保险公司收益主要来源于承保利润和投资收益,其中承保利润受政策变动、市场条件等外部环境的影响较大,而投资收益则更多地取决于保险公司的投资能力,因此保险公司如何构建资产组合、如何确定最优投资比例就是获取投资收益最大化的重要因素。本文通过理论推导得出了保险公司的资产组合模型并运用非线性规划求解出最优投资比例,进而根据保险公司的投资数据进行了实证研究,为我国保险公司的资产组合及最优投资比例提供了一个可借鉴的思路。     

A model of optimal portfolio selection under liquidity risk and price impact

We study a financial model with one risk-free and one risky asset subject to liquidity risk and price impact. In this market, an investor may transfer funds between the two assets at any discrete time. Each purchase or sale policy decision affects the rice of the risky asset and incurs some fixed transaction cost. The objective is to maximize the expected utility from terminal liquidation value over a finite horizon and subject to a solvency constraint. This is formulated as an impulse control problem under state constraints and we characterize the value function as the unique constrained viscosity solution to the associated quasi-variational Hamilton–Jacobi–Bellman inequality. We would like to thank Mihail Zervos for useful discussions.     

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.     

基于随机微分博弈的保险公司最优决策模型

本文研究了基于保险公司与自然之间二人-零和随机微分博弈的最优投资及再保险问题。假设保险公司具有指数效用,自然是博弈的虚拟对手,通过求解最优控制问题对应的HJB I方程,得到了保险公司的最优投资和再保险策略以及最优值函数的闭式解。结果显示,在完全分保时(即自留比例为零),保险公司应该将全部财富购买无风险资产,即风险资产投资额为零;在不完全分保时保险公司将卖空风险资产,且卖空数量及保险自留比例都随保险公司盈余过程与风险资产间的相关性的提高而增大,随终止时刻T的临近而增加,但随市场中无风险资产回报率的增加而减少。     

Globalization and portfolio risk over time: The role of exchange rate

We examine benefits of international diversification for the period 1 January 1988 to 30 June 2000. We introduce a new variable (lambda) that measures these benefits more directly than do the pairwise correlations among equity markets, which are used in most other studies. Our study shows that despite international integrations, the benefits of international diversification measured in USD persist. Using lambda, we provide evidence that the increase in co-movements between equity market returns (measured in local currencies) has been counterbalanced by movements in exchange rates. We confirm our results by subjecting the trend in lambda to several tests.     

An algorithmic approach to deriving the minimum-variance zero-beta portfolio

This paper examines the problem of deriving Black's (1972) minimum-variance zero-beta portfolio. Long's (1971) methods, used by Morgan (1975), are briefly mentioned. Then the complementary pivot algorithm of Lemke (1965), which has been shown to be capable of deriving the optimal solution to certain quadratic programming problems that are subject to a non-negativity constraint, is described. Finally, Lemke's algorithm is shown to be capable of deriving the minimum-variance zero-beta portfolio efficiently from samples of risky assets where both long and short positions are allowed by reformulating the problem so as to avoid the difficulties encountered by having a non-negatively constraint.     

Efficient analytic approximation of the optimal hedging strategy for a European call option with transaction costs

One of the most successful approaches to option hedging with transaction costs is the utility-based approach, pioneered by Hodges and Neuberger [Rev. Futures Markets, 1989, 8, 222–239]. Judging against the best possible trade-off between the risk and the costs of a hedging strategy, this approach seems to achieve excellent empirical performance. However, this approach has one major drawback that prevents the broad application of this approach in practice: the lack of a closed-form solution. We overcome this drawback by presenting a simple yet efficient analytic approximation of the solution. We provide an empirical testing of our approximation strategy against the asymptotic and some other well-known strategies and find that our strategy outperforms all the others.     

Corporate venture capital and the returns to acquiring portfolio companies

A prominent motive for corporate venture capital (CVC) is the identification of entrepreneurial-firm acquisition opportunities. Consistent with this view, we find that one of every five startups purchased by 61 top corporate investors from 1987 through 2003 is a venture portfolio company of its acquirer. Surprisingly, our analysis reveals that takeovers of portfolio companies destroy significant value for shareholders of acquisitive CVC investors, even though these same investors are “good acquirers” of other entrepreneurial firms. We explore numerous explanations for these puzzling findings, which seem rooted in managerial overconfidence or agency problems at the program level.