Optimal portfolio choice in the bond market

We consider the Merton problem of optimal portfolio choice when the traded instruments are the set of zero-coupon bonds. Working within a Markovian Heath–Jarrow–Morton model of the interest rate term structure driven by an infinite-dimensional Wiener process, we give sufficient conditions for the existence and uniqueness of an optimal trading strategy. When there is uniqueness, we provide a characterization of the optimal portfolio as a sum of mutual funds. Furthermore, we show that a Gauss–Markov random field model proposed by Kennedy [Math. Financ. 4, 247–258(1994)] can be treated in this framework, and explicitly calculate the optimal portfolio. We show that the optimal portfolio in this case can be identified with the discontinuities of a certain function of the market parameters.     

Optimal portfolio selection in nonlinear arbitrage spreads

This paper analytically solves the portfolio optimization problem of an investor faced with a risky arbitrage opportunity (e.g. relative mispricing in equity pairs). Unlike the extant literature, which typically models mispricings through the Ornstein–Uhlenbeck (OU) process, we introduce a nonlinear generalization of OU which jointly captures several important risk factors inherent in arbitrage trading. While these factors are absent from the standard OU, we show that considering them yields several new insights into the behavior of rational arbitrageurs: Firstly, arbitrageurs recognizing these risk factors exhibit a diminishing propensity to exploit large mispricings. Secondly, optimal investment behavior in light of these risk factors precipitates the gradual unwinding of losing trades far sooner than is entailed in existing approaches including OU. Finally, an empirical application to daily FTSE100 pairs data shows that incorporating these risks renders our model's risk-management capabilities superior to both OU and a simple threshold strategy popular in the literature. These observations are useful in understanding the role of arbitrageurs in enforcing price efficiency.     

Correlation structure forecasting & ex ante portfolio selection strategies in the Japan market

Using monthly data for 160 stocks covering January 1977 to December 1991, we find that both the Historical Mean and the Industry Mean Models dominate the Global Mean and the Single Index Models. In theex-ante portfolio selection, the Historical Model dominates all other models when evaluated against the benchmark of the Global Minimum Variance Portfolio but a combination of historical correlation structure and Bayes-Stein Shrinkage expected returns dominates other models when the Optimal Tangency Portfolio is used as a benchmark for evaluation.     

Size matters: Optimal calibration of shrinkage estimators for portfolio selection

We carry out a comprehensive investigation of shrinkage estimators for asset allocation, and we find that size matters—the shrinkage intensity plays a significant role in the performance of the resulting estimated optimal portfolios. We study both portfolios computed from shrinkage estimators of the moments of asset returns (shrinkage moments), as well as shrinkage portfolios obtained by shrinking the portfolio weights directly. We make several contributions in this field. First, we propose two novel calibration criteria for the vector of means and the inverse covariance matrix. Second, for the covariance matrix we propose a novel calibration criterion that takes the condition number optimally into account. Third, for shrinkage portfolios we study two novel calibration criteria. Fourth, we propose a simple multivariate smoothed bootstrap approach to construct the optimal shrinkage intensity. Finally, we carry out an extensive out-of-sample analysis with simulated and empirical datasets, and we characterize the performance of the different shrinkage estimators for portfolio selection.     

Behavioral portfolio selection and optimization: an application to international stocks

The behavioral approach of decision making has emerged as a diversified solution in the presence of risk and uncertainty. Using the popular cumulative prospect theory as an objective function for portfolio selection, this study implements the classical mean–variance model to compare the portfolio performance of high behavioral stocks with that of stocks with lower behavioral values. Based on a sample of 37 international stocks over the period from October 1998 to November 2017, empirical results from D-vine pair copula GARCH-GEV indicate that the portfolio of high behavioral prospect stocks outperforms the portfolio of stocks with low behavioral scores. This finding may suggest that portfolios with high behavioral values coincide with rational efficiency sets.     

Testing asset pricing models with changing expectations and an unobservable market portfolio

When the assumption of constant risk premiums is relaxed, financial valuation models may be tested, and risk measures estimated without specifying a market index or state variables. This is accomplished by examining the behavior of conditional expected returns. The approach is developed using a single risk premium asset pricing model as an example and then extended to models with multiple risk premiums. The methodology is illustrated using daily return data on the common stocks of the Dow Jones 30. The tests indicate that these returns are consistent with a single, time-varying risk premium.     

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.     

Search for information and portfolio selection

The paper examines the problem of how to allocate scarce resources between increasing the investor's knowledge, that is reducing his uncertainty, and the actual investment—that is a kind of an ex ante decision before the final parameters of the securities are known. Our model provides answers to questions of how the search for knowledge affects portfolio selection, to what extent additional information can improve estimates of securities' statistical parameters and how the benefits and costs of additional search alter the investor's efficient mean-variance portfolio set.     

Modelling fundamental analysis in portfolio selection

We derive a closed-form appraisal/information ratio of the investors who are able to observe some information about security fundamentals, by solving a simple instantaneous mean-variance portfolio choice problem in a continuous-time framework. Both analytical and numerical results suggest that investors should choose securities with a more volatile mispricing, a less volatile fundamental, a higher mean-reverting speed and a larger dividend. Our model calibrated with realistic parameters easily outperforms top-percentile portfolio managers in reality, which suggests that the implementation of fundamental analysis may be impeded in practice due to limits of arbitrage. Our paper is a first, necessarily simple, step towards filling the gap of modelling fundamental analysis in portfolio selection.     

Spectral risk measures and portfolio selection

This paper deals with risk measurement and portfolio optimization under risk constraints. Firstly we give an overview of risk assessment from the viewpoint of risk theory, focusing on moment-based, distortion and spectral risk measures. We subsequently apply these ideas to an asset management framework using a database of hedge funds returns chosen for their non-Gaussian features. We deal with the problem of portfolio optimization under risk constraints and lead a comparative analysis of efficient portfolios. We show some robustness of optimal portfolios with respect to the choice of risk measure. Unsurprisingly, risk measures that emphasize large losses lead to slightly more diversified portfolios. However, risk measures that account primarily for worst case scenarios overweight funds with smaller tails which mitigates the relevance of diversification.     

Optimal monetary policy in an economy with incomplete markets and idiosyncratic risk

This study investigates an incomplete markets economy in which the saving behavior of a continuum of infinitely lived agents is influenced by precautionary saving motives and borrowing constraints. Agents can use two types of assets (interest bearing IOUS and money) to smooth consumption. Money is valued because of a timing friction in the bond market. In particular, the bond market closes before agents observe their idiosyncratic productivity shock. I find that the Friedman rule is not optimal for this economy. The results indicate that the optimal allocation has a rate of inflation of 10%, and a positive amount of private credit held by the government. A positive inflation rate transfers resources from agents with big endowments to those holding bonds which improves risk sharing, and therefore, welfare. However, for higher rates of inflation, agents economize on money holdings, offsetting the insurance effects, and causing a reduction in welfare. Furthermore, higher rates of inflation discourage agents from borrowing, and the endogenous lower bound on bond holdings is higher than the exogenous borrowing limit. High rates of inflation, therefore, exacerbate frictions in the bond market.     

The significance of the market portfolio

Arguments for creating a market to allow trading the portfolioof all endowments in the entire world, the 'market portfolio',are considered. This world share market would represent a radicalinnovation, since at the present time only a small fractionof world endowments are traded. Using a stochastic endowmenteconomy where preference are mean variance, it is shown thatcreating such a market may be justified in terms of its contributionto social welfare. It is also argued that creating a marketfor world shares is attractive for certain reasons of robustnessand simplicity.     

Optimal portfolio allocation with higher moments

We model the risky asset as driven by a pure jump process, with non-trivial and tractable higher moments. We compute the optimal portfolio strategy of an investor with CRRA utility and study the sensitivity of the investment in the risky asset to the higher moments, as well as the resulting wealth loss from ignoring higher moments. We find that ignoring higher moments can lead to significant overinvestment in risky securities, especially when volatility is high.      

An approximation pricing algorithm in an incomplete market: A differential geometric approach

The minimal distance equivalent martingale measure (EMM) defined in Goll and Rüschendorf (2001) is the arbitrage-free equilibrium pricing measure. This paper provides an algorithm to approximate its density and the fair price of any contingent claim in an incomplete market. We first approximate the infinite dimensional space of all EMMs by a finite dimensional manifold of EMMs. A Riemannian geometric structure is shown on the manifold. An optimization algorithm on the Riemannian manifold becomes the approximation pricing algorithm. The financial interpretation of the geometry is also given in terms of pricing model risk.Received: February 2004, Mathematics Subject Classification (2000): 62P05, 91B24, 91B28JEL Classification: G11, G12, G13Yuan Gao: Present address Block 617, Bukit Panjang Ring Road, 16-806,Singapore 670617. I am currently working in a major investment bank.This paper is based on parts of my doctoral dissertation Gao (2002),which isavailable upon request.Part of the research was done during my visit to HumboldtUniversity in 2002 and was partially supported by Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 373. I am especially thankful to Professor Hans Föllmer for the invitation and helpful discussions.We would like to thank Professor Martin Schweizer,the associate editor and the referee for their constructive comments.     

Optimal hedging in an extended binomial market under transaction costs

We develop an approach to optimal hedging of a contingent claim under proportional transaction costs in a discrete time financial market model which extends the binomial market model with transaction costs. Our model relaxes the binomial assumption on the stock price ratios to the case where the stock price ratio distribution has bounded support. Non-self-financing hedging strategies are studied to construct an optimal hedge for an investor who takes a short position in a European contingent claim settled by delivery. We develop the theoretical basis for our optimal hedging approach, extending results obtained in our previous work. Specifically, we derive a no-arbitrage option price interval and establish properties of the non-self-financing strategies and their residuals. Based on the theoretical foundation, we develop a computational algorithm for optimizing an investor relevant criterion over the set of admissible non-self-financing hedging strategies. We demonstrate the applicability of our approach using both simulated data and real market data.     

Optimal portfolio and spending rules for endowment funds

Review of Quantitative Finance and Accounting - Prior studies show that investor learning about earnings-based return predictors from academic research erodes return predictability. However, the...