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.     

Optimal liquidation strategies regularize portfolio selection

We consider the problem of portfolio optimization in the presence of market impact, and derive optimal liquidation strategies. We discuss in detail the problem of finding the optimal portfolio under expected shortfall (ES) in the case of linear market impact. We show that, once market impact is taken into account, a regularized version of the usual optimization problem naturally emerges. We characterize the typical behavior of the optimal liquidation strategies, in the limit of large portfolio sizes, and show how the market impact removes the instability of ES in this context.     

Optimal portfolio choice of gold assets in the differential market and differential game structures

Portfolio choices of gold-related assets for market investors and dealers may not only depend on price differences and the inflation rate, but may also react to the market participants’ strategic behavior and risk attitude. This study develops a two-agent stochastic differential game model to solve the portfolio choice problem of the asset allocations of gold spot, futures, and cash for market participators who are exposed to inflation risks. The equilibrium prices of spot and futures driven by the volatility rate and co-variances that reflect various risk sources are also determined. Specifically, regarding the choice of hedging tools, market participators may prefer gold spot to futures for the purpose of hedging inflation risk. By capturing the stylistic facts of differential market and multiple agent structures, the article can develop a more reasonable and practical model to usefully explain the gold portfolio choices and pricing in the gold markets.     

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.     

Optimal reinsurance and portfolio selection: Comparison between partial and complete information models

We consider partial and complete information models to investigate how partial information has a unique quality over complete information for insurers. We find that optimal reinsurance and investment strategies for the partially informed insurer depend on prior beliefs, whereas those for the completely informed insurer do not. In addition, information quality can affect insurer behaviour, mainly through the relative difference between risk-adjusted market premium and risk-adjusted insurance premium projected on the financial markets. Numerical results indicate that partial information increases the conservativeness of insurer strategies.     

Foreign market portfolio concentration and performance

Using security holdings of 49,857 foreign investors on the Oslo Stock Exchange (OSE), I test whether concentrated investment strategies in international markets result in excess risk-adjusted returns. I find that investors with higher learning capacity increase returns, while investors with lower learning capacity decrease returns from the portfolio concentration. I measure learning capacity as institutional classification, geographical proximity to Norway, and cultural closeness to Norwegian investors (as based on the Hofstede cultural closeness measures). I conclude, consistent with the information advantage theory, that concentrated investment strategies in foreign markets can be optimal (disastrous) for investors with higher (lower) learning capacity.     

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.     

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.     

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.     

Comment on “Optimal portfolio selection in a value-at-risk framework”

This comment discusses some errors in [Journal of Banking and Finance 25 (2001) 1789]. Given the portfolio rate of return is normally distributed, the following can be inferred. First, taking expected portfolio return rate as the benchmark of value-at-risk (VaR), the risk–return ratio collapses to a multiple of the Sharpe index. However, using risk-free rate as the benchmark, then above inference does not hold. Second, whether the benchmark of VaR is expected portfolio return rate or the risk-free rate, the optimal asset allocations for maximizing the risk–return ratio and Sharpe index are identical.     

Optimal granularity for portfolio choice

Many optimization-based portfolio rules fail to beat the simple 1/N rule out-of-sample because of parameter uncertainty. In this paper we suggest a grouping strategy in which we first form groups of equally weighted stocks and then optimize over the resulting groups only. This strategy aims at balancing the trade-off between the benefits from optimization and the losses from estimation risk. We rely on Monte-Carlo simulations to illustrate the performance of the strategy, and we derive the optimal group size for a simplified setup. Furthermore, we show that estimation risk also has an impact via the criterion by which the assets are sorted into groups (like the expected excess returns or betas), but does not negate the grouping approach. We relate our work to linear asset pricing models, and we conduct out of sample back-tests in order to confirm the validity of our grouping strategy empirically.     

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.