A Scalable Algorithm for Sparse Portfolio Selection

The sparse portfolio selection problem is one of the most famous and frequently studied problems in the optimization and financial economics literatures. In a universe of risky assets, the goal is to construct a portfolio with maximal expected return and minimum variance, subject to an upper bound on the number of positions, linear inequalities, and minimum investment constraints. Existing certifiably optimal approaches to this problem have not been shown to converge within a practical amount of time at real-world problem sizes with more than 400 securities. In this paper, we propose a more scalable approach. By imposing a ridge regularization term, we reformulate the problem as a convex binary optimization problem, which is solvable via an efficient outer-approximation procedure. We propose various techniques for improving the performance of the procedure, including a heuristic that supplies high-quality warm-starts, and a second heuristic for generating additional cuts that strengthens the root relaxation. We also study the problem’s continuous relaxation, establish that it is second-order cone representable, and supply a sufficient condition for its tightness. In numerical experiments, we establish that a conjunction of the imposition of ridge regularization and the use of the outer-approximation procedure gives rise to dramatic speedups for sparse portfolio selection problems.

A new behavioral finance mean variance framework

PurposeThe author proposes an update to the mean variance (MV) framework that replaces a constant risk aversion parameter using a dynamic risk aversion indicator. The contribution to the literature is made through making the static risk aversion parameter operational using an indicator of market sentiment. Results suggest that Sharpe ratios improve when the author replaces the traditional risk aversion parameter with a dynamic sentiment indicator from the behavioral finance literature when allocating between a risky portfolio and a risk-free asset. However, results are mixed when using the behavioral framework to allocate between two risky assets.Design/methodology/approachThe author includes a dynamic risk aversion parameter in the mean variance framework and back test using the traditional and updated behavioral mean variance (BMV) framework to see which framework leads to better performance.FindingsThe author finds that the behavioral framework provides superior performance when allocating between a risky and risk-free asset; however, it under performs when allocating between risky assets.Research limitations/implicationsThe research is based on back testing; therefore, it cannot be concluded that this strategy will perform well in real-time circumstances.Practical implicationsPortfolio managers may use this strategy to optimize the allocation between a risky portfolio and a risk-free asset.Social implicationsAn improved allocation between risk-free and risky assets that could lead to less leverage in the market.Originality/valueThe study is the first to use such a sentiment indicator in the traditional MV framework and show the math.

Non-Arbitrage Models of Financial Markets

In the first part of the paper, we construct the models of the complete non-arbitrage financial markets for a wide class of evolutions of risky assets.This construction is based on the observation that for a certain class of risky as set evolutions the martingale measure is invariant with respect to these evolutions. For such a financial market model the only martingale measure being equivalent to an initial measure is built. On such a financial market,formulas for the fair price of contingent liabilities are presented. A multi-parameter model of the financial market is proposed, the martingale measure of which does not depend on the parameters of the model of the evolution of risky assets and is the only one.

Leaning against the Bubble: Central Bank Intervention in Walrasian Asset Markets

The paper presents a two-period Walrasian financial market model composed of informed and uninformed rational investors, and noise traders. The rational investors maximize second period consumption utility from the payoffs of trading risk-free holdings to risky assets in the first period. The central bank reacts directly to asset price movements by selling or buying assets to stabilize the market price. It is found that the intervention makes the risky asset’s market price per share less sensitive to information shocks, which presses the market price towards its average price thus reducing price variance. The informed investors’ prediction coefficient remains unaffected, but that of the uninformed investors is magnified, which cancels out the negative effect on shock sensitivity thus keeping the expected value of the risky asset’s dividend constant. Finally, the introduction of the policy rule does not affect rational investors’ risk per share. A general conclusion is that the central bank’s policy can be regarded as an effective automatic stabilizer of financial markets.

The Study of Mean-Variance Risky Asset Management with State-Dependent Risk Aversion under Regime Switching Market

How do investors require a distribution of the wealth among multiple risky assets while facing the risk of the uncontrollable payment for random liabilities? To cope with this problem, firstly, this paper explores the approach of asset-liability management under the state-dependent risk aversion with only risky assets, which has been considered under a continuous-time Markov regime-switching setting. Next, based on this realistic modelling, an extended Hamilton-Jacob-Bellman (HJB) system has been necessarily established for solving the optimization problem of asset-liability management. It has been derived closed-form analytical expressions applied in the time-inconsistent investment with optimal control theory to see that happens to the optimal value of the function. Ultimately, numerical examples presented with comparisons of the analytical results under different market conditions are exposed to analyse numerically the developed mean variance asset liability management strategy. We find that our proposed model can explain the financial phenomena more effectively and accurately.

Macroeconomic Implications of Inequality and Income Risk

We explore the long-run relationship between income risk, inequality, and the macroeconomy in an overlapping-generations model in which households face uncertain streams of labor income and returns on their savings. To manage those risks, households can apportion their savings to a bond, whose return is safe and identical across households, and a productive asset, whose return is uncertain and can differ persistently across households. We find that greater polarization in households’ labor income and returns on their savings generally accentuates households’ demand for risk-free assets and the compensation they require for bearing risk, leading to higher measured income and wealth inequality, a lower risk-free real interest rate, and higher risk premiums. These findings suggest that the factors behind the observed rise in inequality over the past few decades might have contributed to the observed fall in the risk-free real interest rate and widening gap between the risk-free real interest rate and the rate of return on capital. We also find that the magnitude of the decline in the risk-free real interest rate and offsetting rise in risk premiums depend importantly on the source of income polarization, with the effects being especially large when greater inequality is caused by increased dispersion in returns on risky assets. Thus, the macroeconomic implications not only depend on the amount of inequality, but also the source of this inequality.

Can Financial Literacy Explain Lack of Investment in Risky Assets in Japan?

Although household savings in Japan are among the highest in the world, investment in risky assets is still very low. This study examines whether financial literacy explains the lack of investment in risky assets in Japan. We use data from the Preference Parameter Study, a nationwide survey in Japan that has been conducted by Osaka University. We use investment in stocks, investment trusts, futures/options, Japanese government bonds, government bonds of foreign countries, and foreign currency deposits as a proxy for investment in risky assets. Our results show that investment in risky assets is higher among financially literate people. Moreover, financial literacy has a significantly positive association with investment in risky assets even after controlling the demographic, socio-economic, and psychological factors. We check the robustness of the association between financial literacy and investment in risky assets by segregating investment in risky assets into investment in equity securities and investment in bonds and foreign currencies. Financial literacy is found to be associated with both investment in equity securities and investment in bonds and foreign currencies. Our results are also robust in terms of the endogeneity issue. The results imply that investment in risky assets in financial markets could be increased by introducing financial literacy programs at a mass level.

Impact of Noninterest Income on Bank Risk-Taking and Bank Lending Spread

This study investigates the impact of diversification between traditional margin income and nontraditional income (noninterest-based income) on bank risk-taking and bank lending spread for banks operating in Pakistan. Bank risk is measured with the nonperforming loan ratio and bank [Formula: see text]-score. Data of this study is obtained from financial statements, which are an annual publication of State Bank of Pakistan, for the period 2006–2016 for 52 banks in Pakistan. Panel regression with the generalized method of moments (GMM) estimator is employed. The study reveals that an increase in noninterest income increases bank risk-taking (spending on highly risky assets), as noninterest income is riskier than interest income. It is also revealed that banks with greater dependence on noninterest income may grant a loan with lower lending spread. These results have implications for the betterment of the banking system, regulatory authority, and stakeholders as well. From a regulatory perspective, the study provides guidelines for making rules and regulations to control and monitor the dependence on noninterest income as well as on interest income. Pakistan banks regulatory authority should focus on the increase in disclosure of the composition of noninterest income and this disclosure would increase understanding of changing environment of banking in Pakistan.

Tools for modeling the capital dynamics of financial organizations

The issues of ensuring the financial stability of financial institutions, which is understood as the sufficiency of assets to meet obligations, are of paramount importance both for clients and the management of a financial institution, and for the country's economy as a whole. Most often, the inability to fulfill obligations is associated with a lack of funds, therefore it is important to monitor the dynamics of the monetary capital of organizations, to assess their financial risks, including in the conditions of investment. Purpose of the study: development of tools for assessing the risks of financial organizations. Statement of the problem: to develop a simulation model that allows one to study the dynamics of the capital of an organization, whose financial resources are formed due to heterogeneous flows of inflow and outflow of funds and investment, including in risky assets, in an inflationary environment. The paper proposes a modeling algorithm that allows to collect a descriptive statistics on the distribution of financial resources, to estimate the dynamics of the money capital of financial organizations and investigate the "sufficiency" of the company's funds to meet financial obligations basing on data of cash flows for various types of contracts and returns (growth rates) of assets, presented in the form of statistical data and/or characteristics of time series models. The description of the software tool is given. A computational experiment was based on data of the inflow and outflow of funds of a non-state pension Fund under the program of non-state pension provision. Descriptive statistics are given for the distributions of the size of organization's funds constructed as a result of modeling. The probability of organization’s downfall in dynamics and the risk of entering the zone of financial insecurity are assessed. The proposed tools have scientific novelty in the field of designing simulation models and decision support systems for analyzing the activities of financial organizations and determining effective directions for their development.