The Expected Return on Risky Assets: International Long-run Evidence

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.

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Intertemporal Relation Between The Expected Return And Risk: An Evaluation Of Emerging Market

Journal of Applied Business Research (JABR) ◽

10.19030/jabr.v29i3.7782 ◽

2013 ◽

Vol 29 (3) ◽

pp. 809 ◽

Cited By ~ 2

Author(s):

Zhongyi Xiao ◽

Peng Zhao

Keyword(s):

Risk Premium ◽

Emerging Market ◽

Multivariate Garch ◽

Capital Asset Pricing ◽

Font Size ◽

Expected Return ◽

Cross Sectional ◽

Risky Assets ◽

Market Portfolio

This paper explores the intertemporal relationship between the expected return and risk in Chinese exchange market. We investigate the characterization of time-series variation in conditional variance and capture the cross-sectional correlation among equity portfolios by incorporating multivariate GARCH-M model with dynamic conditional covariance (DCC). Restricting the slope to be the same across risky assets, the risk-return coefficient is estimated to be positive and highly significant. In addition, the estimates of portfolio-specific slopes provide evidence to support the robustness across different portfolio formations. Our findings, in the Intertemporal Capital Asset Pricing Model (ICAPM) framework, reveal that the risk premium induced by the conditional covariation of equity portfolio with the market portfolio remain positive after controlling for risk premia induced by conditional covariation with Fama French benchmark factors (HML and SMB). The SMB factor might provide a significant predictive power to hedge against market risk. However, four indices of alternative investments are not consistently priced in the ICAPM framework.

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Determining the Best Trade-Off Between Expected Economic Return and the Risk of Undesirable Events When Managing a Randomly Varying Population

Journal of the Fisheries Research Board of Canada ◽

10.1139/f79-131 ◽

1979 ◽

Vol 36 (8) ◽

pp. 939-947 ◽

Cited By ~ 10

Author(s):

Roy Mendelssohn

Keyword(s):

Markov Decision Processes ◽

Population Based ◽

Decision Processes ◽

Expected Return ◽

Trade Off ◽

Long Run ◽

Optimal Policies ◽

Markov Decision ◽

Long Run Risk ◽

Varying Population

Conditions are given that imply there exist policies that "minimize risk" of undesirable events for stochastic harvesting models. It is shown that for many problems, either such a policy will not exist, or else it is an "extreme" policy that is equally undesirable. Techniques are given to systematically trade-off decreases in the long-run expected return with decreases in the long-run risk. Several numerical examples are given for models of salmon runs, when both population-based risks and harvest-based risks are considered. Key words: Markov decision processes, risk, salmon management, Pareto optimal policies, trade-off curves, linear programing

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Disaster Risk and Business Cycles

The American Economic Review ◽

10.1257/aer.102.6.2734 ◽

2012 ◽

Vol 102 (6) ◽

pp. 2734-2766 ◽

Cited By ~ 287

Author(s):

François Gourio

Keyword(s):

Business Cycles ◽

Interest Rates ◽

Stock Prices ◽

Disaster Risk ◽

Expected Return ◽

Risky Assets ◽

The Great Depression ◽

Business Cycle Model ◽

Well Data ◽

Real Business Cycle Model

Motivated by the evidence that risk premia are large and countercyclical, this paper studies a tractable real business cycle model with a small risk of economic disaster, such as the Great Depression. An increase in disaster risk leads to a decline of employment, output, investment, stock prices, and interest rates, and an increase in the expected return on risky assets. The model matches well data on quantities, asset prices, and particularly the relations between quantities and prices, suggesting that variation in aggregate risk plays a significant role in some business cycles. (JEL E13, E32, E44, G32)

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Abstract: Institutional Portfolio Restrictions, Diverse Investor Opportunity Sets, and Securities Market Equilibrium

Journal of Financial and Quantitative Analysis ◽

10.1017/s0022109000023358 ◽

1977 ◽

Vol 12 (4) ◽

pp. 637-637 ◽

Cited By ~ 1

Author(s):

David W. Glenn

Keyword(s):

Securities Market ◽

Securities Markets ◽

Expected Return ◽

Market Prices ◽

Risky Assets ◽

Opportunity Sets ◽

Market Portfolio ◽

Risk Dimensions ◽

The Impact ◽

Two Parameter

This paper utilizes a two-parameter model of segmented securities markets to develop equilibrium implications concerning the impact of statutory investment restrictions upon the market prices and allocation of risky securities. The distinguishing feature of the model is the existence of a subset of securities common to the opportunities of all investors and therefore said to “span” the investor population. These common opportunities are shown to permit intersubset security transactions which integrate the various market segments and lead to the following theorem and tendency concerning equilibrium prices and portfolios:Theorem: In the absence of active barriers against short positions, the equilibrium expected return for any security spanning the investor population is an exact linear function of its contribution to total market risk, irrespective of the number of distinct investor segments that may exist.Tendency: The economic characteristics of the equilibrium risky portfolio for any investor, irrespective of the market segment to which he or she may belong, will approximate the characteristics of the market portfolio of all risky assets in the economy in all relevant risk dimensions.

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Consumption-Based Asset Pricing When Consumers Make Mistakes

Finance and Economics Discussion Series ◽

10.17016/feds.2021.015 ◽

2021 ◽

Vol 2021 (015) ◽

pp. 1-71

Author(s):

Chris Anderson ◽

Keyword(s):

Asset Pricing ◽

Stock Returns ◽

Equity Premium ◽

Expected Returns ◽

Power Utility ◽

Expected Return ◽

Risk Return ◽

Asset Pricing Models ◽

Long Run ◽

Wide Range

I analyze the implications of allowing consumers to make mistakes on the risk-return relationships predicted by consumption-based asset pricing models. I allow for consumption mistakes using a model in which a portfolio manager selects investments on a consumer's behalf. The consumer has an arbitrary consumption policy that could reflect a wide range of mistakes. For power utility, expected returns do not generally depend on exposure to single-period consumption shocks, but robustly depend on exposure to both long-run consumption and expected return shocks. I empirically show that separately accounting for both types of shocks helps explain the equity premium and cross section of stock returns.

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A Robust Application of the Arbitrage Pricing Theory: Evidence from Nigeria

Journal of Economics and Behavioral Studies ◽

10.22610/jebs.v9i1.1565 ◽

2017 ◽

Vol 9 (1) ◽

pp. 141

Author(s):

Oyetayo Oluwatosin J. ◽

Adeyeye Patrick Olufemi

Keyword(s):

Stock Returns ◽

Stock Price ◽

Ordinary Least Squares ◽

Arbitrage Pricing Theory ◽

Arbitrage Pricing ◽

Expected Return ◽

Long Run ◽

Short Run ◽

Pricing Theory ◽

Relationship Of

Arbitrage pricing theory (APT) is a testable theory based on the idea that in competitive financial markets arbitrage will ensure that riskless assets provide the same expected return. We sought to confirm the relevance of the arbitrage pricing theory in Nigeria. Guided by a good understanding of macroeconomic variables and stock price movements as found in the extant literature on arbitrage pricing theory (APT), we specified our APT equation for estimation. Having satisfied the integration and co-integration issues, we employ the error-correction (ECM) and the fully modified ordinary least squares (FMOLS) methods for the short-run and long-run regressions. Our short-run results seem to agree with existing theories on APT thus confirming that APT is relevant in Nigeria. However, the long-run relationship of stock returns and RGDP was found to be contentious. Even though our result runs contrary to predictions on the relationship between the two, we found peculiar events and circumstances within the Nigerian macroeconomic context that provides logical reasons for the deviation.

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STATISTICAL ARBITRAGE IN THE MULTI-ASSET BLACK–SCHOLES ECONOMY

Annals of Financial Economics ◽

10.1142/s201049521750004x ◽

2017 ◽

Vol 12 (01) ◽

pp. 1750004

Author(s):

AHMET GÖNCÜ ◽

ERDINC AKYILDIRIM

Keyword(s):

Model Parameters ◽

Expected Return ◽

Risky Assets ◽

Quantitative Finance ◽

No Arbitrage ◽

Statistical Arbitrage ◽

Arbitrage Opportunities ◽

Complete Market ◽

Black Scholes ◽

Analytical Formulas

In this study, we consider the statistical arbitrage definition given in Hogan, S, R Jarrow, M Teo and M Warachka (2004). Testing market efficiency using statistical arbitrage with applications to momentum and value strategies, Journal of Financial Economics, 73, 525–565 and derive the statistical arbitrage condition in the multi-asset Black–Scholes economy building upon the single asset case studied in Göncü, A (2015). Statistical arbitrage in the Black Scholes framework. Quantitative Finance, 15(9), 1489–1499. Statistical arbitrage profits can be generated if there exists at least one asset in the economy that satisfies the statistical arbitrage condition. Therefore, adding a no-statistical arbitrage condition to no-arbitrage pricing models is not realistic if not feasible. However, with an example we show that what excludes statistical arbitrage opportunities in the Black–Scholes economy, and possibly in other complete market models, is the presence of uncertainty or stochasticity in the model parameters. Furthermore, we derive analytical formulas for the expected value and probability of loss of the statistical arbitrage portfolios and compute optimal boundaries to sell the risky assets in the portfolio by maximizing the expected return with a constraint on the probability of loss.

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INCORPORATING RISKY ASSETS IN DIVISIA MONETARY AGGREGATES

Buletin Ekonomi Moneter dan Perbankan ◽

10.21098/bemp.v3i1.289 ◽

2003 ◽

Vol 3 (1) ◽

pp. 98-120

Author(s):

Leigh Drake ◽

Andy Mullineux ◽

Juda Agung

Keyword(s):

Mutual Funds ◽

Money Demand ◽

Demand Function ◽

Monetary Aggregate ◽

Risky Assets ◽

Monetary Aggregates ◽

Divisia Monetary Aggregates ◽

Long Run ◽

Causality Tests ◽

Monetary Assets

Capital uncertain or risky assets are typically excluded from traditional broad monetary aggregates. Barnett et al (1997), however, extend the Divisia aggregation methodology to incorporate such assets. In addition, recent evidence provided by Drake et al (1998) suggests that risky assets are close substitutes for monetary assets. This paper constructs “wide” Divisia monetary aggregates which include risky assets such as unit trusts (mutual funds), equities and bonds, and contrasts their empirical properties with conventional Divisia and simple sum broad money aggregates. The key finding in the paper is that a “wide” monetary aggregate, which incorporates unit trusts, exhibits a stable long run and dynamic money demand function, has good leading indicator properties in the context of Granger causality tests, and tends to outperform all other aggregates on the basis of non-nested tests.JEL : E41, C43, E52

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Analisis Portofolio Investasi dengan Metode Multi Objektif

Jurnal Varian ◽

10.30812/varian.v3i1.476 ◽

2019 ◽

Vol 3 (1) ◽

pp. 6-12

Author(s):

Gilang Primajati ◽

Ahmad Zuli Amrullah ◽

Ahmad Ahmad

Keyword(s):

Minimum Variance ◽

Optimal Portfolio ◽

Risk Level ◽

Risk Averse ◽

Expected Return ◽

Risky Assets ◽

Variant Method ◽

The Mean ◽

Mean Variance ◽

Constraint Method

In the formation of an efficient portfolio, many methods can be used. Of course with its own assumptions and advantages. In the process, reasonable investor assumptions tend to be risk averse. Investors who are risk averse are investors who, when faced with two investments with the same expected return, will choose an investment with a lower risk level. If an investor has several efficient portfolio choices, then the most optimal portfolio will be chosen. Optimal portfolio with mean-variance efficient portfolio criteria, investors only invest in risky assets. Investors do not include risk free assets in their portfolios. Mean-variance efficient portfolio is defined as a portfolio that has a minimum variance among all possible portfolio that can be formed, at the mean level of the same expected return. The mean variant method of the two constraints can be used as a basis in determining the optimal portfolio weight by minimizing the risk of portfolio return with two constraints. In this article the problem referred to is symbolized by lamda and beta. With this two-constraint method, the results obtained are more detailed so that they can describe the results of a sharper analysis for an investor.

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