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Portfolio selection is recognized as the birth-place of modern finance; Markowitz emphasizes computing whole efficient frontiers. Moreover, computing efficient sets has long been a topic in multiple-objective optimization. After portfolio selection, an important research direction is capital asset pricing models (CAPM). Black and Fama prove the existence of a unique zero-covariance portfolio on the minimum-variance frontier. By the zero-covariance relationship, Roll then classifies the minimum-variance frontier into a positive-covariance side and a negative-covariance side; Fama and Roll further prove zero-covariance CAPM. Recently, researchers gradually realize additional criteria and extend portfolio selection into multiple-objective portfolio selection. Consequently, the minimum-variance frontier extends to a minimum-variance surface. Moreover, the extension naturally raises questions of classifying the surface for multiple-objective CAPM. There has been no such research until now. In such an area, this paper contributes to the literature by extending the classification. We classify the surface into a positive-covariance side and a negative-covariance side, although the classification depends on specific portfolios and is thus non-uniform. We then analyze classification properties and extend relevant theorems by proposing conjectures, although the conjectures are disproved by theorems and counter-examples. Moreover, we forward the research methodology to general k-objective models, so research arenas for multiple-objective CAPM are opened. This paper brings researchers one step closer to classifying the minimum-variance surface and extending CAPM.

International audience; This paper introduces a new approach of multifactor asset pricing model estimation. This approachassumes that the monthly returns of financial assets are fuzzy random variables and estimates themultifactor asset pricing model as a fuzzy linear model. The fuzzy random representations allows us toincorporate bias on prices induced by the market microstructure noise and to reflect the intra-periodactivity in the analysis. The application of fuzzy linear regression enables the uncertainty assessment in analternative way to confidence interval or hypothesis testing, which is subjected the binding assumption ofnormal distribution of returns. However, it is well known that the distribution of many asset returnsdeviates significantly from the normal assumption. We illustrate this estimation in the particular case of theFama and French’s (J Financ Econ 33:3–56, 1993) three factor model. Finally, empirical studies based onFama and French’s portfolios and risk factors, historical dataset highlight the effectiveness of ourestimation method and a comparative analysis with the ordinary least square estimation shows its ability tobe applied for an optimal decision decision making in the financial market.

This paper explores the mispricing relative to the capital asset pricing model through an equilibrium model. We find that both the strong risk preference dependent on good market states and strong risk aversion dependent on bad market states can produce high mispricing. Choosing the China stock market, the largest emerging market dominated by individual investors and known for its volatile nature in a short history as our sample, the empirical results also support our theoretical findings. Overall, our paper sheds light on the mispricing caused by the investor’s risk preference reference-dependent on market states.

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link. Open access This paper reports a new methodology and results on the forecast of the numerical value of the fat tail(s) in asset returns distributions using the irrational fractional Brownian motion model. Optimal model parameter values are obtained from fits to consecutive daily 2-year period returns of S&P500 index over [1950–2016], generating 33-time series estimations. Through an econometric model,the kurtosis of returns distributions is modelled as a function of these parameters. Subsequently an auto-regressive analysis on these parameters advances the modelling and forecasting of kurtosis and returns distributions, providing the accurate shape of returns distributions and measurement of Value at Risk.

Bitcoin is emerging as a distinct asset class among investors given its seemingly detached price behavior relative to market and economic fundamentals. Its incomparably high returns in recent years has further fuelled intense interest and investment into Bitcoin and cryptocurrencies at large. This paper cautions that Bitcoin prices, despite their seemingly attractive independent behavior relative to economic variables, may still be exposed to the same types of market risks which afflict the performance of conventional financial assets. Using a Markov regime-switching model to distinguish between regimes of high and low Bitcoin price volatility, this paper shows that while returns on the aggregate market portfolio cannot explain Bitcoin returns, other asset pricing risk factors, such as interest rates and implied stock market and foreign exchange market volatilities, are important determinants of Bitcoin returns. Distinguishing between periods of high and low Bitcoin price volatility reveals heterogeneity in the explanatory power of market risk factors; in particular, Bitcoin returns are more difficult to explain during periods of high volatility relative to periods with low volatility. This finding can partially explain why extant studies, which neglect to distinguish between exchange rate regimes in Bitcoin, have difficulty linking Bitcoin prices to economic fundamentals.

We develop an international capital asset pricing model in the presence of shadow costs of incomplete information and short sales. Our model shows the direct effect of exchange rate risk, information costs and short sales costs on asset prices. At equilibrium, this model gives an explicit expression of two systematic risk premium. The first one is linked to the exchange rate. The second one is related to international market risk. Our model explains in part the well-known home bias equity by market segmentation. This model, which is proposed for the first time in the literature, can be seen as an international version of Wu et al. (Rev Quant Finance Account 7:119–136, 1996) and Merton (J Finance 42:483–511, 1987) models of capital market equilibrium in international markets. Our analysis shows that the dispersion in beliefs increases the market inefficiency, and that short sale constraints can reduce the cost of ignorance and the magnitude of the home bias equity. Our model provides an operational approach in asset pricing to take account of previous important costs.

This paper examines the extent to which herding and feedback trading behaviors drive price dynamics across nine major cryptocurrencies. Using sample price data from bitcoin, ethereum, XRP, bitcoin cash, EOS, litecoin, stellar, cardano and IOTA, respectively, we document heterogeneity in the types of feedback trading strategies investors utilize across markets. Whereas some cryptocurrency markets show evidence of herding, or, 'trend chasing', behaviors, in other markets we show evidence of contrarian-type behaviors. These findings are important because they elucidate upon, firstly, what forces drive cryptocurrency markets and, secondly, how this type of trading behavior affects autocorrelation patters for cryptocurrencies. Finally, and from our intertemporal asset pricing model, we shed new light on the observed nature of the risk-return tradeoffs for each of our sampled cryptocurrencies.

This paper provides the inter-temporal capital asset pricing model with incomplete information and short sales constraints. We derive the general equilibrium market equation and the security market line of the “classical” capital asset pricing model in continuous time in the presence of incomplete information and short sales.

© The Author(s) 2018. A key prediction of the Capital Asset Pricing Model (CAPM) is that idiosyncratic risk is not priced by investors because in the absence of frictions it can be fully diversified away. In the presence of constraints on diversification, refinements of the CAPM conclude that the part of idiosyncratic risk that is not diversified should be priced. Recent empirical studies yielded mixed evidence with some studies finding positive correlation between idiosyncratic risk and stock returns, while other studies reported none or even negative correlation. We examine whether idiosyncratic risk is priced by the stock market and what are the probable causes for the mixed evidence produced by other studies, using monthly data for the US market covering the period from 1980 until 2013. We find that one-period volatility forecasts are not significantly correlated with stock returns. The mean-reverting unconditional volatility, however, is a robust predictor of returns. Consistent with economic theory, the size of the premium depends on the degree of ‘knowledge’ of the security among market participants. In particular, the premium for Nasdaq-traded stocks is higher than that for NYSE and Amex stocks. We also find stronger correlation between idiosyncratic risk and returns during recessions, which may suggest interaction of risk premium with decreased risk tolerance or other investment considerations like flight to safety or liquidity requirements. We identify the difference between the correlations of the idiosyncratic volatility estimators used by other studies and the true risk metric the mean-reverting volatility as the likely cause for the mixed evidence produced by other studies. Our results are robust with respect to liquidity, momentum, return reversals, unadjusted price, liquidity, credit quality, omitted factors, and hold at daily frequency. Korea National Research Foundation through Global Research Network Program

This paper proposes an investor-friendly random fuzzy portfolio selection model considering both robustness and adjustment of future asset returns derived from investor’s forecasts for financial tendency using a fuzzy inference method. It is important to predict the price or the return of each asset appropriately considering current market trends in portfolio optimization. In this paper, a standard multi-factor model, namely Arbitrage Pricing Theory (APT), is introduced as an asset pricing model. In addition, in order to extend standard APT by integrating important rules of current markets trends derived from technical analysis and fundamental analysis, each factor of APT is assumed to be a random fuzzy variable whose mean is adjusted by the fuzzy reasoning method, particularly product–sum-gravity method. Furthermore, it is also important for the investor to reduce the worst case of the total loss in terms of risk-averse. Therefore, worst-case conditional Value-at-Risk, which is a robust programming approach without assuming some specific random distribution, is considered. Since the proposed model is formulated as a biobjective programming problem both minimizing the value of worst-case conditional Value-at-Risk and maximizing the total expected return, it is equivalently transformed into the deterministic nonlinear programming problem using the satisficing trade-off method, and the efficient algorithm to obtain the optimal portfolio is developed. By solving our proposed model, the investor can obtain the risk-averse optimal portfolio with the large total return complying with current market trends.

The cited reference Nguyen et al. (2017) should have been set as Al Janabi et al. (2017) in the first paragraph of introduction.

An asset allocation problem of a member of a defined contribution (DC) pension fund is discussed in a hidden, Markov regime-switching, economy using backward stochastic differential equations, (BSDEs). A risk-based approach is considered, where the member selects an optimal asset mix with a view to minimizing the risk described by a convex risk measure of his/her terminal wealth. Firstly, filtering theory is adopted to transform the hidden, Markov regime-switching, economy into one with complete observations and to develop, (robust), filters for the hidden Markov chain. Then the optimal asset allocation problem of the member is formulated as a two-person, zero-sum stochastic differential game between the member and the market in the economy with complete observations. The BSDE approach is then used to solve the game problem and to characterize the saddle point of the game problem. An explicit expression for the optimal asset mix is obtained in the case of a convex risk measure with quadratic penalty and it can be considered a generalized version of the Merton ratio. An explicit expression for the optimal strategy of the market is also obtained, which leads to a risk-neutral wealth dynamic and may provide some insights into asset pricing in the economy with inflation risk and regime-switching risk. Numerical examples are provided to illustrate financial implications of the BSDE solution.

Since the establishment of the Shanghai Stock Exchange (SHSE) in 1990 and the Shenzhen Stock Exchange (SZSE) in 1991, China’s stock markets have expanded rapidly. Although this rapid growth has attracted considerable academic interest, few studies have examined the ability of conventional financial models to predict the share price movements of Chinese stock. This gap in the literature is significant, given the volatility of the Chinese stock markets and the added risk that arises from the Chinese legal and regulatory environment. In this paper we address this research gap by examining the predictive ability of several well-established forecasting models, including dynamic versions of a single-factor CAPM-based model and Fama and French’s three-factor model. In addition, we compare the forecasting ability of each of these models with that of an artificial neural network (ANN) model that contains the same predictor variables but relaxes the assumption of model linearity. Surprisingly, we find no statistical differences in the forecasting accuracy of the CAPM and three-factor model, a result that may reflect the emerging nature of the Chinese stock markets. We also find that each ANN model outperforms the corresponding linear model, indicating that neural networks may be a useful tool for stock price prediction in emerging markets.

The returns on most financial assets exhibit kurtosis and many also have probability distributions that possess skewness as well. In this paper a general multivariate model for the probability distribution of assets returns, which incorporates both kurtosis and skewness, is described. It is based on the multivariate extended skew-Student-t distribution. Salient features of the distribution are described and these are applied to the task of asset pricing. The paper shows that the market model is non-linear in general and that the sensitivity of asset returns to return on the market portfolio is not the same as the conventional beta, although this measure does arise in special cases. It is shown that the variance of asset returns is time varying and depends on the squared deviation of market portfolio return from its location parameter. The first order conditions for portfolio selection are described. Expected utility maximisers will select portfolios from an efficient surface, which is an analogue of the familiar mean-variance frontier, and which may be implemented using quadratic programming.

This paper addresses the problem of dynamic asset allocation under a bounded shortfall risk in a market composed of three assets: cash, stocks and a zero coupon bond. The dynamics of the instantaneous short rates is driven by a Hull and White model. In this setting, we determine and compare optimal investment strategies maximizing the CRRA utility of terminal wealth with and without value at risk constraint.

We develop a market-wide illiquidity risk factor based on run lengths and find that it is priced using standard asset-pricing specifications. Our theoretical framework of equity returns derives the result that average run lengths of individual stocks proxy for illiquidity, and are related to common measures of liquidity such as trading volume and trade price-impact. This relationship holds irrespective of the sampling frequency in the computation of run lengths. Thus, liquidity can be quantified by examining a stock’s run length signature, providing a statistical mechanics link across illiquidity metrics. Tests using daily equity return data for all stocks over the period 1962–2005 find that run lengths are decreasing in turnover, and increasing with bid-ask spreads, and price-impact. Illiquidity is shown to be a risk factor/characteristic in explaining equity returns.

We extend the classic mean-variance framework to a broad class of investment decisions under risk where investors select optimal portfolios of risky assets that include perfectly divisible as well as perfectly indivisible assets. We develop an algorithm for solving the associated mixed-integer nonlinear program and report on the results of a computational study. We then study the mean-variance structure of the investment frontier facing an individual investor in the presence of investment opportunities in both risky divisible and indivisible assets. Finally, we analyze the economic implications of the presence of investment opportunities in risky indivisible assets on the investor’s investment strategy and on his risk evaluation.

We focus on affine term structure models as tools for active bond portfolio management. Our financial exercise comprises the following steps: 1) forecast the future values of the state variables implied by several multi-factor models; 2) approximate the conditional moments of the state vector to come up with discrete scenarios for the future state variables 3) compute bond returns for various maturities at future dates from the theoretical asset pricing relations 4) solve the portfolio problem faced by an investor with a six month horizon who takes into account the possibility to rebalance after one quarter. The sequence of optimal portfolios is evaluated in terms of financial properties. We show that a financial based evaluation of term structure models may yield results conflicting with those obtained from a statistical evaluation.

The investor's preference in risk estimation of portfolio selection problems is important as it influences investment strategies. In this paper a minimax risk criterion is considered. Specifically, the investor aims to restrict the standard deviation for each of the available stocks. The corresponding portfolio optimization problem is formulated as a linear program. Hence it can be implemented easily. A capital asset pricing model between the market portfolio and each individual return for this model is established using nonsmooth optimization methods. Some numerical examples are given to illustrate our approach for the risk estimation.

In this paper, we first define risk in an axiomatic way and a class of utility functions suitable for the so-called mean-risk analysis. Then, we show that, in a portfolio selection problem with multiple risky investments, an investor who is more risk averse in the Arrow-Pratt sense prefers less risk, in the sense of this paper, with less mean return, and an investor who displays increasing (decreasing) relative risk aversion becomes more conservative (aggressive) as the initial capital increases. The risk aversion effect for diversification on optimal portfolios is also discussed.