Market-wide illiquidity and the distribution of non-parametric stochastic discount factors

Employing out-of-sample non-parametric estimation techniques, we show that market-wide liquidity risk matters for asset pricing independently of the specific functional form of the stochastic discount factor (SDF) and, therefore, of the asset pricing model specification. Market-wide illiquidity significantly affects the distribution of the SDF. Specifically, it boosts up the volatility of the SDF, causing minor effects on higher moments of its distribution. This finding is robust to the use of different sets of test assets in the estimation of the SDF, including equity and corporate bond portfolios, and the use of a high-dimensional data estimation procedure.     

Financial Intermediaries and the Cross‐Section of Asset Returns

Financial intermediaries trade frequently in many markets using sophisticated models. Their marginal value of wealth should therefore provide a more informative stochastic discount factor (SDF) than that of a representative consumer. Guided by theory, we use shocks to the leverage of securities broker‐dealers to construct an intermediary SDF. Intuitively, deteriorating funding conditions are associated with deleveraging and high marginal value of wealth. Our single‐factor model prices size, book‐to‐market, momentum, and bond portfolios with an R² of 77% and an average annual pricing error of 1%—performing as well as standard multifactor benchmarks designed to price these assets.     

Dynamic Portfolio Selection by Augmenting the Asset Space

We present a novel approach to dynamic portfolio selection that is as easy to implement as the static Markowitz paradigm. We expand the set of assets to include mechanically managed portfolios and optimize statically in this extended asset space. We consider “conditional” portfolios, which invest in each asset an amount proportional to conditioning variables, and “timing” portfolios, which invest in each asset for a single period and in the risk‐free asset for all other periods. The static choice of these managed portfolios represents a dynamic strategy that closely approximates the optimal dynamic strategy for horizons up to 5 years.     

The coskewness puzzle

We propose a novel approach to testing non-linear stochastic discount factor (SDF) specifications that arise in rational representative investor models. Our approach does not require overly-restrictive assumptions about the shape of investors’ preferences, typically imposed by the extant literature, and is based instead on restrictions that rule out “good deals”, i.e., arbitrage opportunities as well as unduly large Sharpe ratios. We apply this framework to test the empirical admissibility of 3 and 4-moment versions of the CAPM. We find that, while coskewness and cokurtosis risk help price a number of stock strategies and portfolios, including static strategies based on a fine industry-level diversification, momentum strategies and portfolios managed on the basis of available information, the CAPM and its 3 and 4-moment versions cannot provide an exhaustive account of observed asset returns.     

Least-squares approach to risk parity in portfolio selection

The risk parity portfolio selection problem aims to find such portfolios for which the contributions of risk from all assets are equally weighted. Portfolios constructed using the risk parity approach are a compromise between two well-known diversification techniques: minimum variance optimization and the equal weighting approach. In this paper, we discuss the problem of finding portfolios that satisfy risk parity over either individual assets or groups of assets. We describe the set of all risk parity solutions by using convex optimization techniques over orthants and we show that this set may contain an exponential number of solutions. We then propose an alternative non-convex least-squares model whose set of optimal solutions includes all risk parity solutions, and propose a modified formulation which aims at selecting the most desirable risk parity solution according to a given criterion. When general bounds are considered, a risk parity solution may not exist. In this case, the non-convex least-squares model seeks a feasible portfolio which is as close to risk parity as possible. Furthermore, we propose an alternating linearization framework to solve this non-convex model. Numerical experiments indicate the effectiveness of our technique in terms of both speed and accuracy.     

Bank Capital Regulation of Trading Portfolios: An Assessment of the Basel Framework

In setting minimum capital requirements for trading portfolios, the Basel Committee on Banking Supervision (1996, 2011a, 2013) initially used Value‐at‐Risk (VaR), then both VaR and stressed VaR (SVaR), and most recently, stressed Conditional VaR (SCVaR). Accordingly, we examine the use of SCVaR to measure risk and set these requirements. Assuming elliptically distributed asset returns, we show that portfolios on the mean‐SCVaR frontier generally lie away from the mean‐variance (M‐V) frontier. In a plausible numerical example, we find that such portfolios tend to have considerably higher ratios of risk (measured by, e.g., standard deviation) to minimum capital requirement than those of portfolios on the M‐V frontier. Also, we find that requirements based on SCVaR are smaller than those based on both VaR and SVaR but exceed those based on just VaR. Finally, we find that requirements based on SCVaR are less procyclical than those based on either VaR or both VaR and SVaR. Overall, our paper suggests that the use of SCVaR to measure risk and set requirements is not a panacea.     

Mitigating Estimation Risk in Asset Allocation: Diagonal Models Versus 1/N Diversification

Recent literature suggests that optimal asset‐allocation models struggle to consistently outperform the 1/N naïve diversification strategy, which highlights estimation‐risk concerns. We propose a dichotomous classification of asset‐allocation models based on which elements of the inverse covariance matrix that a model uses: diagonal only versus full matrix. We argue that parsimonious diagonal‐only strategies, which use limited information such as volatility or idiosyncratic volatility, are likely to offer a good tradeoff between incorporating limited information while mitigating estimation risk. Evaluating five sets of portfolios over 1926–2012, we find that 1/N is generally not optimal when compared with these diagonal strategies.     

Bond portfolio optimization using dynamic factor models

A general class of dynamic factor models is used to obtain optimal bond portfolios, and to develop a duration-constrained mean-variance optimization, which can be used to improve bond indexing. An empirical application involving two large data sets of U.S. Treasuries shows that the proposed portfolio policy outperforms a set of yield curve strategies used in bond desks. Additionally, we propose a dynamic rule to switch among alternative bond investment strategies, and find that the benefits of such dynamic rule are even more pronounced when the set of available policies is augmented with the proposed mean-variance portfolios.     

A neural‐network‐based decision‐making model in the peer‐to‐peer lending market

This study proposes an investment recommendation model for peer‐to‐peer (P2P) lending. P2P lenders usually are inexpert, so helping them to make the best decision for their investments is vital. In this study, while we aim to compare the performance of different artificial neural network (ANN) models, we evaluate loans from two perspectives: risk and return. The net present value (NPV) is considered as the return variable. To the best of our knowledge, NPV has been used in few studies in the P2P lending context. Considering the advantages of using NPV, we aim to improve decision‐making models in this market by the use of NPV and the integration of supervised learning and optimization algorithms that can be considered as one of our contributions. In order to predict NPV, three ANN models are compared concerning mean square error, mean absolute error, and root‐mean‐square error to find the optimal ANN model. Furthermore, for the risk evaluation, the probability of default of loans is computed using logistic regression. Investors in the P2P lending market can share their assets between different loans, so the procedure of P2P investment is similar to portfolio optimization. In this context, we minimize the risk of a portfolio for a minimum acceptable level of return. To analyse the effectiveness of our proposed model, we compare our decision‐making algorithm with the output of a traditional model. The experimental results on a real‐world data set show that our model leads to a better investment concerning both risk and return.     

Creating Fama and French Factors with Style

This paper utilizes Frank Russell style portfolios to create useful proxies for the Fama and French (1992) factors. The proxy‐mimicking portfolios are shown to represent a pervasive source of exposure across U.S. industry portfolios and to generally possess similar properties to those utilized in the finance literature. Further, a set of multivariate asset‐pricing tests of the three‐factor Fama and French asset‐pricing (FF) model based on the proxy factors fails to reject the model. However, these tests do not reveal strong evidence of significantly positive risk premiums, particularly in the case of the size and book‐to‐market factors.     

Reduction of estimation risk in optimal portfolio choice using redundant constraints

It is well known that when the moments of the distribution governing returns are estimated from sample data, the out-of-sample performance of the optimal solution of a mean–variance (MV) portfolio problem deteriorates as a consequence of the so-called “estimation risk”. In this document we provide a theoretical analysis of the effects caused by redundant constraints on the out-of-sample performance of optimal MV portfolios. In particular, we show that the out-of-sample performance of the plug-in estimator of the optimal MV portfolio can be improved by adding any set of redundant linear constraints. We also illustrate our findings when risky assets are equally correlated and identically distributed. In this specific case, we report an emerging trade-off between diversification and estimation risk and that the allocation of estimation risk across portfolios forming the optimal solution changes dramatically in terms of number of assets and correlations.     

Hedging volatility risk

Volatility risk plays an important role in the management of portfolios of derivative assets as well as portfolios of basic assets. This risk is currently managed by volatility “swaps” or futures. However, this risk could be managed more efficiently using options on volatility that were proposed in the past but were never introduced mainly due to the lack of a cost efficient tradable underlying asset.The objective of this paper is to introduce a new volatility instrument, an option on a straddle, which can be used to hedge volatility risk. The design and valuation of such an instrument are the basic ingredients of a successful financial product. In order to value these options, we combine the approaches of compound options and stochastic volatility. Our numerical results show that the straddle option is a powerful instrument to hedge volatility risk. An additional benefit of such an innovation is that it will provide a direct estimate of the market price for volatility risk.     

Stochastic volatility and time-varying country risk in emerging markets

This study suggests an alternative method to estimate time-varying country risk. We first apply a new multivariate stochastic volatility (SV) model to a set of emerging stock markets. To estimate the SV model, we use a Bayesian Markov chain Monte Carlo simulation procedure. By applying the deviance information criterion, we show that the new model performs well relative to alternative multivariate SV models. We then compute the conditional betas for the different markets and compare the results with an often-used procedure based on multivariate GARCH models. We show that the new multivariate SV model more accurately captures the time-varying nature of country risk. The conditional betas show signs of large variations, indicating the importance of taking time-varying country risk into consideration when managing emerging market portfolios.     

Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps

Green and Hollifield (1992) argue that the presence of a dominant factor would result in extreme negative weights in mean‐variance efficient portfolios even in the absence of estimation errors. In that case, imposing no‐short‐sale constraints should hurt, whereas empirical evidence is often to the contrary. We reconcile this apparent contradiction. We explain why constraining portfolio weights to be nonnegative can reduce the risk in estimated optimal portfolios even when the constraints are wrong. Surprisingly, with no‐short‐sale constraints in place, the sample covariance matrix performs as well as covariance matrix estimates based on factor models, shrinkage estimators, and daily data.     

A Critique of the Stochastic Discount Factor Methodology

In this paper, we point out that the widely used stochastic discount factor (SDF) methodology ignores a fully specified model for asset returns. As a result, it suffers from two potential problems when asset returns follow a linear factor model. The first problem is that the risk premium estimate from the SDF methodology is unreliable. The second problem is that the specification test under the SDF methodology has very low power in detecting misspecified models. Traditional methodologies typically incorporate a fully specified model for asset returns, and they can perform substantially better than the SDF methodology.     

On Bayesian Value at Risk: From Linear to Non-Linear Portfolios

This paper proposes the use of Bayesian approach to implement Value at Risk (VaR) model for both linear and non-linear portfolios. The Bayesian approach provides risk traders with the flexibility of adjusting their VaR models according to their subjective views. First, we deal with the case of linear portfolios. By imposing the conjugate-prior assumptions, a closed-form expression for the Bayesian VaR is obtained. The Bayesian VaR model can also be adjusted in order to deal with the ageing effect of the past data. By adopting Gerber-Shiu's option-pricing model, our Bayesian VaR model can also be applied to deal with non-linear portfolios of derivatives. We obtain an exact formula for the Bayesian VaR in the case of a single European call option. We adopt the method of back-testing to compare the non-adjusted and adjusted Bayesian VaR models with their corresponding classical counterparts in both linear and non-linear cases.     

Sequential Learning,Predictability, and Optimal Portfolio Returns

This paper finds statistically and economically significant out‐of‐sample portfolio benefits for an investor who uses models of return predictability when forming optimal portfolios. Investors must account for estimation risk, and incorporate an ensemble of important features, including time‐varying volatility, and time‐varying expected returns driven by payout yield measures that include share repurchase and issuance. Prior research documents a lack of benefits to return predictability, and our results suggest that this is largely due to omitting time‐varying volatility and estimation risk. We also document the sequential process of investors learning about parameters, state variables, and models as new data arrive.     

INTERNATIONAL DIVERSIFICATION OF EQUITIES AND FIXED-INCOME SECURITIES

Portfolio selection models have been applied principally to common stocks traded in the United States and in foreign stock markets. This study examines the efficient set of portfolios selected from a choice set that includes returns derived from domestic and international corporate bond and government bond indices as well as domestic and international stock indices. To assess the benefits of international multi-asset diversification, the authors examine the following issues: (1) the extent to which international and domestic fixed-income securities are included in efficient portfolios; (2) the effect on efficient set composition of using the Sharpe portfolio selection model as compared to the Markowitz portfolio selection model; (3) the sensitivity of efficient set characteristics produced from a single-index based portfolio selection model to alternative world market indices; and (4) the correspondence between expected and realized portfolio risk and return for the different portfolio selection models.