An intertemporal asset pricing model with stochastic consumption and investment opportunities

This paper derives a single-beta asset pricing model in a multi-good, continuous-time model with uncertain consumption-goods prices and uncertain investment opportunities. When no riskless asset exists, a zero-beta pricing model is derived. Asset betas are measured relative to changes in the aggregate real consumption rate, rather than relative to the market. In a single-good model, an individual's asset portfolio results in an optimal consumption rate that has the maximum possible correlation with changes in aggregate consumption. If the capital markets are unconstrained Pareto-optimal, then changes in all individuals' optimal consumption rates are shown to be perfectly correlated.     

A note on the geometry of Shanken's CSR T2 test for mean/variance efficiency

Shanken (1985) derives a test for the zero-beta capital asset pricing model (CAPM) which, as he points out, is equivalent to a test of the mean/variance efficiency of the market portfolio. This note illustrates the geometry of Shanken's test in the mean/variance space.     

Using linear and goal programming to immunize bond portfolios

Bierwag and Khang's (1979) model of immunizing a portfolio of default-free government bonds is expanded here to include default-grade corporate bonds. The immunizing equation is found to be slightly different. Both linear and goal programming are shown to be alternative techniques for identifying an investor's optimal immunizing portfolio.     

Optimum consumption and portfolio rules with money as an asset

This article generalizes Merton's optimum consumption and portfolio rules in continuous time by introducing money as a capital asset and allowing for uncertain inflation. Assuming that prices are log-normally distributed, a three-funds theorem is derived and the introduction of money is shown not to change the form of the standard inflation-adjusted CAPM but to change the market price of risk. The individual's consumption-portfolio problem is completely solved under uncertain inflation if his utility function is iso-elastic in its arguments. Comparative statics are used to assess the influence of changes in exogenous parameters on the individual's optimal rules.     

An application of a three-factor performance index to measure stockholder gains from merger

This article re-examines the magnitude of stockholder gains from merger. To measure stockholder gains we employ four alternative two-factor market-industry models in combination with a matched non-merging control group. The four two-factor models are based on either the capital asset pricing model or Black's (1972) zero-beta model combined with two alternative industry factors. The four models are shown to produce generally consistent results. However, the results from a two-factor model are sometimes different from the results of a simpler one-factor model. Also, the introduction of a third factor, the non-merging control group, is shown to have a substantial impact on performance measurement.     

On portfolio optimization: Imposing the right constraints

We reassess the recent finding that no established portfolio strategy outperforms the naively diversified portfolio, 1/N, by developing a constrained minimum-variance portfolio strategy on a shrinkage theory based framework. Our results show that our constrained minimum-variance portfolio yields significantly lower out-of-sample variances than many established minimum-variance portfolio strategies. Further, we observe that our portfolio strategy achieves higher Sharpe ratios than 1/N, amounting to an average Sharpe ratio increase of 32.5% across our six empirical datasets. We find that our constrained minimum-variance strategy is the only strategy that achieves the goal of improving the Sharpe ratio of 1/N consistently and significantly. At the same time, our developed portfolio strategy achieves a comparatively low turnover and exhibits no excessive short interest.     

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.     

Exact Arbitrage Pricing and the Minimum-Variance Frontier

The author examines the relationship between the Arbitrage Pricing Theory of Ross and mean-variance analysis. In particular, conditions are derived on the vector of the factor risk premia that are equivalent to the existence of a strictly positively weighted portfolio on the minimum-variance frontier. Also, a sufficient condition is given under which the existence of a positive minimum-variance portfolio of all the assets in the economy will imply the existence of a positive minimum-variance portfolio on a subset. This means that rejection of the hypothesis of the existence of a positive minimum-variance portfolio on a subset satisfying this condition implies rejection for the whole set.     

Using industry momentum to improve portfolio performance

Minimum-variance portfolios, which ignore the mean and focus on the (co)variances of asset returns, outperform mean–variance approaches in out-of-sample tests. Despite these promising results, minimum-variance policies fail to deliver a superior performance compared with the simple 1/N rule. In this paper, we propose a parametric portfolio policy that uses industry return momentum to improve portfolio performance. Our portfolio policies outperform a broad selection of established portfolio strategies in terms of Sharpe ratio and certainty equivalent returns. The proposed policies are particularly suitable for investors because portfolio turnover is only moderately increased compared to standard minimum-variance portfolios.     

Dynamic mean–VaR portfolio selection in continuous time

The value-at-risk (VaR) is one of the most well-known downside risk measures due to its intuitive meaning and wide spectra of applications in practice. In this paper, we investigate the dynamic mean–VaR portfolio selection formulation in continuous time, while the majority of the current literature on mean–VaR portfolio selection mainly focuses on its static versions. Our contributions are twofold, in both building up a tractable formulation and deriving the corresponding optimal portfolio policy. By imposing a limit funding level on the terminal wealth, we conquer the ill-posedness exhibited in the original dynamic mean–VaR portfolio formulation. To overcome the difficulties arising from the VaR constraint and no bankruptcy constraint, we have combined the martingale approach with the quantile optimization technique in our solution framework to derive the optimal portfolio policy. In particular, we have characterized the condition for the existence of the Lagrange multiplier. When the opportunity set of the market setting is deterministic, the portfolio policy becomes analytical. Furthermore, the limit funding level not only enables us to solve the dynamic mean–VaR portfolio selection problem, but also offers a flexibility to tame the aggressiveness of the portfolio policy.     

Applying portfolio theory to global bank lending

Portfolio theory provides some insights into how a bank should manage its global exposures. Practical application of some of the principles of portfolio analysis is possible if comparable credit ratings are available and if the impact on each loan's rating of likely future events can be assessed. If further restrictive assumptions are made about which quality dimensions of the portfolio are more important (and how much more important), and if judgements can be quantified about what risk-return tradeoffs are acceptable, then it is possible to derive measures to guide exposure and pricing decisions. This article is related to the other papers in this special issue in that country and corporate risk assessment methodologies can provide important inputs into the portfolio analysis. This paper, however, attempts to go beyond the evaluation of risk at the level of individual companies, countries, or other loan customers, and to focus instead on the problem of managing the riskiness of the overall bank loan portfolio.     

Tests of the CAPM with Time-Varying Covariances: A Multivariate GARCH Approach

This paper examines an asset pricing model in which the Sharpe-Lintner CAPM and the zero-beta CAPM are special cases. The model allows the ratio of expected market risk premium to market variance, the conditional expected excess returns, and the risks to change over time. The results are found to be sensitive to the choice of the portfolio formation techniques. Significant time variability is shown in the conditional expected excess asset returns and risks and also in the reward-to-risk ratio.     

Consumption correlatedness and risk measurement in economies with non-traded assets and heterogeneous information

A technique is presented for deriving equilibrium models of asset risk premia in continuous time models which does not require the complete solution of a consumer's continuous time stochastic control problem. The technique is used to show that even if traders have heterogeneous information about asset returns and/or there are non-traded assets, then the risk premium of a traded asset is determined by the covariance between the asset's return and the rate of change in per capita consumption. We only require the assumption that traders' consumptions and traded asset values form an Ito process.     

High-dimensional index tracking based on the adaptive elastic net

When a portfolio consists of a large number of assets, it generally incorporates too many small and illiquid positions and needs a large amount of rebalancing, which can involve large transaction costs. For financial index tracking, it is desirable to avoid such atomized, unstable portfolios, which are difficult to realize and manage. A natural way of achieving this goal is to build a tracking portfolio that is sparse with only a small number of assets in practice. The cardinality constraint approach, by directly restricting the number of assets held in the tracking portfolio, is a natural idea. However, it requires the pre-specification of the maximum number of assets selected, which is rarely practicable. Moreover, the cardinality constrained optimization problem is shown to be NP-hard. Solving such a problem will be computationally expensive, especially in high-dimensional settings. Motivated by this, this paper employs a regularization approach based on the adaptive elastic-net (Aenet) model for high-dimensional index tracking. The proposed method represents a family of convex regularization methods, which nests the traditional Lasso, adaptive Lasso (Alasso), and elastic-net (Enet) as special cases. To make the formulation more practical and general, we also take the full investment condition and turnover restrictions (or transaction costs) into account. An efficient algorithm based on coordinate descent with closed-form updates is derived to tackle the resulting optimization problem. Empirical results show that the proposed method is computationally efficient and has competitive out-of-sample performance, especially in high-dimensional settings.     

Prospect theory–based portfolio optimization: an empirical study and analysis using intelligent algorithms

The behaviourally based portfolio selection problem with investor’s loss aversion and risk aversion biases in portfolio choice under uncertainty is studied. The main results of this work are: developed heuristic approaches for the prospect theory model proposed by Kahneman and Tversky in 1979 as well as an empirical comparative analysis of this model and the index tracking model. The crucial assumption is that behavioural features of the prospect theory model provide better downside protection than traditional approaches to the portfolio selection problem. In this research the large-scale computational results for the prospect theory model have been obtained for real financial market data with up to 225 assets. Previously, as far as we are aware, only small laboratory tests (2–3 artificial assets) have been presented in the literature. In order to investigate empirically the performance of the behaviourally based model, a differential evolution algorithm and a genetic algorithm which are capable of dealing with a large universe of assets have been developed. Specific breeding and mutation, as well as normalization, have been implemented in the algorithms. A tabulated comparative analysis of the algorithms’ parameter choice is presented. The prospect theory model with the reference point being the index is compared to the index tracking model. A cardinality constraint has been implemented to the basic index tracking and the prospect theory models. The portfolio diversification benefit has been found. The aggressive behaviour in terms of returns of the prospect theory model with the reference point being the index leads to better performance of this model in a bullish market. However, it performed worse in a bearish market than the index tracking model. A tabulated comparative analysis of the performance of the two studied models is provided in this paper for in-sample and out-of-sample tests. The performance of the studied models has been tested out-of-sample in different conditions using simulation of the distribution of a growing market and simulation of the t-distribution with fat tails which characterises the dynamics of a decreasing or crisis market.     

Taxes,transactions costs and the clientele effect of dividends

This paper is an empirical investigation into the extent to which transactions costs and taxes influence individual investors' portfolios. Using actual portfolio and demoraphic data made available by the Individual Investor Research Project at Purdue University, this study finds evidence of a significant dividend clientele effect. Reasonable proxy variables used to measure time preferences and tax rates in part explain the cross sectional variability of investors' portfolio dividend yields. The variables that are most important in influencing the individual's dividend decision are age, and a measure of the investor's differential tax rate on dividends and capital gains.     

Systematic risk and the theory of the firm: A reexamination

A recent microeconomic model of the determinants of equity betas (Subrahmanyam and Thomadakis 1980) is generalized by including risky human capital in the market portfolio and allowing a general covariance structure between the model's sources of uncertainty. This provides an explanation of the ambiguous effect of operating leverage on beta by viewing human capital and equity contributors as risk sharers in the firm's output risk. This explanation may help to clarify the apparent conflict with the previous literature. The relationship between systematic risk and monopoly power is rederived and shown to depend upon a plausible condition on the correlation between wage rate and price uncertainty. Finally, the public policy implications of this analysis are presented.     

Consumption and Investment Motives and the Portfolio Choices of Homeowners

This article investigates the portfolio choices of homeowners, taking into account the investment constraint introduced by Henderson and Ioannides (1983). This constraint requires housing investment by homeowners to be at least as large as housing consumption. It is shown that when the constraint is binding, the homeowner's optimal portfolio is ineffcient in a mean-variance sense. Thus, portfolio inefficiency is not an indication that consumers are irrational or careless in their financial decisions. Instead, inefficiency can be seen as the result of a rational balancing of the consumption benefits and portfolio distortion associated with housing investment.     

Comments on the valuation of derivative assets

This paper presents an alternative approach to derive the Breeden-Litzenberger valuation formula, which expresses the price of an arbitrary derivative security in terms of call options' prices. This valuation formula follows from the observation that a continuous derivative security can be replicated by a portfolio including a bond and call options with all possible exercise prices. Discrete terms are added to the original Breeden-Litzenberger formula to reflect possible discontinuities of the call option price's derivative with respect to the exercise price. These discontinuities are subsequently shown to correspond to mass points of the probability distribution of the stock price. Several applications of the Breeden-Litzenberger valuation formula are demonstrated.     

Risky asset pricing based on safety first fund management

We study a portfolio selection model based on Kataoka's safety-first criterion (KSF model in short). We assume that the market is complete but without risk-free asset, and that the returns are jointly elliptically distributed. With these assumptions, we provide an explicit analytical optimal solution for the KSF model and obtain some geometrical properties of the efficient frontier in the plane of probability risk degree z _α and target return r _α. We further prove a two-fund separation and tangency portfolio theorem in the spirit of the traditional mean-variance analysis. We also establish a risky asset pricing model based on risky funds that is similar to Black's zero-beta capital asset pricing model (CAPM, for short). Moreover, we simplify our risky asset pricing model using a derivative risky fund as a reference for market evaluation.