Normative portfolio theory

In this paper, we correct the adverse impact of estimation risk on both portfolio weights and performance with two new equity allocation methods we implement with estimation-free and estimated ex-ante returns. Portfolios with estimation-free ex-ante returns and systematic-to-unsystematic risk weights have statistically higher Sharpe ratios than both similar portfolios with estimated ex-ante returns and 1/N′th portfolios. Optimal portfolio methods with well-behaved weights guide investors in a way not hitherto possible (normative portfolio theory).     

Instantaneous portfolio theory

Instantaneous risk is described by the arrival rate of jumps in log price relatives. As a consequence there is then no concept of a mean return compensating risk exposures, as zero is the only instantaneous risk-free return. From this perspective, all portfolios are subject to risk and there are only bad and better ways of holding risk. For the purpose of analysing portfolios, the univariate variance gamma model is extended to higher dimensions with an arrival rate function with full high-dimensional support and independent levels of marginal skewness and excess kurtosis. Investment objectives are given by concave lower price functionals formulated as measure distorted variations. Specific measure distortions are calibrated to data on S&P 500 index options and the time series of the index. The time series estimation is conducted by digital moment matching applied to uncentred data and it is shown that data centring is a noisy activity to be generally avoided. The evaluation of the instantaneous investment objective requires the computation of measure distorted integrals. This is done using Monte Carlo applied to gamma distributed ellipitical radii with a low shape parameter. The resulting risk reward frontiers are between finite variation as the reward and measure distorted variations as risk. In the absence of an instantaneous risk-free return, portfolios on the efficient frontier are characterized by differences in asset variations being given by differences in asset covariations with the risk charge differential of the efficient portfolio. Portfolio variations seen as the equivalent of excess returns, may optimally be negative. Lower price maximizing portfolios are presented in two, six and twenty five dimensions.     

The numeraire portfolio: a new perspective on financial theory

The numeraire portfolio, also called the optimal growth portfolio, allows simple derivations of the main results of financial theory. The prices of self financing portfolios, when the optimal growth portfolio is the numeraire, are martingales in the ‘true’ (historical) probability. Given the dynamics of the traded securities, the composition of the numeraire portfolio as well as its value are easily computable. Among its numerous properties, the numeraire portfolio is instantaneously mean variance efficient. This key feature allows a simple derivation of standard continuous time CAPM, CCAPM, APT and contingent claim pricing. Moreover, since the Radon-Nikodym derivatives of the usual martingale measures are very simple functions of the numeraire portfolio, the latter provides a convenient link between the standard Capital Market Theory a la Merton and the probabilistic approach a la Harrison-Kreps-Pliska.     

Diversification in lottery-like features and portfolio pricing discount: Evidence from closed-end funds

Why do portfolios often trade at discounts relative to the sum of their components? I provide a new explanation based on the diversification in lottery-like features. I argue that portfolios trade at discounts when their components exhibit a strong lottery-like feature but a low tendency of producing extreme payoffs together. This discount can be partially mitigated if lottery-like components tend to produce extreme payoffs at the same time. I use the closed-end fund setting to provide empirical supports for this explanation. My findings support prospect theory from an alternative perspective and provide a novel explanation for the closed-end fund puzzle.     

International portfolio selection with exchange rate risk: A behavioural portfolio theory perspective

This paper analyzes international portfolio selection with exchange rate risk based on behavioural portfolio theory (BPT). We characterize the conditions under which the BPT problem with a single foreign market has an optimal solution, and show that the optimal portfolio contains the traditional mean–variance efficient portfolio without consideration of exchange rate risk, and an uncorrelated component constructed to hedge against exchange rate risk. We illustrate that the optimal portfolio must be mean–variance efficient with exchange rate risk, while the same is not true from the perspective of local investors unless certain conditions are satisfied. We further establish that international portfolio selection in the BPT with multiple foreign markets consists of two sequential decisions. Investors first select the optimal BPT portfolio in each market, overlooking covariances among markets, and then allocate funds across markets according to a specific rule to achieve mean–variance efficiency or to minimize the loss in efficiency.     

Market-to-book ratio in stochastic portfolio theory

Finance and Stochastics - We study market-to-book ratios of stocks in the context of stochastic portfolio theory. Functionally generated portfolios that depend on auxiliary economic variables other...     

Stochastic portfolio theory and the low beta anomaly

Many studies have found that portfolios of low beta stocks have higher growth rates than portfolios of high beta stocks and have concluded that low beta stocks have higher growth rates than high beta stocks. Since rational investor behavior is thought to imply that additional risk is rewarded with additional return, the alleged higher growth rates of low beta versus high beta stocks has been termed a ‘Low Beta Anomaly’ (LBA). However, it is premature to conclude that these observed LBAs are due to stocks’ differential growth rates, because the tested portfolios are traded. Stochastic Portfolio Theory (SPT) shows that traded portfolios’ growth rates can exceed the growth rates of their stocks. This paper presents several SPT models of an LBA that do not require investment constraints, irrational investor behavior, or that low beta stocks have higher growth rates than high beta stocks. These LBAs are due to reconstitution relative volatility capture that favors portfolios of low vs. high beta stocks. They result from trading profit, not differential growth rates between low and high beta stocks. Monte Carlo simulations demonstrate a reconstitution relative volatility capture LBA that is consistent with the models and the literature.     

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.     

Trading volume: definitions, data analysis, and implications of portfolio theory

We examine the implications of portfolio theory for the cross-sectionalbehavior of equity trading volume. Two-fund separation theoremssuggest a natural definition for trading activity: share turnover.If two-fund separation holds, share turnover must be identicalfor all securities. If (K + 1)-fund separation holds, we showthat turnover satisfies an approximately linear K-factor structure.These implications are examined empirically using individualweekly turnover data for NYSE and AMEX securities from 1962to 1996. We find strong evidence against two-fund separation,and a principal-components decomposition suggests that turnoveris well approximated by a two-factor linear model.     

A portfolio based theory of excessive foreign borrowing and capital control in a small open economy

We develop a simple model of portfolio choice in a mean variance framework to address the issue of international borrowing and financial crisis. Instead of adverse selection or moral hazard of lending and borrowing activities we emphasise the role of exchange rate movement. Syndicated borrowing by way of internalising the aggregate effect tends to restrict excessive borrowing from external source. However, this may undermine the welfare consequences by further aggravating the extent of risk undertaken in the process. There is a built-in externality in the model that leads to over exposure to foreign currency debt and readily calls for intervention by the government. Government intervention by way of a tax on foreign borrowing may help restrain the amount of external debt and implement the first best.     

International portfolio diversification: a synthesis and an update

This paper provides a synthesis of the existing literature on international portfolio diversification and presents some new results on the subject. We address the question of whether international portfolio diversification is always a reasonable method of reducing the risk of an investment portfolio without negatively affecting its return expectations. Unfortunately, there is still not a simple answer to this question. When ex-post data is examined, potential benefits of international diversification can certainly be detected. However, we also argue that it might be difficult for investors to select an optimal investment strategy ex-ante, when the correlation structure among the international equity is unstable over time. While such findings do not completely rule out the potential benefits of international diversification, they certainly make them more difficult to realize in practice.     

Positive accounting theory: A review

Watts and Zimmerman's Positive Accounting Theory provides a refreshing, controversial and important contribution to accounting thought. It is important because of its vigorous emphasis on the entity's actual choice of financial accounting technique (or, more broadly, financial reporting activity). It is controversial because the theory and empirical techniques it conveys are not fully developed. It is refreshing because it challenges us to expand our thinking about the nature of accounting institutions.In this essay, I try to document these claims about the content and significance of Positive Accounting Theory. The first section presents my interpretation of the work. The next section lists some concerns which I feel are important in consuming the work and in providing directions for continued labor. The third section discusses some unusual strengths in the work, while the final one provides some speculation about where accounting thought might next venture.Before proceeding, though, a caveat emptor warning must be issued. This essay presents both aspects which I learned about and also those which I worried about while consuming Positive Accounting Theory. It is an experiential report.     

Transfers and bequests: a portfolio analysis in a Nash game

This paper develops a two-stage non-cooperative Nash game framework of parental–children interactions to explain the equal division puzzle in bequests. In the analysis, a portfolio approach is adopted for characterizing how altruistic parents allocate their inheritable wealth between inter-vivos transfers and post-mortem bequests. The model includes elements of strategic altruism, exchange of family-specific merit goods, transfer-seeking behavior by competing siblings, and parents’ “post-mortem reputation” in bequest division. Allowing for children’s heterogeneity and interactions, we find that inter-vivos transfers are unevenly distributed between the children, despite an equal degree of parental altruism. Moreover, we show the compatibility of unequal inter-vivos transfers and equal bequests, regardless of earnings differentials across children.      

Benchmark-based evaluation of portfolio performance: a characterization

Benchmarking is a universal practice in portfolio management and is well-studied in the optimal portfolio selection literature. This paper derives axiomatic foundations of the relative return, which underlies a benchmark-based evaluation of portfolio performance. We show that the existence of a benchmark naturally arises from a few basic axioms and is tightly linked to the economic theory. Our method relies on the use of both axiomatic and economic approaches to index number theory. We also analyze the problem of optimal portfolio selection under complete uncertainty about a future price system, where the objective function is the relative return.     

Continuous Maturity Diversification of Default-Free Bond Portfolios and a Generalization of Efficient Diversification

This paper presents a method for solving the mean-variance portfolio selection problem that is applicable to the case where the number of securities is nondenumerably infinite. Necessary conditions for the existence of an optimal portfolio density are obtained and an expression for the efficient frontier is derived. The conditions for the existence of an optimal portfolio of continuously maturing bonds when their covariance matrix is singular are used to derive an arbitrage-free bond pricing equation. A method for estimating the covariance matrix and the associated efficient frontier is presented.     

Non-bank public and commercial bank portfolio behavior in the Brunner-Meltzer model: A review and clarification

This paper investigates the relationship between a portfolio theoretic model of non-bank public and commercial bank behavior and the Brunner-Meltzer non-linear money supply hypothesis. We examine the recent modification of the Brunner-Meltzer macroeconomic model suggested by Friedman and Froewiss (1977), discuss its shortcomings, and argue that the unmodified model is valid if one adopts the monetary sector equilibria definition of Saving (1977).     

The effect of mortgage form on borrower interest rate risk: A portfolio theory approach

The problems faced by U.S. regulatory authorities in controlling residential housing cycles have resulted in a continuing search for methods of reducing the volatility of housing construction. One of the most widely discussed methods of decreasing volatility in mortgage credit is the variable rate mortgage (VRM) whose interest rate is linked to some interest rate index. In this paper we employ a portfolio theory approach to examine the relative riskiness of the VRM and fixed rate mortgage (FRM) for borrower and lender. As expected, we find that relative riskiness depends on the composition of the borrower/lender portfolio of assets and liabilities.