Haim Levy

• professor
• Hebrew University of Jerusalem

By the Almost First-degree Stochastic Dominance (AFSD) rule, corresponding only to economically relevant preferences, for an infinite horizon the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}...

Buy and hold and periodical revisions are two competing investment strategies. Revising to the optimal one-period investment weights seemingly dominates the buy-and-hold strategy with random and uncontrolled investment weights determined by asset price changes. This intuition is misleading as both investment strategies are theoretically included in...

Expected returns, variances, betas, and alphas are all non-linear functions of the investment horizon. This seems to be a fatal conceptual problem for the capital asset pricing model (CAPM), which assumes a unique common horizon for all investors. We show that under the standard assumptions, the theoretical CAPM equilibrium surprisingly holds with...

The Black–Scholes model and many of its extensions imply a log-normal distribution of stock total returns over any finite holding period. However, for a holding period of up to one year, empirical stock return distributions (both conditional and unconditional) are not log-normal, but rather much closer to the logistic distribution. This paper deriv...

Does the famous idiom “stocks for the long run” have an empirical or a theoretical foundation? Bali et al. (2009) show that the cumulative return distributions of stocks and bonds intersect for all investment horizons, implying that stocks do not dominate bonds, regardless of the horizon. This paper shows that adding the riskless asset to the analy...

Prospect Theory (PT) and Constant-Relative-Risk-Aversion (CRRA) preferences have clear-cut and very different implications for the optimal asset allocation between a riskless asset and a risky stock as a function of the investment horizon. While CRRA implies that the optimal allocation is independent of the horizon, we show that PT implies a dramat...

Diversification across time means changing the asset allocation over time. We show that under mild conditions diversification across time is inferior for all risk-averters and for all investment horizons, relative to a portfolio with the same average asset allocation, held constant over time. Target-date funds help reduce the variation in the asset...

Observed international diversification implies an investment home bias (IHB). Can bivariate preferences with a local domestic peer group rationalize the IHB? For example, it is argued that wishing to have a large correlation with the Standard and Poor’s 500 stock index (S&P 500 stock index) may induce an increase in the domestic investment weight b...

In theorem 1 given in my paper, “Aging Population, Retirement, and Risk Taking” [Levy H (2016a) Aging population, retirement, and risk taking. Management Sci. 62(5):1415–1430.], there is indeed a technical error. Yet, adding one condition to the theorem (which can be added in two alternate ways) is sufficient to ensure the dominance of stocks over...

The most commonly employed decision-making paradigms are expected utility, prospect theory and regret theory. We examine the simple heuristic of maximizing the probability of being ahead, which we call Probability Dominance (PD). We set up head-to-head situations where all preferences of a given class (expected utility, original or cumulative prosp...

Purpose The purpose of this paper is to expand the peer effect analysis to investments in the stock market, where neither direct competition nor interaction with other investors exists. Design/methodology/approach A total of 772 subjects dwelling in six countries completed a questionnaire about their satisfaction with the performance of their hy...

Market efficiency is often evaluated through the ability of fundamental analysis or technical trading rules to exploit predictable patterns in asset prices. The evidence following decades of empirical research is mixed. This paper reexamines the evidence using a novel database from the TV show “Talking Numbers.” We assess the performance of 1,599 i...

Market efficiency is often evaluated through the ability of fundamental analysis or technical trading rules to exploit predictable patterns in asset prices. The evidence following decades of empirical research is mixed. This paper reexamines the evidence using a novel database from the TV show “Talking Numbers.” We assess the performance of 1,599 i...

We compare prospect ordering with and without envy and altruism. We find that envy may induce a violation of the univariate First-degree Stochastic Dominance (FSD) and thus a violation of the classic expected utility monotonicity axiom. Surprisingly, altruism may also violate FSD preferences. The intuitive explanation of the result in the case of a...

We analyze the role that financial analysts play in the sentiment effect on stock prices. Causality analysis reveals that sentiment affects various aspects of analysts’ forecasts and recommendations. We show that experienced analysts are aware of sentiment, consciously incorporate it and have some control over its effect. As a result, the sentiment...

Choices made according to regret theory (RT) may violate the expected utility (EU) model. We propose a stochastic dominance (SD) method for comparing RT and EU paradigms holistically, without focusing on a specific axiom or on a specific numerical example. We show that in some important cases, including the two-state case, e.g., war or peace, Repub...

Studies which attribute markets’ seasonality to sentiment assume that seasonal affective disorder (SAD) creates seasonal fluctuations in risk-aversion which, in turn, affects prices. Employing the variance risk premium (VP) we directly test for seasonality in risk-aversion. We find significant seasonality in the VP which is not explained by exogeno...

We analyze the role that financial analysts play in the sentiment effect on stock prices. Causality analysis reveals that sentiment affects various aspects of analysts’ work. We show that experienced analysts are aware of sentiment, consciously incorporate it and have some control over its effect. As a result, the effect replicates the sentiment ef...

We analyze the role that financial analysts play in the sentiment effect on stock prices. Causality analysis reveals that sentiment affects various aspects of analysts’ forecasts and recommendations. We show that experienced analysts are aware of sentiment, consciously incorporate it and have some control over its effect. As a result, the sentiment...

A common wisdom asserts that the wider the universe of assets to choose from, the greater the investor's welfare. We show that this is not the case in practice, where parameters have to be estimated even when the estimates are unbiased. Surprisingly, risk aversion plays a crucial role corresponding to the desirability of asset expansion by dividing...

We find that human perception contradicts the market efficiency assertions that high expected returns are accompanied by high risk and that past returns are not correlated with future returns. A survey of investors reveals that the last month realized returns are positively correlated with next month perceived returns and that they are negatively c...

Stochastic dominance (SD) rules are applicable in the selection between mutually exclusive investments but, unlike the mean-variance rule, they cannot identify in a simple way all SSD efficient diversification strategies. To be more specific, the SD rules can tell us whether investment F dominates investment G, or investment G dominates H, but they...

We have seen in the previous chapters that even if the rates of return on uncertain assets are independent over time, the various parameters characterizing the distribution of returns are not invariant to the assumed length of the investment horizon. Moreover, these parameters do not change randomly, but rather change in some systematic way with th...

It was common in the past to evaluate projects by their expected outcome, until Saint Petersburg Paradox emerges. The well-known Saint Petersburg Paradox has led Bernoulli in 1738 to develop a theory asserting that investor make choices based on expected utility from wealth and not based on the expected wealth itself. Note that the paradox emerges...

It is accepted by virtually all economists that generally “there is no free lunch” in the capital market, implying that if one wishes to increase her expected return she must be exposed to more risk. While expected return, or average profitability, is well defined, the concept of risk and particularly how to measure it remains vague. Indeed as we s...

Although we focus in Chap. 1 on various definitions of risk, recall that in the eyes of the investor, profitability is probably the main raison d’être of investment. Thus, focusing on risk in our first chapter, by no means do we belittle this all-important function of investment. Our discussion of risk simply serves to emphasize that, in arriving a...

To obtain the efficient sets corresponding to the various stochastic dominance (SD) rules, we need to know the precise shape of the various distributions under comparison. For example, for SSD, in order to check whether dominance exists or not, we need to calculate the area enclosed between the two distributions under consideration, F and G up to a...

As some investors plan to invest for a relatively short investment horizon and others for a relatively long horizon, it is interesting to analyze whether the assumed length of the investment horizon affects the optimal diversification. Numerous studies are devoted to this topic. Indeed, the importance of the investment horizon and its effect on the...

Stochastic dominance rules are employed in numerous research fields, particularly in the following research areas: finance, economics, insurance, statistics, agriculture, and medicine. Due to space constraints, we will mention only a few such applications in this chapter.

We have seen that the MEUC is the optimal investment criterion. If there is full information on preferences (e.g., U(w) = log (w)), we simply calculate EU(w) of all the competing investments and choose the one with the highest expected utility. In such a case, we arrive at a complete ordering of the investments under consideration: there will be on...

In evaluating the quality of various competing investment decision making rules a few factors should be taken into account:

The classic expected utility paradigm of von-Neumann and Morgenstern assumes a univariate utility function where only one element, one’s own wealth, determines her welfare. Specifically, assuming a self-interest utility function U(w) where w stands for wealth, and in addition making a set of compelling axioms, the expected utility (EU) paradigm has...

Since the publication of the Second Edition of this book in 2006, numerous stochastic dominance (SD) studies have been published, where the new wave of publications contributes to the SD theory, SD applications and statistical inference of SD rules. The applications are also in areas which are remote from portfolio selection and investment theory,...

In Chap. 3 the various stochastic dominance rules were stated in terms of cumulative distributions denoted by F and G. In this chapter FSD and SSD stochastic dominance are restated in terms of distribution quantiles. Both methods yield the same partition of the feasible set into efficient and inefficient sets. The formulas and the stochastic domina...

There are various measures of risk (see Chap. 1) and each of them has its pros and cons. This chapter focuses on the notion of risk in the stochastic dominance framework. We first discuss the concept of mean preserving spread (MPS) and various risk measures suggested by Rothschild and Stiglitz (R&S) and then extend it to the case where riskless ass...

In 2003 Daniel Kahneman won the Nobel Prize for Economics for numerous important contributions. Probably the study with the greatest impact on economic research is his joint contribution with Amos Tversky, called Prospect Theory (PT) and its latest modified version called Cumulative Prospect Theory (CPT). The impact of PT on academic research is tr...

In this chapter we employ SD rules to prove that the CAPM is theoretically intact in a wide range of frameworks corresponding to the assumption about the distribution of returns and the length of the investment horizon. This is a surprising integration of the MV and SD paradigms, as these two paradigms represent two distinct branches of expected ut...

In the derivation of the SD and SDR rules presented in the previous chapters (see Chaps. 3 and 4), assumptions on preference, Ui are made but no assumptions are made on the shape of the distributions of rates of return of the prospects under consideration. Therefore, the stochastic dominance rules are considered distribution-free decision rules. If...

We have seen in Chap. 6 that the SD criteria as well as the MV rule may lead to paradoxes in decision making. To avoid such paradoxes and to make the theoretical distributions to be closer to the empirical distributions it suggested in the previous chapter to truncate the theoretical distributions. By doing so, we achieve one more advantage: extrem...

The increase in life expectancy spells disaster at retirement. One can solve this problem by investing in the maximum geometric mean (MGM) portfolio, which is empirically composed from equity. For a T = 30 year horizon or more, the MGM portfolio dominates other investment strategies by almost first-degree stochastic dominance. The MGM portfolio als...

We find that weekend, holiday and overnight trading breaks generate excessive perceived risk in the option markets, presumably due to asymmetric information, which, in turn, encourages uninformed option traders to postpone trading. This perceived risk subsides after two days accompanied by an increase in the option trading volume and the underlying...

Do happy people predict future risk and return differently from unhappy people, or do individuals rely only on economic facts? We survey investors on their subjective sentiment-creating factors, return and risk expectations, and investment plans. We find that non-economic factors systematically affect return and risk expectations, where the return...

We find that weekend, holiday and overnight trading breaks generate excessive perceived risk in the option markets, presumably due to asymmetric information, which, in turn, encourages uninformed option traders to postpone trading. This perceived risk subsides after two days accompanied by an increase in the option trading volume and the underlying...

Peer-effects have been shown to affect behavior, and can generally lead to investments choices that are mean-variance inefficient. This paper analyzes optimal diversification with peer-effects. We show that if individuals have keeping-up with the Joneses preferences and they take their peer-group reference as the market portfolio, Markowitz’s mean-...

In this study, the Mean-Variance framework is employed to analyze the impact of the Basel VaR market risk regulation on the institution’s optimal investment policy, the stockholders’ welfare, as well as the tendency of the institution to change the risk profile of the held portfolio. It is shown that with the VaR regulation, the institution faces a...

Do happy people predict future risk and return differently from unhappy people, or do individuals rely only on economic facts? We survey investors on their subjective sentiment-creating factors, return and risk expectations, and investment plans. We find that non-economic factors systematically affect return and risk expectations, where the return...

Soccer games create sentiment, which affects stock prices. The World Cups before 2010 created exploitable abnormal profit in the U.S. stock market. The effect was not exploited, presumably because it was unknown before the 2010 games. However, just before the 2010 World Cup, the exploitable effect was published and widely cited by practitioners who...

Investment experiment with changes in subject’s wealth, her friends’ wealth and the average wealth of all investors supports a preference that depends on relative wealth. While, as expected, subjects’ satisfaction increases with an increase in their own wealth it decreases with an increase in their friends’ wealth. We find that when success in inve...

A common wisdom asserts that the wider the universe of assets to choose from the greater the investor’s welfare. We show that this is not the case in practice where parameters have to be estimated even when the estimates are unbiased. Surprisingly, risk aversion plays a crucial and rather uncommon role corresponding to the desirability of asset exp...

One of the main pillars of the academic sphere is publication of articles, the scientific purity of which should be as higher as possible. Allegedly, scientists may prefer to cite journal editors more frequently than they would do when those personae are not in editors′ position, and quite a few of the formers in quite a few instances do not seem t...

We find that human perception contradicts the market efficiency assertions that high expected returns are accompanied by high risk and that past returns are not correlated with future returns. A survey of investors reveals that the last month realized returns are positively correlated with next month perceived returns and that they are negatively c...

Experimental findings and in particular Prospect Theory and Cumulative Prospect Theory contradict Expected Utility Theory, which in turn may have a direct implication to theoretical models in finance and economics. We show growing evidence against Cumulative Prospect Theory. Moreover, even if one accepts the experimental results of Cumulative Prosp...

We analyze the role that financial analysts play in the sentiment effect on stock prices. Causality analysis reveals that sentiment affects various aspects of analysts’ forecasts and recommendations. We show that experienced analysts are aware of sentiment, consciously incorporate it and have some control over its effect. As a result, the sentiment...

The main problem of portfolio optimization is parameter estimation error. Various methods have been suggested to mitigate this problem, among which are shrinkage, resampling, Bayesian updating, naïve diversification, and imposing constraints on the portfolio weights. This study suggests two substantial extensions of the constrained optimization app...

When one prospect is certain and the other uncertain, Cumulative Prospect Theory employs the certainty equivalent methodology to estimate Decision Weights (DW). However, DW may be different with two uncertain prospects. In this study, we neutralize the "certainty effect" and propose Stochastic Dominance (SD) to estimate DW for the first time with s...

Having the maximum geometric mean (MGM) is necessary but not sufficient condition for dominance among log-normal prospects. However, when T→ ∞, the MGM portfolio dominates all other portfolios by asymptotic FSD (AFSD), so long the variance of the log-return of the MGM portfolio is the largest and the marginal utility is bounded. Without bounding th...

Employing the “keeping up with the Joneses” (KUJ) preferences with domestic peer group (e.g., the S&P 500 index) is a natural path aiming to rationalize the home bias phenomenon. Employing bivariate stochastic dominance (BSD) we, counter-intuitively, find that the KUJ preference is theoretically neither necessary nor sufficient condition for home b...

American investors tilt to overinvest domestically, well-known as a home bias puzzle. Hedging various types of domestic risks, differences in taxes and transaction costs, informational frictions and behavioral effects are commonly employed in an attempt to explain the home bias puzzle. We show in this study that even abstracting from the above fact...

The home bias is typically explained by various extra costs for foreign investments, such as higher transaction costs and information asymmetries. These costs have dramatically decreased over the last 15 years: the internet has revolutionized the global flow of information, accounting reports have been converging to uniform international standards,...

In 23 out of 26 U.S. industries, the annual CEO bonus is larger than the annual salary, suggesting that the bonus strongly affects the CEO’s decisions. As the high leverage of financial institutions is often blamed for the 2008 financial crises, in this study we focus on leveragre as a factor determining risk, particularly in finnacial institutuion...

The current study shows that real estate prices in several countries reveal a significant and persistent seasonality, where the highest rates of return are obtained in the spring and early summer, and the lowest rates of return are obtained in the fall. This seasonality is explained by a joint effect of the change in the number of daylight hours an...

The effect of envy and altruism on investment choices is analyzed by employing bivariate utility-free Stochastic Dominance (SD) rules. We find that correlation loving or correlation aversion (between the individual’s wealth and the peer group’s wealth) greatly affects choices. The positive result is that the bivariate SD efficient set always contai...

The shape of the demand curve for stocks and the marginal cost of capital are two related issues.The CAPM and APT imply that demand curves for equity are virtually flat. In Modigliani and Miller's firm valuation model the demand curve for a financial asset is also perfectly elastic, implying that the asset’s price is independent of its supply. Henc...

Several empirical studies reveal that holidays generally create positive sentiment in the stock market, whereas negative events, such as wars or disasters, are accompanied by negative sentiment. However, what happens if a negative event occurs on a holiday? In such a case, we expect two conflicting sentiment effects, which may cancel one another ou...

IntroductionPt, Cpt, and the Stochastic Dominance (Sd) ApproachThe Experiments and the ResultsSummary and Conclusions Discussion QuestionsAbout the Author

The Israeli government borrows internally and externally, and the Bank of Israel invests the foreign exchanges in various currencies. The borrowing interest rate is generally higher than the lending rate. In addition, the reserves are invested in relatively short-maturity safe assets, while borrowing is for relatively long maturities. This paper st...

Under the assumption of normally distributed returns, we analyze whether the Cumulative Prospect Theory of Tversky and Kahneman (1992) is consistent with the Capital Asset Pricing Model. We find that in every financial market equilibrium, the Security Market Line Theorem holds. However, under the functional form for the utility index suggested by T...

Markowitz and Sharpe won the Nobel Prize in Economics more than a decade ago for the development of Mean-Variance analysis and the Capital Asset Pricing Model (CAPM). In the year 2002, Kahneman won the Nobel Prize in Economics for the development of Prospect Theory. Can these two apparently contradictory paradigms coexist? In deriving the CAPM, Sha...

The Capital Asset Pricing Model (CAPM) and the mean-variance (M-V) rule, which are based on classic expected utility theory, have been heavily criticized theoretically and empirically. The advent of behavioral economics, prospect theory and other psychology-minded approaches in finance challenges the rational investor model from which CAPM and M-V...

Behavioral economic studies reveal that negative sentiment driven by bad mood and anxiety affects investment decisions and may hence affect asset pricing. In this study we examine the effect of aviation disasters on stock prices. We find evidence of a significant negative event effect with an average market loss of more than $60 billion per aviatio...

The common investment decision rules, Markowitz’s Mean-Variance (MV) rule and the non-parametric Stochastic Dominance (SD) rules, suffer from one severe drawback: there are pairs of prospects where experimentally 100% of the subjects choose one prospect, yet these rules are unable to rank the two prospects—a paradoxical result. Thus, the set of all...

Value-at-Risk (VaR) has become a standard measure for risk management and regulation. In the case of a two-parameter distribution, a common method among practitioners is first to calculate the daily VaR and then to apply it to a longer investment horizon by using the Square Root Rule (SRR). We show that the SRR is theoretically incorrect and propos...

In a recently published paper, Edmans, Garca, and Norli (2007) reveal a strong association between results of soccer games and local stock returns. Inspired by their work, we propose a novel approach to exploit this effect on the aggregate international level with the following three unique features: i) The aggregate effect does not depend on the g...

Markowitz’s breakthrough Mean–Variance theoretical article is the foundation of the CAPM and many other models in economics and finance. But the Mean–Variance rule is also widespread in practice, and this is the focus of this paper. While expected utility theory and Markowitz’s classical diversification theory assert that the optimal diversificatio...

Mean-Variance (M-V) analysis and the CAPM are derived in the expected utility framework. Behavioural Economists and Psychologists (BE&P) advocate that expected utility is invalid, suggesting Prospect Theory as a substitute paradigm. Moreover, they show that the M-V rule, which is the foundation of the CAPM, is not always consistent with peoples’ ch...

Although expected utility theory and the classical mean-variance diversification theory of Markowitz assert that optimal diversification depends on the joint distribution of returns, investors tend to ignore these well-accepted theoretical approaches in favor of the naive investment strategy promulgated in the Babylonian Talmud called the 1/3 rule...

Risk Sentiment Index (RSI), which is affected by sentiment rather than by economic factors, is suggested, after which it is empirically estimated in the U.S. and in Japan. The RSI and actual returns are negatively correlated, implying that for the whole studied period the RSI, which measures illusionary risk rather than actual risk, affects the mar...

It has become increasingly popular to advise investors to relocate their funds from a primarily stock portfolio to a primarily bond portfolio as they get older. However, the well-known decision rules such as mean–variance or stochastic dominance rules are unable to explain this common practice. Almost stochastic dominance (ASD) and almost mean–vari...

Roy’s [Roy, A., 1952. Safety first and the holding of assets. Econometrica 20 (3), 431–449] safety first criterion advocates the minimization of the probability of outcomes below a certain “disaster” level. This paper examines safety first theoretically and experimentally. We find that safety first plays a crucial role in decision-making, inducing...

This paper examines the intertemporal relation between downside risk and expected stock returns. Value at Risk (VaR), expected shortfall, and tail risk are used as measures of downside risk to determine the existence and significance of a risk-return tradeoff. We find a positive and significant relation between downside risk and the portfolio retur...

Mean-Variance (M-V) analysis and the CAPM are derived in the expected utility framework. Behavioral Economists and Psychologists (BE&P) advocate that expected utility is invalid, suggesting Prospect Theory as a substitute paradigm. Moreover, they show that the M-V rule, which is the foundation of the CAPM, is not always consistent with peoples' cho...

Expected Utility Theory, Rank Dependent Expected Utility and Cumulative Prospect Theory imply no First Degree Stochastic Dominance (FSD) violations. Prospect Theory and Configural Weight models either allow for FSD violation or even predict this phenomenon. I find experimentally that FSD violations are not significant, and hence conclude that they...

This paper provides new evidence on the time-series predictability of stock market returns by introducing a test of nonlinear mean reversion. The performance of extreme daily returns is evaluated in terms of their power to predict short- and long-horizon returns on various stock market indices and size portfolios. The paper shows that the speed of...

Data obtained from the intention-to-buy scale often are used for early product screening. The authors discuss current procedures to evaluate these data and indicate the minor rote that risk assessment has played. Evaluation rules that incorporate the risk factor are presented, and their usefulness for product selection is discussed.

This paper studies the impact of variable and fixed transaction costs on investment decisions under conditions of risk. The decision model is first formulated as a mixed-integer nonlinear program. The following subjects are then examined: the structure of the investment frontier facing the investor and the effects of transaction costs on this front...