Reinforcement Learning and Savings Behavior

We show that individual investors over‐extrapolate from their personal experience when making savings decisions. Investors who experience particularly rewarding outcomes from 401(k) saving—a high average and/or low variance return—increase their 401(k) savings rate more than investors who have less rewarding experiences. This finding is not driven by aggregate time‐series shocks, income effects, rational learning about investing skill, investor fixed effects, or time‐varying investor‐level heterogeneity that is correlated with portfolio allocations to stock, bond, and cash asset classes. We discuss implications for the equity premium puzzle and interventions aimed at improving household financial outcomes.     

Downside Risk in Practice

Although investors associate risk with negative outcomes and downside fluctuations, modern portfolio theory does not. For investors, volatility per se is not necessarily bad; volatility below a benchmark is. A stock that magnifies the market's fluctuations is not necessarily bad; one that magnifies the market's downside swings is. Even Harry Mar‐kowitz, the father of modern portfolio theory, viewed downside risk as a better way to assess risk than the “mean‐variance” framework that he ultimately proposed and that has since become the standard. This article highlights the shortcomings of traditional measures of risk (the standard deviation and beta), introduces the concept of downside risk, and discusses two measures of it—the “semideviation” and “downside beta.” It also discusses the use of such measures in asset pricing models to estimate required returns on equity. Data from a few well‐known companies are used to illustrate that the cost of equity based on downside risk can be substantially different from that based on the CAPM. The article concludes with a brief discussion of risk‐adjusted returns and a comparison of the traditional method of calculating such returns with both the Sharpe ratio and its counterpart in a downside risk framework, the Sortino ratio. The appendix demonstrates how to calculate these risk measures in Excel.     

REVISITING MARKET EFFICIENCY: THE STOCK MARKET AS A COMPLEX ADAPTIVE SYSTEM

Well‐functioning financial markets are key to efficient resource allocation in a capitalist economy. While many managers express reservations about the accuracy of stock prices, most academics and practitioners agree that markets are efficient by some reasonable operational criterion. But if standard capital markets theory provides reasonably good predictions under “normal” circumstances, researchers have also discovered a number of “anomalies”—cases where the empirical data appear sharply at odds with the theory. Most notable are the occasional bursts of extreme stock price volatility (including the recent boom‐and‐bust cycle in the NASDAQ) and the limited success of the Capital Asset Pricing Model in accounting for the actual risk‐return behavior of stocks. This article addresses the question of how the market's efficiency arises. The central message is that managers can better understand markets as a complex adaptive system. Such systems start with a “heterogeneous” group of investors, whose interaction leads to “self‐organization” into groups with different investment styles. In contrast to market efficiency, where “marginal” investors are all assumed to be rational and well‐informed, the interaction of investors with different “decision rules” in a complex adaptive system creates a market that has properties and characteristics distinct from the individuals it comprises. For example, simulations of the behavior of complex adaptive systems suggest that, in most cases, the collective market will prove to be smarter than the average investor. But, on occasion, herding behavior by investors leads to “imbalances”—and, hence, to events like the crash of '87 and the recent plunge in the NASDAQ. In addition to its grounding in more realistic assumptions about the behavior of individual investors, the new model of complex adaptive systems offers predictions that are in some respects more consistent with empirical findings. Most important, the new model accommodates larger‐than‐normal stock price volatility (in statistician's terms, “fat‐tailed” distributions of prices) far more readily than standard efficient market theory. And to the extent that it does a better job of explaining volatility, this new model of investor behavior is likely to have implications for two key areas of corporate financial practice: risk management and investor relations. But even so, the new model leaves one of the main premises of modern finance theory largely intact–that the most reliable basis for valuing a company's stock is its discounted cash flow.     

The Impact of Inflation Measures on the Real Returns and Risk of U.S. Stocks

Using different inflation measures produces economically significant differences in both the inflation record and inflation‐adjusted stock returns. We introduce a more consistent measure of the monthly Consumer Price Index (CPI) inflation rate to better measure real returns over 1913–2004, for which the official CPI exists. We also extend the series backward to 1871 on a monthly basis, an important addition to the data series. We analyze the impact of inflation on the real standard deviation of stock returns and find that, in contrast to the results for geometric mean returns, inflation adjustments have little impact on estimates of return variability.     

High Idiosyncratic Volatility and Low Returns: A Prospect Theory Explanation

The well‐documented negative relationship between idiosyncratic volatility and stock returns is puzzling if investors are risk‐averse. However, under prospect theory, while investors are risk‐averse in the domain of gains, they exhibit risk‐seeking behavior in the domain of losses. Consistent with risk‐seeking investors’ preference for high‐volatility stocks in the loss domain, we find that the negative relationship between idiosyncratic volatility and stock returns is concentrated in stocks with unrealized capital losses, but is nonexistent in stocks with unrealized capital gains. This finding is robust to control for short‐term return reversals and maximum daily return, among other variables.     

Income Hedging,Dynamic Style Preferences,and Return Predictability

We propose a theoretical measure of income hedging demand and show that it affects asset prices. We focus on the value factor and first demonstrate that our demand estimates are correlated with the actual demands of retail and mutual fund investors. We then show that the aggregate high‐minus‐low (HML) demand predicts HML returns. Exploiting the state‐level variation in income risk, we demonstrate that state‐level hedging demands predict state‐level HML returns. A long‐short portfolio that exploits this hedging‐induced predictability earns an annualized risk‐adjusted return of 6%.     

Subjective Economic Risk to Beneficiaries in Notional Defined Contribution Accounts

This article aims to quantify the aggregate subjective economic risk to which beneficiaries would be exposed if a retirement pension system based on notional account philosophy were introduced. We use scenario generation techniques to make projections of the factors that determine the real expected internal rate of return (IRR) and the expected replacement rate (RR) for the beneficiary according to six retirement formulae based on the most widely accepted rates or indices. We then apply the model to the case of Spain. Our projections are based on Herce and Alonso's macroeconomic scenario 2000–2050 (2000) and include information about the past performance of the indices and the time period the forecast is to cover. The results of the IRR calculation—average value, standard deviation, and value‐at‐risk (VaR)—are analyzed both in objective terms and for different degrees of participants' risk aversion.     

When do investors gamble in the stock market?

Recent studies have uncovered gambling-motivated trading activities in financial markets in which investors seek lottery-type payoffs by using financial assets. Building on prospect theory, this study provides an important complement to prior research and investigates what period that investors make gambling-motivated trading in the stock market. Examining data from the Chinese stock market, investors are revealed to have asymmetric gambling preferences in gain and loss domains. Investors' gambling motivations are more easily triggered when the market is experiencing a loss. In such periods of time, investors may preferentially opt for lottery-type stocks that offer them a small chance to earn an extreme return at the risk of a likely small loss, simply due to their ‘aversion to a sure loss’.     

ANALYZING STOCK MARKET VOLATILITY USING EXTREME‐DAY MEASURES

We develop a simple measure of volatility based on extreme‐day returns and apply it to market returns from 1885 to 2002. Because returns are not normally distributed, the extreme‐day measure, which is distribution free, might provide a better measure of stock market risk than the traditional standard deviation. The extreme‐day measure more accurately explains investor behavior relative to standard deviation as shown by equity fund flows, and we find evidence that large negative changes appear to influence investor behavior more than large positive changes.     

Expectations‐Based Management

The authors begin by summarizing the results of their recently published study of the relation between stock returns and changes in several annual performance measures, including not only growth in earnings and EVA, but changes during the year in analysts' expectations about future earnings over three different periods: (1) the current year; (2) the following year; and (3) the three‐year period thereafter. The last of these measures—changes in analysts' expectations about three‐ to five‐year earnings—had by far the greatest explanatory “power” of any of the measures tested. Besides being consistent with the stock market's taking a long‐term, DCF approach to the valuation of companies, the authors' finding that investors seem to care most about earnings three to five years down the road has a number of important implications for financial management: First, a business unit doesn't necessarily create shareholder value if its return on capital exceeds the weighted average cost of capital—nor does an operation that fails to earn its WACC necessarily reduce value. To create value, the business's return must exceed what investors are expecting. Second, without forecasting returns on capital, management should attempt to give investors a clear sense of the firm's internal benchmarks, both for existing businesses and new investment. Third, management incentive plans should be based on stock ownership rather than stock options. Precisely because stock prices reflect expectations, the potential for prices to get ahead of realities gives options‐laden managers a strong temptation to manipulate earnings and manage for the short term.     

Improving Volatility Forecasts Using Market‐Elicited Ambiguity Aversion Information

Distinguishing between risk and uncertainty, this paper proposes a volatility forecasting framework that incorporates asymmetric ambiguity shocks in the (exponential) generalized autoregressive conditional heteroskedasticity‐in‐mean conditional volatility process. Spanning 25 years of daily data and considering the differential role of investors' ambiguity attitudes in the gain and loss domains, our models capture a rich set of information and provide more accurate volatility forecasts both in‐sample and out‐of‐sample when compared to ambiguity‐free or risk‐based counterparts. Ambiguity‐based volatility‐timing trading strategies confirm the economic significance of our proposed framework and indicate that an annualized excess return of 3.2% over the benchmark could be earned from 1995 to 2014.     

A Tale of Two Anomalies: Higher Returns of Low‐Risk Stocks and Return Seasonality

Prior studies have shown that low beta and low volatility stocks earn higher average returns than high beta and high volatility stocks, contradicting the prediction of the capital asset pricing model and the fundamental relationship between risk and return. In this paper, we demonstrate that this phenomenon is driven by the seasonality of stock returns. We show that the risk‐return tradeoff does hold in the nonsummer months, and that switching to a portfolio of low‐risk stocks in summer outperforms—both in terms of absolute and in risk‐adjusted returns—buy and hold strategies as well as the Sell in May strategy of switching to treasury bills in summer.     

Time Period and Risk Measures in the General Risk Equation

In an earlier paper, a general risk equation, applicable to all non growth systems, and inclusive of financial systems, was derived. It related expected throughput capacity of any system to both system resources and positive risk of loss of throughput capacity. Two risk measures were required, a new MEL‐risk measure, and the conventional standard‐deviation risk measure.

In this paper we show that the two apparently distinct risk measures are intimately related, and that which one is appropriate depends merely on the time period over which the risk is calculated. We show, ultimately by application of the Central Limit Theorem, that if we merely sufficiently alter the time period, at some point the need for one measure will transition into the need for the other, without any change in the underlying physical system.

This leads to a comprehensive risk measure that defaults to either the MEL‐risk measure, or standard‐deviation measure, depending not on the physical system, but merely on the time period over which the risk is calculated.     

The Role of Real Options in Capital Budgeting: Theory and Practice1

Most discussions of capital budgeting take for granted that discounted cash flow (DCF) and real options valuation (ROV) are very different methods that are meant to be applied in different circumstances. Such discussions also typically assume that DCF is “easy” and ROV is “hard”—or at least dauntingly unfamiliar—and that, mainly for this reason, managers often use DCF and rarely ROV. This paper argues that all three assumptions are wrong or at least seriously misleading. DCF and ROV both assign a present value to risky future cash flows. DCF entails discounting expected future cash flows at the expected return on an asset of comparable risk. ROV uses “risk‐neutral” valuation, which means computing expected cash flows based on “risk‐neutral” probabilities and discounting these flows at the risk‐free rate. Using a series of single‐period examples, the author demonstrates that both methods, when done correctly, should provide the same answer. Moreover, in most ROV applications—those where there is no forward price or “replicating portfolio” of traded assets—a “preliminary” DCF valuation is required to perform the risk‐neutral valuation. So why use ROV at all? In cases where project risk and the discount rates are expected to change over time, the risk‐neutral ROV approach will be easier to implement than DCF (since adjusting cash flow probabilities is more straightforward than adjusting discount rates). The author uses multi‐period examples to illustrate further both the simplicity of ROV and the strong assumptions required for a typical DCF valuation. But the simplicity that results from discounting with risk‐free rates is not the only benefit of using ROV instead of—or together with—traditional DCF. The use of formal ROV techniques may also encourage managers to think more broadly about the flexibility that is (or can be) built into future business decisions, and thus to choose from a different set of possible investments. To the extent that managers who use ROV have effectively adopted a different business model, there is a real and important difference between the two valuation techniques. Consistent with this possibility, much of the evidence from both surveys and academic studies of managerial behavior and market pricing suggests that managers and investors implicitly take account of real options when making investment decisions.     

Stock Returns and Volatility: Pricing the Short‐Run and Long‐Run Components of Market Risk

We explore the cross‐sectional pricing of volatility risk by decomposing equity market volatility into short‐ and long‐run components. Our finding that prices of risk are negative and significant for both volatility components implies that investors pay for insurance against increases in volatility, even if those increases have little persistence. The short‐run component captures market skewness risk, which we interpret as a measure of the tightness of financial constraints. The long‐run component relates to business cycle risk. Furthermore, a three‐factor pricing model with the market return and the two volatility components compares favorably to benchmark models.     

The Volatility of Return Revisions and Financial Statement Literacy in Emerging Markets: The Case of Cross‐listed Chinese Firms

Are foreign investors in emerging markets more financial statement literate than domestic investors? If so, this conjecture implies that foreign (domestic) investors are more likely to revise their return expectations to cash flow (discount rate) news. It also implies that cash flow news and discount rate news are likely to be uncorrelated when evaluating return revisions by domestic investors, whereas cash flow news and discount rate news are likely to be negatively correlated when evaluating return revisions by foreign investors. The Chinese equity markets yield robust empirical results that are consistent with both hypotheses.     

Herding and Feedback Trading by Institutional and Individual Investors

We document strong positive correlation between changes in institutional ownership and returns measured over the same period. The result suggests that either institutional investors positive-feedback trade more than individual investors or institutional herding impacts prices more than herding by individual investors. We find evidence that both factors play a role in explaining the relation. We find no evidence, however, of return mean-reversion in the year following large changes in institutional ownership—stocks institutional investors purchase subsequently outperform those they sell. Moreover, institutional herding is positively correlated with lag returns and appears to be related to stock return momentum.     

Accounting Ratios and the Cross‐section of Expected Stock Returns

Under clean‐surplus accounting, the log return on a stock can be decomposed into a linear function of the contemporaneous log return on equity, the contemporaneous log dividend–price ratio (if the stock pays a dividend), and both the contemporaneous and lagged values of the log book‐to‐market equity ratio. This paper studies the implications of this decomposition for the cross‐section of conditional expected stock returns. The empirical analysis reveals that the log accounting ratios capture cross‐sectional variation in both the conditional mean and conditional variance of log stock returns, which is consistent with the decomposition. It also brings fresh insights to the relation between firm size (market equity) and conditional expected stock returns. The evidence indicates that the conditional median return increases with firm size, while the conditional return skewness decreases with firm size. Empirically, the skewness effect outweighs the median effect, leading to the well‐documented inverse relation between size and average returns. The results of out‐of‐sample tests suggest that investors could use the information provided by the observed values of the log accounting ratios to formulate more effective portfolio strategies.     

Individual and institutional herding and the impact on stock returns: Evidence from Taiwan stock market

Using high frequency intraday data, this paper investigates the herding behavior of institutional and individual investors in the Taiwan stock market. The study finds evidence of herding by both investors but a stronger herding tendency among institutional than among individual investors. Institutional investors herd more on firms with small capitalizations and lower turnovers and they follow positive feedback strategies. The portfolios that institutional investors herd buy outperform those they sell by an average of 1.009% during the 20 days after intense trading episodes. By contrast, individual investors herd more on firms with small sizes and higher turnovers, and they crowd to buy (sell) stocks with negative (positive) past returns. The portfolios that individual investors herd buy underperform those they sell by an average of − 0.829% during the following 20 days. Moreover, these return differences of both investors are more pronounced under a market with higher pressure and among small stocks. These findings suggest that the herding of institutional investors speeds up the price-adjustment process and is more likely to be driven by correlated private information, while individual herding is most likely to be driven by behavior and emotions.     

Leverage constraints and asset prices: Insights from mutual fund risk taking

Prior theory suggests that time variation in the degree to which leverage constraints bind affects the pricing kernel. We propose a measure for this leverage constraint tightness by inverting the argument that constrained investors tilt their portfolios to riskier assets. We show that the average market beta of actively managed mutual funds—intermediaries facing leverage restrictions—captures their desire for leverage and thus the tightness of constraints. Consistent with theory, it strongly predicts returns of the betting-against-beta portfolio, and is a priced risk factor in the cross-section of mutual funds and stocks. Funds with low exposure to the factor outperform high-exposure funds by 5% annually, and for stocks this difference reaches 7%. Our results show that the tightness of leverage constraints has important implications for asset prices.