Effect of Analysts' Optimism on Estimates of the Expected Rate of Return Implied by Earnings Forecasts

Recent literature has used analysts' earnings forecasts, which are known to be optimistic, to estimate implied expected rates of return, yielding upwardly biased estimates. We estimate that the bias, computed as the difference between the estimates of the implied expected rate of return based on analysts' earnings forecasts and estimates based on current earnings realizations, is 2.84%. The importance of this bias is illustrated by the fact that several extant studies estimate an equity premium in the vicinity of 3%, which would be eliminated by the removal of the bias. We illustrate the point that cross‐sample differences in the bias may lead to the erroneous conclusion that cost of capital differs across these samples by showing that analysts' optimism, and hence, bias in the implied estimates of the expected rate of return, differs with firm size and with analysts' recommendation. As an important aside, we show that the bias in a value‐weighted estimate of the implied equity premium is 1.60% and that the unbiased value‐weighted estimate of this premium is 4.43%.     

Sentiment-scaled CAPM and market mispricing

This study explores the conditional version of the capital asset pricing model on sentiment to provide a behavioural intuition behind the value premium and market mispricing. We find betas (β) and the market risk premium to vary over time across different sentiment indices and portfolios. More importantly, the state β derived from this sentiment-scaled model provides a behavioural explanation of the value premium and a set of anomalies driven by mispricing. Different from the static β–return relation that gives a flat security market line, we document upward security market lines when plotting portfolio returns against their state βs and portfolios with higher state βs earn higher returns.     

Estimating the equity premium

Accurate estimation of the equity premium (the expected difference between the returns to a well-diversified stock market portfolio and a riskfree asset) is of central importance in many applications of finance theory including project appraisal and portfolio selection. The standard approach is to take the average observed excess returns to the market over some recent time period (sometimes referred to as the ex post equity premium) and apply this as an unbiased estimate of the ex ante equity premium. The paper reviews the problems associated with such an approach and contrasts it with alternative theoretical techniques.     

The intertemporal capital asset pricing model with dynamic conditional correlations

The intertemporal capital asset pricing model of Merton (1973) is examined using the dynamic conditional correlation (DCC) model of Engle (2002). The mean-reverting DCC model is used to estimate a stock’s (portfolio’s) conditional covariance with the market and test whether the conditional covariance predicts time-variation in the stock’s (portfolio’s) expected return. The risk-aversion coefficient, restricted to be the same across assets in panel regression, is estimated to be between two and four and highly significant. The risk premium induced by the conditional covariation of assets with the market portfolio remains positive and significant after controlling for risk premia induced by conditional covariation with macroeconomic, financial, and volatility factors.     

The Conditional CAPM and the Cross-Section of Expected Returns

Most empirical studies of the static CAPM assume that betas remain constant over time and that the return on the value-weighted portfolio of all stocks is a proxy for the return on aggregate wealth. The general consensus is that the static CAPM is unable to explain satisfactorily the cross-section of average returns on stocks. We assume that the CAPM holds in a conditional sense, i.e., betas and the market risk premium vary over time. We include the return on human capital when measuring the return on aggregate wealth. Our specification performs well in explaining the cross-section of average returns.     

Prediction of return with the minimum variance zero-beta portfolio

This paper tests prediction of returns on stocks using a direct estimate of the minimum variance zero beta portfolio z. The composition of this portfolio is implicit in Black's paper on capital market equilibrium in the absence of riskless borrowing or lending. Portfolios of stocks drawn from the same industries are used to estimate z. The predictions of Black's equilibrium return equation are compared with those of cross-sectional regressions of return on risk.     

Can An 'Estimation Factor' Help Explain Cross-Sectional Returns?

Abstract:  We show in a theoretical model that the expected excess return on any asset depends on its covariance not only with the market portfolio, but also with changes in the representative agent's estimate. We test our model using GMM and compare it to the CAPM. The results suggest that adding an 'estimation factor' to the CAPM helps explain cross-sectional returns and that, unconditionally, this estimation factor carries a negative risk premium.     

Mean-variance optimization using forward-looking return estimates

Despite its theoretical appeal, Markowitz mean-variance portfolio optimization is plagued by practical issues. It is especially difficult to obtain reliable estimates of a stock’s expected return. Recent research has therefore focused on minimum volatility portfolio optimization, which implicitly assumes that expected returns for all assets are equal. We argue that investors are better off using the implied cost of capital based on analysts’ earnings forecasts as a forward-looking return estimate. Correcting for predictable analyst forecast errors, we demonstrate that mean-variance optimized portfolios based on these estimates outperform on both an absolute and a risk-adjusted basis the minimum volatility portfolio as well as naive benchmarks, such as the value-weighted and equally-weighted market portfolio. The results continue to hold when extending the sample to international markets, using different methods for estimating the forward-looking return, including transaction costs, and using different optimization constraints.

     

Does It Pay to Bet Against Beta? On the Conditional Performance of the Beta Anomaly

Prior studies find that a strategy that buys high‐beta stocks and sells low‐beta stocks has a significantly negative unconditional capital asset pricing model (CAPM) alpha, such that it appears to pay to “bet against beta.” We show, however, that the conditional beta for the high‐minus‐low beta portfolio covaries negatively with the equity premium and positively with market volatility. As a result, the unconditional alpha is a downward‐biased estimate of the true alpha. We model the conditional market risk for beta‐sorted portfolios using instrumental variables methods and find that the conditional CAPM resolves the beta anomaly.     

A mean/variance approach to long-term fixed-income portfolio allocation

Abstract

Long-term investments in bonds offer known returns, but with risks corresponding to defaults of the underwriters. The excess return for a risky bond is measured by the spread between the expected yield and the risk-free rate. Similarly, the risk can be expressed in the form of a default spread, measuring the difference between the yield when no default occurs and the expected yield. For zero-coupon bonds and for actual market data, the default spread is proportional to the probability of default per year. The analysis of market data shows that the yield spread scales as the square root of the default spread. This relation expresses the risk premium over the risk-free rate that the bond market offers, similarly to the risk premium for equities. With these measures for risk and return, an optimal bond allocation scheme can be built following a mean/variance utility function. Straightforward computations allow us to obtain the optimal portfolio, depending on a pre-set risk-aversion level. As for equities, the optimal portfolio is a linear combination of one risk-free bond and a risky portfolio. Using the scaling law for the default spread allows us to obtain simple expressions for the value, yield and risk of the optimal portfolio.     

Optimal Estimation of the Risk Premium for the Long Run and Asset Allocation: A Case of Compounded Estimation Risk

It is well known that an unbiased forecast of the terminal valueof a portfolio requires compounding at the arithmetic mean returnover the investment horizon. However, the maximum-likelihoodpractice, common with academics, of compounding at the estimatorof mean return results in upward biased and highly inefficientestimates of long-term expected returns. We derive analyticallyboth an unbiased and a small-sample efficient estimator of long-termexpected returns for a given sample size and horizon. Both estimatorsentail penalties that reduce the annual compounding rate asthe investment horizon increases. The unbiased estimator, whichis far lower than the compounded arithmetic average, is stillvery inefficient, often more so than a simple geometric estimatorknown to practitioners. Our small-sample efficient estimatoris even lower. These results compound the sobering evidencein recent work that the equity risk premium is lower than suggestedby post-1926 data. Our methodology and results are robust toextensions such as predictable returns. We also confirm analyticallythat parameter uncertainty, properly incorporated, producesoptimal asset allocations, in stark contrast to conventionalwisdom. Longer investment horizons require lower, not higher,allocations to risky assets.     

The Cost of Equity Capital—a Comment

An algebraic relationship is developed linking the expected long-term yield to an investor with the company's expected internal rate of return on its equity assets. Assuming that the market normally ranks shares by expected yield, allowing where necessary for a risk premium, it is shown that the cost of equity capital must be the company's expected internal rate of return.     

Capital Flow Controls,International Asset Pricing,and Investors' Welfare: A Multi-Country Framework

This paper investigates the impact of capital flow restrictions on the pricing of securities, on the optimal portfolio composition for investors of different nationalities, and on their welfare. Under capital flow controls, the equilibrium price of a security is determined jointly by its international and national risk premiums, and investors acquire nationality-specific portfolios along with a market-wide proxy for the world market portfolio. Removal of investment barriers generally leads to an increase in the aggregate market value of the affected securities, and all investors favor a move toward market integration. Introduction of different types of index funds in the world market generally increases world market integration and investor welfare.     

Time Varying Market Leverage, the Market Risk Premium and the Cost of Capital

This paper shows that, when as usual the market portfolio is proxied by a share portfolio, then the conventional Ibbotson (1999) estimator of the market risk premium violates Miller–Modigliani (1958 and 1963) propositions II and III. A new estimator of the market risk premium is proposed which is free of these defects. In addition, across the range of market leverages experienced in the US in the period 1952–1997, it generates estimates of the market risk premium that differ from those generated by the Ibbotson methodology by up to 2.5 percentage points, and weighted average costs of capital for firms that differ by up to 2.6 percentage points.     

Systematic risk and timescales

Abstract

In this paper we propose a new approach to estimating the systematic risk (the beta of an asset) in a capital asset pricing model (CAPM). The proposed method is based on a wavelet multiscaling approach that decomposes a given time series on a scale-by-scale basis. At each scale, the wavelet variance of the market return and the wavelet covariance between the market return and a portfolio are calculated to obtain an estimate of the portfolio's beta. The empirical results show that the relationship between the return of a portfolio and its beta becomes stronger as the wavelet scale increases. Therefore, the predictions of the CAPM model are more relevant in the medium long run as compared to short time horizons.     

Liquidity risk and stock returns around the world

The recent global financial crisis demonstrates that market liquidity is a prominent systematic risk globally. We find that local liquidity risk, in addition to the local market, value and size factors, demands a systematic premium across stocks in 11 developed markets. This local pricing premium is smaller in countries where the country-level corporate boards are more effective and where there are less insider trading activities. We also discover that global liquidity risk is a significant pricing factor across all developed country market portfolios after controlling for global market, value, and size factors. The contribution of this risk to the return on a country market portfolio is economically and statistically significant within and across regions.     

Is the Market Portfolio a Dynamic Factor? Evidence from Individual Stock Returns

This paper uses a factor model to test whether the market portfolio is a dynamic factor in the sense that individual stock returns contain a premium linked to the conditional risk of the market portfolio. The market conditional risk is based on a decomposition of the market variance into a time-varying trend component and a transitory component. The evidence shows that the conditional market premium is rising when the permanent trend rises relative to the conditional variance. The evidence for individual stock returns supports the notion that the market portfolio is a dynamic factor. Individual stock return autocorrelations are fully explained by the time variation in the market premium. The risk premia attributed to static factors are statistically insignificant.     

Alternate approach to unify CAPM and APT

We utilize the joint elliptical distribution to model a multi-factor return generating process and derive an equilibrium multi-beta capital asset pricing model (CAPM) in which the market portfolio and a set of nonelliptical factors are sufficient to price all financial assets. Most important, it is shown that the market portfolio, while generally nonelliptical, can proxy all elliptical factors and hence: including elliptical factors in addition to the market portfolio in the pricing equation contribute nothing to asset pricing. While the representative investor prices the exposure of aggregate wealth to various nonelliptical systematic risk factors, individual securities are priced in accordance to their contributions to different aspects of the risk of aggregate wealth. The present model collapses to the Sharpe-Lintner CAPM when either the market investor is neutral to nonelliptical risk factors or when all risk factors follow a joint spherical distribution. When residuals cancel out of the market portfolio, the present model collapses to Conner (1984) pricing model.     

Information Consumption and Asset Pricing

We study whether firm and macroeconomic announcements that convey systematic information generate a return premium for firms that experience information spillovers. We use information consumption to proxy for investor learning during these announcements and construct ex ante measures of expected information consumption (EIC) to calibrate whether learning is priced. On days when there are information spillovers, affected stocks earn a significant return premium (5% annualized) and the capital asset pricing model performs better. The positive effect of the Federal Reserve Open Market Committee announcements on the risk premia of individual stocks appears to be modulated by EIC. Our findings are most consistent with a risk‐based explanation.     

The Three‐Factor Model: A Practitioner's Guide

The three‐factor model (3FM) has slowly but steadily become a popular alternative to the CAPM for measuring risk from the perspective of both corporate finance and portfolio management. The evidence clearly shows a negative relationship between market capitalization and returns, and a positive relationship between the book‐to‐market ratio and returns. Under the assumption that size and value are risk factors, the 3FM incorporates a market risk premium, a size premium, and a value premium into a model that aims to assess risk in a more comprehensive way, and ultimately to provide a more reliable estimation of required return. The required return produced by the 3FM has corporate finance applications (such as cost of capital estimation, project evaluation, and firm valuation) as well as portfolio management applications (such as performance evaluation). This article discusses the foundations and intuition behind the 3FM, as well as its application to the estimation of the cost of equity and excess returns.