A conditional regime switching CAPM

The standard Capital Asset Pricing Model (CAPM) is simple, intuitive, and grounded in sound economic theory. Yet, almost half a century's worth of empirical testing has so far failed to demonstrate its relevance. One major reason given for the CAPM's empirical failure is that beta is not the sole measure of systematic risk. In other words, the standard CAPM does not hold. Another important explanation is that the CAPM may hold conditionally rather than unconditionally. The standard CAPM fails to explain the cross-section of returns because it ignores the fact that both the risk and the price of risk are time-varying. The search for conditional models has led researchers to either disregard the theory behind the CAPM or to use statistical procedures that are too complex to be replicated by other researchers and practitioners. In this paper we propose a conditional model that is compatible with the standard CAPM while remaining simple and accessible to both researchers and practitioners. Beta and the risk premium are assumed to be time-varying, with the latter being associated with bull and bear states. We find strong support for the conditional CAPM with beta explaining both bull and bear markets. While the bear market ex-post risk premium is negative, the weighted average risk premium is positive and highly significant.     

Rewards for downside risk in Asian markets

Distributional properties of emerging market returns may impact on investor ability and willingness to diversify. Investors may also place greater weighting on downside losses, compared to upside gains. Using individual equities in a range of emerging Asian markets, we investigate the potential contribution of downside risk measures to explain asset pricing in these markets. As realized returns are used as a proxy for expected returns, we separately examine conditional returns in upturn and downturn periods, in order to successfully identify risk and return relationships. Results indicate that co-skewness and downside beta are priced by investors. Further testing confirms a separate premium for each measure, confirming that they capture different aspects of downside risk. Robustness tests indicate that, when combined with other risk measures, both retain their explanatory power. Tests also indicate that co-skewness may be the more robust measure.     

A novel downside beta and expected stock returns

A number of studies have found that the cross-section of stock returns reflects a risk premium for bearing downside beta; however, existing measures of downside beta have poor power for predicting returns. This paper proposes a novel measure of downside beta, the ES-implied beta, to improve the prediction of the cross-section of asset returns. The ES-implied beta explains stock returns over the same period as well as the widely used downside beta, but improves the prediction for future returns due to its high persistence. In the empirical analysis, the widely used downside beta shows a weak relation with future expected returns, but the ES-implied beta implies a statistically and economically significant risk premium of 0.6% per month and explains 0.6% of the variation in the cross-sectional returns. The effect cannot be explained by traditional cross-sectional effects and is different from the CAPM beta, the downside beta in Ang et al. (2006), coskewness, and cokurtosis.     

THE STRUCTURE OF SKEWNESS PREFERENCES IN ASSET PRICING MODELS WITH HIGHER MOMENTS: AN EMPIRICAL TEST

In this paper, the authors employ a nonlinear formulation to examine empirically the structural content of the three moment capital asset pricing model (CAPM). Whereas previous research focused on the coefficients of beta and co-skewness, this paper presents empirical results on the market risk premium and elasticity coefficient components of these two coefficients. The results indicate that although the estimated coefficient of coskewness gives important information on the marginal rate of substitution between skewness and expected return, the elasticity coefficient can provide additional (albeit different) information on skewness preference that is independent of the effects of the market risk premium. This research also shows how the non-linear formulation provides a direct linkage between the twomoment and three-moment CAPM versions and thus provides an empirical test of the theoretical conditions under which skewness preference is consistent with the two-moment CAPM empiricial results.     

An international CAPM for partially integrated markets: Theory and empirical evidence

This article proposes a theoretical testable capital asset pricing model for partially segmented markets. We establish that if some investors do not hold all international assets because of direct and/or indirect barriers, the world market portfolio is not efficient and the traditional international CAPM must be augmented by a new factor reflecting the local risk undiversifiable internationally. We also introduce a suitable framework to test this model empirically. Using a sample of six emerging markets and three mature markets, we find that the degree of stock market integration varies through time and that most of the sample emerging markets have become more integrated in the recent years. The local risk premium for emerging markets represents the most important component of the total risk premium, but its relative importance has decreased recently. Differently, the total risk premium for developed countries is largely driven by global factors.     

Firm size and volatility analysis in the Spanish stock market

Using Spanish stock market data, this paper examines volatility spillovers between large and small firms and their impact on expected returns. By using a conditional capital asset pricing model (CAPM) with an asymmetric multivariate GARCH-M covariance structure, it is shown that there exist bidirectional volatility spillovers between both types of companies, especially after bad news. After estimating the model, a positive and significant price of risk is obtained. This result is consistent with the volatility feedback effect, one of the most popular explanations of the asymmetric volatility phenomenon, and explains why risk premiums are much more sensitive to negative return shocks coming from the whole market or other related markets.     

The pricing of capital assets in a multiperiod world

This paper proposes a general framework for the pricing of capital assets in a multiperiod world. Under quite general conditions, the analysis shows that the equilibrium expected nominal return on any asset can always be expressed as the sum of the risk-free rate and various risk premiums. The first risk premium is identical to the usual risk premium in the Sharpe-Lintner-Mossin capital asset pricing model. The mathematical forms of all the remaining risk premiums are identical even though each individual risk premium may be present for a different reason.     

Testing asset pricing models with changing expectations and an unobservable market portfolio

When the assumption of constant risk premiums is relaxed, financial valuation models may be tested, and risk measures estimated without specifying a market index or state variables. This is accomplished by examining the behavior of conditional expected returns. The approach is developed using a single risk premium asset pricing model as an example and then extended to models with multiple risk premiums. The methodology is illustrated using daily return data on the common stocks of the Dow Jones 30. The tests indicate that these returns are consistent with a single, time-varying risk premium.     

The Effects of Inverted Yield Curves on Asset Returns

Between 1954 and 1991, U.S. stocks, long-term government bonds, and corporate bonds show negative risk premiums during periods preceded by inverted yield curves. Intermediate-term government bonds do not. Going from safer to riskier asset classes, the negative risk premiums increase in absolute value and statistical significance. The consumption CAPM offers a possible explanation for the negative risk premiums. A negative covariance between the growth rate of consumption and the premium on the risky assets will result in a negative risk premium. Empirical tests of the conditional covariance show that the consumption CAPM does not explain the phenomena.     

Extending the capital asset pricing model: the reward beta approach

This paper offers an alternative method for estimating expected returns. The proposed reward beta approach performs well empirically and is based on asset pricing theory. The empirical section compares this approach with the capital asset pricing model (CAPM) and the Fama–French three‐factor model. In out‐of‐sample testing, both the CAPM and the three‐factor model are rejected. In contrast, the reward beta approach easily passes the same test. In robustness checks, the reward beta approach consistently outperforms both the CAPM and the three‐factor model.     

DUAL BETAS FROM BULL AND BEAR MARKETS: REVERSAL OF THE SIZE EFFECT

Significant firm-size-related differences in abnormal returns and systematic risks occur in bull and bear market months from 1926 to 1988. Potential differential return premiums between recessions and expansions appear to be captured by the varying risk model and not the constant risk model. Using a dual-beta market model to adjust for risk differences in bull and bear markets, we find that large firm stocks on average earn significant positive excess returns and small firm stocks earn significant negative excess returns. Superior performance of large firm stocks is even more pronounced outside January.     

Asymmetric Volatility,Skewness, and Downside Risk in Different Asset Classes: Evidence from Futures Markets

This study examines the cross‐sectional variation of futures returns from different asset classes. The monthly returns are positively correlated with downside risk and negatively correlated with coskewness. The asymmetric volatility effect generates negatively skewed returns. Assets with high coskewness and low downside betas provide hedges against market downside risk and offer low returns. The high returns offered by assets with low coskewness and high downside betas are a risk premium for bearing downside risk. The asset pricing model that incorporates downside risk partially explains the futures returns. The results indicate a unified risk perspective to jointly price different asset classes.     

Conditional interest rate risk and the cross‐section of excess stock returns

Differences in excess stock returns can be rationalized by their sensitivities to conditional interest rate risk. Value stocks are particularly sensitive to upside movements in interest rate growth, while growth stocks react strongly to downside movements in interest rate growth. Consistent with the basic asset pricing theory, the upside interest rate risk commands a negative premium which is higher than the premium associated with the downside interest rate risk. Upside beta pertains its explanatory power after controlling for exposure to regular unconditional interest rate and various sources of financial and conditional macroeconomic risk.     

Conditional extreme risk,black swan hedging,and asset prices

Motivated by the asset pricing theory with safety-first preference, we introduce and operationalize a conditional extreme risk (CER) measure to describe expected stock performance conditional on a small-probability market downturn (black swan). We document a significant CER premium in the cross-section of expected returns. We also demonstrate that CER explains the premia to downside beta, coskewness, and cokurtosis. CER provides distinct information regarding black swan hedging that cannot be captured by co-crash-based tail dependence measures. As we find that the pricing effect is stronger among black swan hedging stocks, this distinction helps explain the absence of premium to tail dependence.     

THE TIME‐VARYING EQUITY PREMIUM AND THE S&P 500 IN THE TWENTIETH CENTURY

I present a new hindcast stock market index for the United States over the twentieth century. This is constructed by calibrating a rational asset pricing model that allows for a time‐varying equity premium driven by heteroskedasticity in consumption growth. By incorporating this variation in risk, the mean square error of the generated index series, when compared to the observed levels of the S&P 500, is significantly reduced. The model also explains the broad magnitudes and timings of the major bull and bear markets of the twentieth century, particularly before 1973, and the excess volatility puzzle is largely resolved.     

INFLATION MEASUREMENT,INFLATION RISK,AND THE PRICING OF TREASURY BILLS

One explanation for the high real interest rates on Treasury bills during the period from 1980 to 1985 is that the risk premium had risen. A procedure for testing this hypothesis is to apply the Black version of the capital asset pricing model to real Treasury bill returns. This paper examines that procedure in detail. The main conclusion is that nonstationarity and measurement error, which are always impediments to empirical implementation of the CAPM, are particularly difficult to handle when estimating changes in Treasury bill risk premiums. Furthermore, the behavior of the premium depends on the index used to measure inflation.     

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.     

The critical role of conditioning information in determining if value is really riskier than growth

Conditional asset pricing models have been used to determine whether the value premium and other CAPM anomalies are due to risk. We show that the conclusions on whether these anomalies are due to risk are very sensitive to the choice of the information variables used to define good and bad states of the world. We use a conditional CAPM framework allowing for alternative sets of plausible conditioning information and find that value appears to be riskier than growth in only about ten to twenty percent of specifications. We find even less evidence that size, issuance, momentum, and asset growth portfolio returns are due to risk. Overall, our results suggest that common CAPM anomalies are not due to risk.     

International asset pricing under segmentation and PPP deviations

We analyze the impact of both purchasing power parity (PPP) deviations and market segmentation on asset pricing and investor's portfolio holdings. The freely traded securities command a world market risk premium and an inflation risk premium. The securities that can be held by only a subset of investors command two additional premiums: a conditional market risk premium and a segflation risk premium. Our model is empirically supported with important implications for tests of international asset pricing.     

Aggregate implications of micro asset market segmentation

An extensive empirical literature finds that micro asset markets are segmented from one another. We develop a consumption-based asset pricing model to quantify the aggregate implications of a financial system comprised of many such segmented micro asset markets. We specify exogenously the level of segmentation that determines how much idiosyncratic risk traders bear in their micro market and calibrate the segmentation to match facts about systematic and idiosyncratic return volatility. In our benchmark model traders bear 30% of their idiosyncratic risk, the unconditional aggregate equity premium is 2.4% annual, and the welfare costs of segmentation are substantial, 1.8% of lifetime consumption.