Do Beta Pricing Models Explain January Mean Reversion in Stock Returns?

Jegadeesh (1991) finds evidence of January mean reversion in stock returns. In this paper we attempt to distinguish between two competing economic explanations of January mean reversion in returns: (1) mispricing in irrational markets versus (2) predictable time variation in security risk premia. Excess portfolio returns are decomposed into “explained” and “unexplained” components using the Fama-French (1993) pricing model. The explained excess returns exhibit January mean reversion. The unexplained excess returns are not mean reverting. Mean reversion is therefore consistent with rational pricing in the framework of the Fama-French model. Mean reversion can be attributed to the component of return related to a relative distress factor (SMB). A comparison with the Chen, Roll, and Ross (1986) macroeconomic factors reveals that mean reversion is due to the components related to SMB and bond default premium.     

Does an intertemporal tradeoff between risk and return explain mean reversion in stock prices?

When volatility feedback is taken into account, there is strong evidence of a positive tradeoff between stock market volatility and expected returns on a market portfolio. In this paper, we ask whether this intertemporal tradeoff between risk and return is responsible for the reported evidence of mean reversion in stock prices. There are two relevant findings. First, price movements not related to the effects of Markov-switching market volatility are largely unpredictable over long horizons. Second, time-varying parameter estimates of the long-horizon predictability of stock returns reject any systematic mean reversion in favour of behaviour implicit in the historical timing of the tradeoff between risk and return.     

Pricing Currency Risks

The currency market features a small cross-section, and conditional expected returns can be characterized by few signals: interest differential, trend, and mean reversion. We exploit these properties to construct the ex ante mean-variance efficient portfolio of individual currencies. The portfolio is updated in real time and prices all prominent currency trading strategies, conditionally and unconditionally. The fraction of risk in these assets that does not affect their risk premiums is at least 85%. Extant explanations of carry strategies based on intermediary capital or global volatility are related to these unpriced components, while consumption growth is related to the priced component of returns.     

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.     

The Presidential Puzzle: Political Cycles and the Stock Market

The excess return in the stock market is higher under Democratic than Republican presidencies: 9 percent for the value‐weighted and 16 percent for the equal‐weighted portfolio. The difference comes from higher real stock returns and lower real interest rates, is statistically significant, and is robust in subsamples. The difference in returns is not explained by business‐cycle variables related to expected returns, and is not concentrated around election dates. There is no difference in the riskiness of the stock market across presidencies that could justify a risk premium. The difference in returns through the political cycle is therefore a puzzle.     

Nonlinear mean reversion in stock prices

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 mean reversion is significantly higher during the large falls of the market. The parameter estimates indicate a negative and significant relation between the monthly portfolio returns and the extreme daily returns observed over the past one to eight months. Specifically, in a quarter in which the minimum daily return is −2% the expected excess return is 37 basis points higher than in a month in which the minimum return is only −1%. This result holds for the value-weighted and equal-weighted stock market indices and for each of the size decile portfolios. The findings are also robust to different sample periods, different indices, and investment horizons.     

TIME-VARYING FACTORS AND CROSS-AUTOCORRELATIONS IN SHORT-HORIZON STOCK RETURNS

In this paper I show that the lead-lag pattern between large and small market value portfolio returns is consistent with differential variations in their expected return components. I find that the larger predictability of returns on the portfolio of small stocks may be due to a higher exposure of these firms to persistent (time-varying) latent factors. Additional evidence suggests that the asymmetric predictability cannot be fully explained by lagged price adjustments to common factor shocks: (i) lagged returns on large stocks do not have a strong causal effect on returns on small stocks; (ii) trading volume is positively related to own- and cross-autocorrelations in weekly portfolio returns; and (iii) significant cross-autocorrelation exists between current returns on large stocks and lagged returns on small stocks when trading volume is high.     

Asymmetric reverting behavior of short-horizon stock returns: An evidence of stock market overreaction

This paper investigates the uneven mean reverting pattern of monthly return indexes of the NYSE, AMEX and NASDAQ, using asymmetric non-linear smooth-transition (ANST) GARCH models. It also evaluates the extent to which time-varying volatility in the index returns support the stock market overreaction hypothesis. The models illuminate patterns of asymmetric mean reversion and risk decimation. Between 1926:01 and l997:12, not only did negative returns reverse to positive returns quicker than positive returns reverted to negative ones, but negative returns, in fact, reduced risk premiums from predictable high volatility. The findings support the market overreaction hypotheses. The asymmetry is due to the mispricing behavior on the part of investors who overreact to certain market news. The findings also corroborate arguments for the “contrarian” portfolio strategy.     

Idiosyncratic risk and the cross-section of expected stock returns

Theories such as Merton [1987. A simple model of capital market equilibrium with incomplete information. Journal of Finance 42, 483–510] predict a positive relation between idiosyncratic risk and expected return when investors do not diversify their portfolio. Ang, Hodrick, Xing, and Zhang [2006. The cross-section of volatility and expected returns. Journal of Finance 61, 259–299], however, find that monthly stock returns are negatively related to the one-month lagged idiosyncratic volatilities. I show that idiosyncratic volatilities are time-varying and thus, their findings should not be used to imply the relation between idiosyncratic risk and expected return. Using the exponential GARCH models to estimate expected idiosyncratic volatilities, I find a significantly positive relation between the estimated conditional idiosyncratic volatilities and expected returns. Further evidence suggests that Ang et al.'s findings are largely explained by the return reversal of a subset of small stocks with high idiosyncratic volatilities.     

Stock market return predictability: Does network topology matter?

This paper provides new evidence for the predictability of excess market portfolio returns using a network approach. In particular, this article introduces a measure of interconnectedness to capture the interrelationship of returns of 100 largest stocks in S&P500 during 1990–2014. In the financial network literature, the interconnection of a stock network is often regarded as a channel through which an idiosyncratic shock propagates. The idiosyncratic risk propagation is crucial to the debate over the relationship between idiosyncratic risk and market returns because the idiosyncratic risk is not always diversified away. Rather, the network can sometimes amplify the effect of the idiosyncratic risk to cause aggregate fluctuation. In accordance with this theoretical argument, I empirically show that the network topology, measured by diameter, works together with the idiosyncratic risk, measured by average stock variance, to affect the market portfolio returns. This relationship persists after controlling for well-known variables known to forecast the stock market returns.     

Risk aversion and skewness preference

Empirically, co-skewness of asset returns seems to explain a substantial part of the cross-sectional variation of mean return not explained by beta. This finding is typically interpreted in terms of a risk averse representative investor with a cubic utility function. This paper questions this interpretation. We show that the empirical tests fail to impose risk aversion and the implied utility function takes an inverse S-shape. Unfortunately, the first-order conditions are not sufficient to guarantee that the market portfolio is the global maximum for this utility function, and our results suggest that the market portfolio is more likely to represent the global minimum. In addition, if we do impose risk aversion, then co-skewness has minimal explanatory power.     

Mean reversion in Southeast Asian stock markets

This paper assesses the predictable component of South East Asian stock markets using a bootstrap resampling method to estimate the small sample distributions of variance ratio statistics. We find evidence of mean reversion in long horizon dollar adjusted excess returns. The robustness of the results is assessed by adjusting stock returns for potential time-varying expected returns and partial integration of these emerging markets into world capital markets. In all but one case, mean reversion is shown to be due to either time-variation of risk exposure and prices of risk or partial integration of the local market into world stock markets. These results clearly illustrate the dangers of testing market efficiency without carefully adjusting stock returns for time variation in expected returns and the partial integration of local markets into world markets.     

An introduction to security returns

The equity premium - the difference between the return achievable from investment in the equity market (R_M ) and the risk-free rate of return (R_F )- plays an important part in corporate finance. The expression equity premium (sometimes referred to as the equity risk premium) is used to denote the ex ante expectation of investors. The term excess return refers to the ex post achievement of stock returns over and above the risk-free return. If we compare US and UK returns, we find that total returns, real returns and the value of (R_M - R_F ) are all marginally higher for the UK. Summarized evidence appears in Table 1 and Table 6. Such greater returns may be due to an increased risk premium related to increasing unexpected inflation. Particularly important in estimating the equity risk premium is whether excess returns are measured using a geometric or an arithmetic mean return. To a significant extent, this question revolves around mean reversion in stock returns. Evidence of mean reversion is substantial, although it cannot be proved unequivocally. Given the weight of evidence of mean reversion, there may be a strong case for the use of a geometric mean with an equity premium of between 3% and 5% - or even less.     

The pricing of systematic liquidity risk: Empirical evidence from the US stock market

In this study, we examine whether aggregate market liquidity risk is priced in the US stock market. We define a bivariate Garch (1,1)-in-mean specification for the market portfolio excess returns and the changes in the standardized number of shares in the S&P 500 Index, the aggregate market liquidity proxy. The findings, based on monthly data, suggest that systematic liquidity risk is priced in the US over the period January 1973–December 1997. The liquidity premium represents a non-negligible, negative and time-varying component of the total market risk premium whose magnitude is not influenced by the October’87 Crash.     

Excess Cash and Stock Returns

I document a positive relationship between corporate excess cash holdings and future stock returns. The difference in returns of portfolios of high and low excess cash firms amounts to 5% annually or 6% after standard three-factor risk adjustment. Firms with more excess cash have higher market betas and earn lower returns during market downturns. High excess cash companies invest considerably more in the future than do their low cash peers, but do not experience stronger future profitability. On the whole, this evidence is consistent with the notion that excess cash holdings proxy for risky growth options.     

Portfolio Returns,Market Volatility,and Seasonality

This paper examines three important issues related to the relationship between stock returns and volatility. First, are Duffee's (1995) findings of the relationship between individual stock returns and volatility valid at the portfolio level? Second, is there a seasonality of the market return volatility? Lastly, do size portfolio returns react symmetrically to the market volatility during business cycles? We find that the market volatility exhibits strong autocorrelation and small size portfolio returns exhibit seasonality. However, this phenomenon is not present in large size portfolios. For the entire sample period of 1962–1995, the highest average monthly volatility occurred in October, followed by November, and then January. Examining the two sub-sample periods, we find that the average market volatility increases by 15.4% in the second sample period of 1980–1995 compared to the first sample period of 1962–1979. During the contraction period, the average market volatility is 60.9% higher than that during the expansion period. Using a binary regression model, we find that size portfolio returns react asymmetrically with the market volatility during business cycles. This paper documents a strongly negative contemporaneous relationship between the size portfolio returns and the market volatility that is consistent with the previous findings at the aggregate level, but is inconsistent with the findings at the individual firm level. In contrast with the previous findings, however, we find an ambiguous relationship between the percentage change in the market volatility and the contemporaneous stock portfolio returns. This ambiguity is attributed to strongly negative contemporaneous and one-month ahead relationships between the market volatility and portfolio returns.

     

Do jumps contribute to the dynamics of the equity premium?

This paper investigates whether risks associated with time-varying arrival of jumps and their effect on the dynamics of higher moments of returns are priced in the conditional mean of daily market excess returns. We find that jumps and jump dynamics are significantly related to the market equity premium. The results from our time-series approach reinforce the importance of the skewness premium found in cross-sectional studies using lower-frequency data; and offer a potential resolution to sometimes conflicting results on the intertemporal risk-return relationship. We use a general utility specification, consistent with our pricing kernel, to evaluate the relative value of alternative risk premium models in an out-of-sample portfolio performance application.     

MODELS OF STOCK MARKET PREDICTABILITY

I briefly review the success of past studies purporting to explain equity valuations and predict future equity returns. The Campbell‐Shiller mean reversion models are contrasted with an expanded version of the so‐called Federal Reserve model. At least from 1970 to 2003, Federal Reserve–type models did somewhat better at predicting long‐horizon returns than did a mean reversion model based on dividend yields and price‐earnings multiples. However, timing investment strategies based on any of these prediction models do no better than a buy‐and‐hold strategy. Although some predictability of returns exists, there is no evidence of any systematic inefficiency that would enable investors to earn excess returns.     

Momentum trading,mean reversal and overreaction in Chinese stock market

The vast majority of the literature reports momentum profitability to be overwhelming in the US market and widespread in other countries. However, this paper finds that the pure momentum strategy in general does not yield excess profitability in the Chinese stock markets. We find instead strong mean reversion with an average half-life slightly shorter than 1 year. A pure contrarian investment strategy produces positive excess returns and in general outperforms the pure momentum strategy. Furthermore, momentum may interact with mean reversion. A strategy based on the rolling-regression parameter estimates of the model combining mean reversion and momentum generates both statistically and economically significant excess returns. The combined strategy outperforms both pure momentum and pure contrarian strategies. We conduct a number of robustness tests and confirm the basic findings. Collectively, our results support the overreaction hypothesis.     

Risk‐Adjusted Long‐Term Contrarian Profits: Evidence from Non‐S&P 500 High‐Volume Stocks

Can trading volume help unravel the long‐term overreaction puzzle? With portfolios of non‐S&P 500 NYSE stocks, we show that (1) both the high‐ and low‐volume (abnormal volume) contrarian portfolios earn a much higher market‐adjusted excess return than the normal‐volume contrarian portfolio, (2) however, when leverage‐induced risk is factored in, excess returns from contrarian portfolios with normal‐ and low‐volume stocks are insignificant, (3) only excess returns from high‐volume contrarian stocks are significant and cannot be explained by the time‐varying risk and return framework, and (4) such high‐volume, risk‐adjusted excess returns arise mainly from winner (glamour) stocks.