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.     

How Does Information Quality Affect Stock Returns?

Using a simple dynamic asset pricing model, this paper investigates the relationship between the precision of public information about economic growth and stock market returns. After fully characterizing expected returns and conditional volatility, I show that (i) higher precision of signals tends to increase the risk premium, (ii) when signals are imprecise the equity premium is bounded above independently of investors' risk aversion, (iii) return volatility is U-shaped with respect to investors' risk aversion, and (iv) the relationship between conditional expected returns and conditional variance is ambiguous.     

Conditional Skewness in Asset Pricing Tests

If asset returns have systematic skewness, expected returns should include rewards for accepting this risk. We formalize this intuition with an asset pricing model that incorporates conditional skewness. Our results show that conditional skewness helps explain the cross-sectional variation of expected returns across assets and is significant even when factors based on size and book-to-market are included. Systematic skewness is economically important and commands a risk premium, on average, of 3.60 percent per year. Our results suggest that the momentum effect is related to systematic skewness. The low expected return momentum portfolios have higher skewness than high expected return portfolios.     

Optimal Investment, Growth Options, and Security Returns

As a consequence of optimal investment choices, a firm's assets and growth options change in predictable ways. Using a dynamic model, we show that this imparts predictability to changes in a firm's systematic risk, and its expected return. Simulations show that the model simultaneously reproduces: (i) the time-series relation between the book-to-market ratio and asset returns; (ii) the cross-sectional relation between book-to-market, market value, and return; (iii) contrarian effects at short horizons; (iv) momentum effects at longer horizons; and (v) the inverse relation between interest rates and the market risk premium.     

The relation between stock returns and short-term interest rates

This study examines the relation between the expected returns on common stocks and short-term interest rates. Using a two-factor model of stock returns, we show that the expected returns on common stocks are systematically related to the market risk and the interest-rate risk, which are estimated as the sensitivity of common-stock excess returns to the excess return on the equally weighted market index and to the federal fund premium, respectively. We find that the interest-rate risk for small firms is a significant source of investors' portfolio risk, but is not properly reflected in the single-factor market risk. We also find that the interest-rate risk for large firms is “negative” in the sense that the market risk estimated from the single-factor model overstates the true risk of large firms. An application of the Fama-MacBeth methodology indicates that the interest-rate risk premium as well as the market's risk premium are significant, implying that both the market risk and the interest-rate risk are priced. We show that the interest-rate risk premium explains a significant portion of the difference in expected returns between the top quintile and the bottom quintile of the NYSE and AMEX firms. We also show that the turn-of-the-year seasonal is observed for the interest-rate risk premium; however, the risk premium for the rest of the year is still significant, although small in mangitude.     

An examination of the relation between asymmetric risk measures,prior returns and expected daily stock returns

We use a sample of individual firm stock returns over the 1988–2009 time period to determine whether: (1) expected daily returns are related to asymmetric risk measures, (2) expected daily returns are related to the directional change of the prior day's price, and (3) our results are robust to the addition of firm size, book-to-market equity and liquidity. We find that investors are compensated for asymmetric risk; however, the positive risk–return relation is present only for our smallest firm quintile. We find a short-term return reversal present in all subgroups, except for the largest firms in our sample. We also document that the low volatility anomaly may be related to firm size and liquidity.     

ESTIMATING EXPECTED EXCESS RETURNS USING HISTORICAL AND OPTION‐IMPLIED VOLATILITY

We test the relation between expected and realized excess returns for the S&P 500 index from January 1994 through December 2003 using the proportional reward‐to‐risk measure to estimate expected returns. When risk is measured by historical volatility, we find no relation between expected and realized excess returns. In contrast, when risk is measured by option‐implied volatility, we find a positive and significant relation between expected and realized excess returns in the 1994–1998 subperiod. In the 1999–2003 subperiod, the option‐implied volatility risk measure yields a positive, but statistically insignificant, risk‐return relation. We attribute this performance difference to the fact that, in the 1994–1998 subperiod, return volatility was lower and the average return was much higher than in the 1999–2003 subperiod, thereby increasing the signal‐to‐noise ratio in the latter subperiod.     

Estimating the Intertemporal Risk–Return Tradeoff Using the Implied Cost of Capital

We argue that the implied cost of capital (ICC), computed using earnings forecasts, is useful in capturing time variation in expected stock returns. First, we show theoretically that ICC is perfectly correlated with the conditional expected stock return under plausible conditions. Second, our simulations show that ICC is helpful in detecting an intertemporal risk–return relation, even when earnings forecasts are poor. Finally, in empirical analysis, we construct the time series of ICC for the G–7 countries. We find a positive relation between the conditional mean and variance of stock returns, at both the country level and the world market level.     

Stock Liquidity Risk and the Cross‐sectional Earnings‐Returns Relationship

We argue that a higher sensitivity to aggregate market‐wide liquidity shocks (i.e., a higher liquidity risk) implies a tendency for a stock's price to converge to fundamentals. We test this intuition within the framework of the earnings‐returns relationship. We find a positive liquidity risk effect on the relationship between return and expected change in earnings. This effect on the earnings‐returns relationship is distinct from the negative effect observed for stock illiquidity level. Notably, the liquidity risk effect is evident (absent) during periods of neutral/low (high) aggregate market liquidity. We also show that the liquidity risk effect is dominant in firms that: (a) are of intermediate size; (b) are of intermediate book‐to‐market; and (c) are profit making.     

Using Expectations to Test Asset Pricing Models

Asset pricing models generate predictions relating assets' expected rates of return and their risk attributes. Most tests of these models have employed realized rates of return as a proxy for expected return. We use analysts' expected rates of return to examine the relation between these expectations and firm attributes. By assuming that analysts' expectations are unbiased estimates of market-wide expected rates of return, we can circumvent the use of realized rates of return and provide evidence on the predictions emanating from traditional asset pricing models. We find a positive, robust relation between expected return and market beta and a negative relation between expected return and firm size, consistent with the notion that these are risk factors. We do not find that high book-to-market firms are expected to earn higher returns than low book-to-market firms, inconsistent with the notion that book-to-market is a risk factor.     

The role of exchange rates in intertemporal risk–return relations

This paper investigates the significance of an intertemporal relation between expected returns on countries’ stock market portfolios and their risk exposures to the world market portfolio. We find that the intertemporal risk–return relation differs significantly under different currency denominations. The slope coefficient is the largest at around seven when the returns are denominated in Japanese yen, moderate at about five when the returns are denominated in the Canadian or US dollars, and the smallest at around three when the returns are denominated in pound or euro and its predecessors. The ranking of the risk–return coefficients across different currency denominations remains the same when we replace country equity indices with global industry portfolios in estimating the intertemporal relations, when we change the return frequency from monthly to daily, and when we consider different specifications for the conditional covariance process.     

Stock market risk and return: an equilibrium approach

Empirical evidence that expected stock returns are weakly relatedto volatility at the market level appears to contradict theintuition that risk and return are positively related. We investigatethis issue in a general equilibrium exchange economy characterizedby a regime-switching consumption process with time-varyingtransition probabilities between regimes. When estimated usingconsumption data, the model generates a complex, non-linearand time-varying relation between expected returns and volatility,duplicating the salient features of the risk/return trade-offin the data. The results emphasize the importance of time-varyinginvestment opportunities and highlight the perils of relyingon intuition from static models.     

Value-at-risk and the cross section of emerging market hedge fund returns

This paper examines the cross-sectional relationship between downside risk (Value at Risk) and expected returns in a sample of 1370 emerging market hedge funds (EMHF). We find that downside risk significantly drives expected returns for these funds, particularly before the global financial crisis, commanding an annual risk premium of over 12%. While EMHF differ from their advanced market counterparts in risk/return patterns, we show that the global financial crisis of 2008 has caused a structural shift in that pattern. Finally, we show that the risk premium associated with downside risk is predictable by the global financial cycle, even after we control for emerging market systematic risk factors.     

Cross‐Section of Expected Returns and Extreme Returns: The Role of Investor Attention and Risk Preferences

Previous work finds a negative and significant relation between the maximum daily return over the past one month and expected future stock returns. We determine that this effect is more pronounced for stocks that achieve their maximum daily returns toward the end of the month and stocks that are associated with capital losses show greater reversals. These results suggest the effect is related to investor attention and risk preferences.     

Preserving Value through Adaptation to Climate Change

Corporate “mitigation” efforts to limit greenhouse gases alone will not be sufficient to protect companies against future environmental impacts. For most companies intent on preserving their operating efficiency and value, “adaptation”—the process of changing behavior in response to actual or expected climate change impacts—is emerging as a critical partner to mitigation efforts aimed at reducing the accumulation of greenhouse gases in the atmosphere. The recent growth in the expected costs associated with the risk of climate change emphasizes the importance of developing new technology and redesigning infrastructure and other assets that will enable companies to respond to such change without excessive reductions in profitability. The nature and extent of adaptation in each situation will depend on the costs involved relative to the benefits of adopting different adaptation strategies to achieve a target level of resilience. Companies that choose to adapt and do so effectively are expected to benefit from an improvement in their net risk‐return profile. Consistent with this expectation, the authors found that a sample of companies from the European energy sector that adapted to the 2005 EU climate change mandate by diversifying their fuel sources (mainly away from coal) experienced reductions in both risk and return while non‐adapting firms experienced roughly the same returns, but at the cost of higher risk. The benefit of adapting is thus seen as showing up not in higher returns per se, but in higher risk‐adjusted returns.     

Return dispersion and expected returns

This paper proposes a two-factor asset-pricing model that incorporates market return and return dispersion. Consistent with this model, we find that stocks with higher sensitivities to return dispersion have higher average returns, and that return dispersion carries a significant positive price of risk. In particular, the return dispersion factor dominates the book-to-market factor in explaining cross-sectional expected returns. The return dispersion model outperforms the CAPM, MVM, IVM, and FF-3M when using a set of 5×5 test portfolios constructed from NYSE and AMEX stock returns from August 1963 to December 2005. Return dispersion continues to play an important role in explaining the cross-sectional variation of expected returns, even when market volatility, idiosyncratic volatility, size, book-to-market factors, and a momentum factor are included. This study sheds some light on the ability of return dispersion to explain expected returns beyond the standard asset-pricing factors. Our finding suggests that return dispersion captures two dimensions of systematic risk: the business cycle and fundamental economic restructuring.     

Asset Pricing and Expected Inflation

This paper provides an equilibrium model in which expected real returns on common stocks are negatively related to expected inflation and money growth. It is shown that the fall in real wealth associated with an increase in expected inflation decreases the real rate of interest and the expected real rate of return of the market portfolio. The expected real rate of return of the market portfolio falls less, for a given increase in expected inflation, when the increase in expected inflation is caused by an increase in money growth rather than by a worsening of the investment opportunity set. The model has empirical implications for the effect of a change in expected inflation on the cross-sectional distribution of asset returns and can help to understand why assets whose return covaries positively with expected inflation may have lower expected returns. The model also agrees with explanations advanced by Fama [5] and Geske and Roll [10] for the negative relation between stock returns and inflation.     

Asset pricing and foreign exchange risk

According to the International Capital Asset Pricing Model (ICAPM), the covariance of assets with foreign exchange currency returns should be a risk factor that must be priced when the purchasing power parity is violated. The goal of this study is to re-examine the relationship between stock returns and foreign exchange risk. The novelties of this work are: (a) a data set that makes use of daily observations for the measurement of the foreign exchange exposure and volatility of the sample firms and (b) data from a Eurozone country.The methodology we make use in reference to the estimation of the sensitivity of each stock to exchange rate movements is that it allows regressing stock returns against factors controlling for market risk, size, value, momentum, foreign exchange exposure and foreign exchange volatility. Stocks are then classified according to their foreign exchange sensitivity portfolios and the return of a hedge (zero-investment) portfolio is calculated. Next, the abnormal returns of the hedge portfolio are regressed against the return of the factors. Finally, we construct a foreign exchange risk factor in such manner as to obtain a monotonic relation between foreign exchange risk and expected returns.The empirical findings show that the foreign exchange risk is priced in the cross section of the German stock returns over the period 2000-2008. Furthermore, they show that the relationship between returns and foreign exchange sensitivity is nonlinear, but it takes an inverse U-shape and that foreign exchange sensitivity is larger for small size firms and value stocks.     

Macroeconomic Seasonality and the January Effect

Many financial markets researchers have sought an explanation for the role of January in stock returns. Any explanation of this phenomenon that is consistent with rational pricing must specify a source of seasonality in expected returns. The pervasive seasonality in the macroeconomy is an appealing possibility. A multifactor model that links macroeconomic risk to expected return is found to show substantial seasonality in expected returns. This model accounts for the seasonality in average returns, while the capital asset pricing model cannot.     

On the relation between expected returns and implied cost of capital

We examine the relation between implied cost of capital and expected returns under an assumption that expected returns are stochastic, a property supported by theory and empirical evidence. We demonstrate that implied cost of capital differs from expected return, on average, by a function encompassing volatilities of, as well as correlation between, expected returns and cash flows, growth in cash flows, and leverage. These results provide alternative explanations for findings from empirical studies employing implied cost of capital on the magnitude of the market risk premium; predictability of future returns; and the relations between cost of capital and a host of firm characteristics, such as growth, leverage, idiosyncratic risk and the firm’s information environment.