The Risk‐Return Relation in International Stock Markets

We investigate the risk‐return relation in international stock markets using realized variance constructed from MSCI (Morgan Stanley Capital International) daily stock price indices. In contrast with the capital asset pricing model, realized variance by itself provides negligible information about future excess stock market returns; however, we uncover a positive and significant risk‐return tradeoff in many countries after controlling for the (U.S.) consumption‐wealth ratio. U.S. realized variance is also significantly related to future international stock market returns; more importantly, it always subsumes the information content of its local counterparts. Our results indicate that stock market variance is an important determinant of the equity premium.     

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.     

Volatility as an Asset Class: European Evidence

Abstract

Volatility movements are known to be negatively correlated with stock index returns. Hence, investing in volatility appears to be attractive for investors seeking risk diversification. The most common instruments for investing in pure volatility are variance swaps, which now enjoy an active over-the-counter (OTC) market. This paper investigates the risk-return tradeoff of variance swaps on the Deutscher Aktienindex and Euro STOXX 50 index over the time period from 1995 to 2004. We synthetically derive variance swap rates from the smile in option prices. Using quotes from two large investment banks over two months, we validate that the synthetic values are close to OTC market prices. We find that variance swap returns exhibit an option-like profile compared to returns of the underlying index. Given this pattern, it is crucial to account for the non-normality of returns in measuring the performance of variance swap investments. As in the US, the average returns of selling variance swaps are found to be strongly positive and too large to be compatible with standard equilibrium models. The magnitude of the estimated risk premium is related to variance uncertainty and past index returns. This indicates that the variance swap rate does not seem to incorporate all past information relevant for forecasting future realized variance.     

Value versus Growth: Time‐Varying Expected Stock Returns

Is the value premium predictable? We study time variations of the expected value premium using a two‐state Markov switching model. We find that when conditional volatilities are high, the expected excess returns of value stocks are more sensitive to aggregate economic conditions than the expected excess returns of growth stocks. As a result, the expected value premium is time varying. It spikes upward in the high volatility state, only to decline more gradually in the subsequent periods. However, out‐of‐sample predictability of the value premium is close to nonexistent.     

The skewness risk premium in equilibrium and stock return predictability

In this study, we investigate the skewness risk premium in the financial market under a general equilibrium setting. Extending the long-run risks (LRR) model proposed by Bansal and Yaron (J Financ 59:1481–1509, 2004) by introducing a stochastic jump intensity for jumps in the LRR factor and the variance of consumption growth rate, we provide an explicit representation for the skewness risk premium, as well as the volatility risk premium, in equilibrium. On the basis of the representation for the skewness risk premium, we propose a possible reason for the empirical facts of time-varying and negative risk-neutral skewness. Moreover, we also provide an equity risk premium representation of a linear factor pricing model with the variance and skewness risk premiums. The empirical results imply that the skewness risk premium, as well as the variance risk premium, has superior predictive power for future aggregate stock market index returns, which are consistent with the theoretical implication derived by our model. Compared with the variance risk premium, the results show that the skewness risk premium plays an independent and essential role for predicting the market index returns.     

Time‐Varying Risk–Return Trade‐off in the Stock Market

We uncover a strong comovement of the stock market risk–return trade‐off with the consumption–wealth ratio (CAY). The finding reflects time‐varying investment opportunities rather than countercyclical aggregate relative risk aversion. Specifically, the partial risk–return trade‐off is positive and constant when we control for CAY as a proxy for investment opportunities. Moreover, conditional market variance scaled by CAY is negatively priced in the cross‐section of stock returns. Our results are consistent with a limited stock market participation model, in which shareholders require an illiquidity premium that increases with CAY, in addition to the risk premium that is proportional to conditional market variance.     

Decomposing the VIX: Implications for the predictability of stock returns

The VIX index is not only a volatility index but also a polynomial combination of all possible higher moments in market return distribution under the risk-neutral measure. This paper formulates the VIX as a linear decomposition of four fundamentally different elements: the realized variance (RV), the variance risk premium (VRP), the realized tail (RT), and the tail risk premium (TRP), respectively. Using an innovative and nonparametric tail risk measure, we find that approximately one-third of the VIX's formation is attributed to the TRP. In addition to VRP, RT and TRP are crucial components for predicting future returns on equity portfolios.     

Average correlation and stock market returns

If the Roll critique is important, changes in the variance of the stock market may be only weakly related to changes in aggregate risk and subsequent stock market excess returns. However, since individual stock returns share a common sensitivity to true market return shocks, higher aggregate risk can be revealed by higher correlation between stocks. In addition, a change in stock market variance that leaves aggregate risk unchanged can have a zero or even negative effect on the stock market risk premium. We show that the average correlation between daily stock returns predicts subsequent quarterly stock market excess returns. We also show that changes in stock market risk holding average correlation constant can be interpreted as changes in the average variance of individual stocks. Such changes have a negative relation with future stock market excess returns.     

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.     

The Return to Direct Investment in Private Firms: New Evidence on the Private Equity Premium Puzzle*

This paper uses a novel dataset to analyze the return to direct investments in private firms by pension funds. We have two key findings. First, direct investments in private firms have underperformed public equity by 392 basis points per annum under conservative risk adjustments. Second, initial mispricing, due to over‐optimism or misperceived risk, and subsequent low capital gains seem to explain the gap in returns to private firms. Overall, these findings complement the finding of Moskowitz and Vissing‐Jørgensen (2002) of low returns on entrepreneurial investments and provide new insight into the existence of what they call the private equity premium puzzle: Even professional investors with well‐diversified portfolios like pension funds seem to get a poor risk‐return tradeoff from investing directly in private firms.     

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.     

Surprise volume and heteroskedasticity in equity market returns

Heteroskedasticity in returns may be explainable by trading volume. We use different volume variables, including surprise volume—i.e. unexpected above-average trading activity—which is derived from uncorrelated volume innovations. Assuming weakly exogenous volume, we extend the Lamoureux and Lastrapes () model by an asymmetric GARCH in-mean specification following Golsten et al. (). Model estimation for the US as well as six large equity markets shows that surprise volume provides superior model fit and helps to explain volatility persistence as well as excess kurtosis. Surprise volume reveals a significant positive market risk premium, asymmetry and a surprise volume effect in conditional variance. The findings suggest that e.g. a surprise volume shock (breakdown)—i.e. large (small) contemporaneous and small (large) lagged surprise volume—relates to increased (decreased) conditional market variance and return.     

Uncertainty,Time‐Varying Fear,and Asset Prices

I construct an equilibrium model that captures salient properties of index option prices, equity returns, variance, and the risk‐free rate. A representative investor makes consumption and portfolio choice decisions that are robust to his uncertainty about the true economic model. He pays a large premium for index options because they hedge important model misspecification concerns, particularly concerning jump shocks to cash flow growth and volatility. A calibration shows that empirically consistent fundamentals and reasonable model uncertainty explain option prices and the variance premium. Time variation in uncertainty generates variance premium fluctuations, helping explain their power to predict stock returns.     

Components of Market Risk and Return

This article proposes a flexible but parsimonious specificationof the joint dynamics of market risk and return to produce forecastsof a time-varying market equity premium. Our parsimonious volatilitymodel allows components to decay at different rates, generatesmean-reverting forecasts, and allows variance targeting. Thesefeatures contribute to realistic equity premium forecasts forthe U.S. market over the 1840–2006 period. For example,the premium forecast was low in the mid-1990s but has recentlyincreased. Although the market's total conditional variancehas a positive effect on returns, the smooth long-run componentof volatility is more important for capturing the dynamics ofthe premium. This result is robust to univariate specificationsthat condition on either levels or logs of past realized volatility(RV), as well as to a new bivariate model of returns and RV.     

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.     

Bond risk premia and realized jump risk

We find that augmenting a regression of excess bond returns on the term structure of forward rates with an estimate of the mean realized jump size almost doubles the R² of the forecasting regression. The return predictability from augmenting with the jump mean easily dominates that offered by augmenting with options-implied volatility and realized volatility from high-frequency data. In out-of-sample forecasting exercises, inclusion of the jump mean can reduce the root mean square prediction error by up to 40%. The incremental return predictability captured by the realized jump mean largely accounts for the countercyclical movements in bond risk premia. This result is consistent with the setting of an incomplete market in which the conditional distribution of excess bond returns is affected by a jump risk factor that does not lie in the span of the term structure of yields.     

International Asset Excess Returns and Multivariate Conditional Volatilities

This paper constructs a multivariate model in relating multi-asset excess returns to their conditional variances. Applying weekly data to investigate the foreign-exchange risk premium, the evidence from a multivariate GARCH model shows that the foreign-exchange excess returns are significantly correlated with economic fundamentals such as the real interest-rate differential, long-short interest-rate spread differential, and equity-premium differential. The evidence also suggests that foreign-exchange excess returns are not independent of the conditional variances of these fundamental variables, supporting the time-varying risk-premium hypothesis.     

Accounting information,disclosure, and expected utility: Do investors really abhor uncertainty?

Investors are said to “abhor uncertainty,” but if there were no uncertainty they could earn only the risk‐free rate. A fundamental result in the analytical accounting literature shows that investors buying into a CARA‐normal CAPM market pay lower asset prices, gain higher ex‐ante expected returns, and obtain higher expected utility, when the market payoff has higher variance. New investors obtain similar “welfare” gains from risk under a log/power utility CAPM. These results do not imply that investors “abhor information.” To realize investors' ex‐ante expectations, the subjective probability distributions representing market expectations must be accurate. Greater payoff risk can add to investors' expected utility, but higher ex‐post(realized) utility comes from better information and more accurate ex‐ante expectations. An important implication for accounting is that greater disclosure can have the simultaneous effects of (i) exposing more fully or perceptibly firms' payoff uncertainty, thereby increasing new investors' expected utility, and (ii) improving market estimates of firms' payoff parameters (means, variances, covariances), thereby giving investors a better chance of realizing their expectations. Paradoxically, better information can be valuable to new investors by exposing more fully and more accurately the risk in firms' business operations and results–new investors maximizing expected utility want both more risk and better information.     

Time-varying excess returns on UK government bonds: A non-linear approach

This paper provides an empirical examination of the behaviour of excess returns on UK government discount bonds in terms of risk factors such as the forward premium, the slope of the term structure, dividend yields and excess stock returns. We identify the existence of a time-varying term structure of expected excess returns. Further, the dynamics of the expected returns are characterised by regime-switching behaviour where the transition from one regime to the other is controlled by the slope of the term structure of interest rates. The first regime, which is characterised by flat or downward sloping term structures, occurs during periods of economic recession. The second regime, which is characterised by upward sloping term structures, occurs during periods of economic expansion. The main risk factors explaining expected returns are the slope of the term structure in the recessionary regime and the excess stock returns in the expansionary regime.     

Asymmetric information and target firm returns

This article examines the relationship between asymmetric information and target firm returns in mergers and acquisitions (M&As). We argue that if managers possess favourable (unfavourable) asymmetric information, they will offer, ceteris paribus, a high (low) premium, affecting target firm returns accordingly. We propose several proxies of asymmetric information. The empirical evidence strongly supports our hypothesis as we find that target firm returns are significantly negatively related to asymmetric information regarding synergy gains. Our results are robust after controlling for several target and deal characteristics.