Intertemporal Risk-return Relation Research Articles

State-dependent intertemporal risk-return tradeoff: Further evidence

We suggest that the intertemporal risk-return tradeoff is not necessarily positive but rather state dependent. We further explore the state dependent risk-return relation by examining how the positive risk-return relation is distorted in response to various market conditions, including extreme price changes, differing levels of investor sentiment, the introduction of stock options, and throughout business cycles. The tendency for uninformed investors to be optimistic (pessimistic) in response to good (bad) market news cause overpricing (underpricing), and the resulting trade activity of arbitrageurs that distorts the positive risk-return tradeoff, is documented consistently across these environments. We find that the attenuation (reinforcement) of the positive risk-return relation under investors’ optimistic (pessimistic) expectations is stronger in high (low) sentiment periods, in the presence of extreme returns, in the period after stock options became available, and during expansionary periods. We argue that the asymmetric intertemporal risk-return relation is a consequence of rational arbitrageurs’ trading to exploit mispricing through the selling of overpriced stocks conditional on good news and buying underpriced stocks conditional on bad news.

Nonparametric estimation of infinite order regression and its application to the risk-return tradeoff

This paper studies nonparametric estimation of the infinite order regression E(Ytk|Ft−1), k∈Z with stationary and weakly dependent data. We propose a Nadaraya–Watson type estimator that operates with an infinite number of conditioning variables. We propose a bandwidth sequence that shrinks the effects of long lags, so the influence of all conditioning information is modelled in a natural and flexible way, and the issues of omitted information bias and specification error are effectively handled. We establish the asymptotic properties of the estimator under a wide range of static and dynamic regressions frameworks, thereby allowing various kinds of conditioning variables to be used. We establish pointwise/uniform consistency and CLTs. We show that the convergence rates are at best logarithmic, and depend on the smoothness of the regression, the distribution of the marginal regressors and their dependence structure in a non-trivial way via the Lambert W function. We apply our methodology to examine the intertemporal risk-return relation for the aggregate stock market, and some new empirical evidence is reported. For the S&P 500 daily data from 1950 to 2017 using our estimator we report an overall positive risk-return relation. We also find evidence of strong time variation and counter-cyclical behaviour in risk aversion. These conclusions are possibly attributable to the allowance of further flexibility and the inclusion of otherwise neglected information in our method.

The Intertemporal Risk-Return Relation is Alive and Well, It's Interpretation? Not So Much

Using data from 1980 through 2005, and implementations of the Intertemporal Capital Asset Pricing Model (ICAPM), this study consistently generates positive intertemporal risk-return relations within venture capital markets. During the first five years of business, venture capitalists (VCs) are shown to be risk averse, and are characterized by a Coefficient of Relative Risk Aversion (CRRA) estimated at about 2.75. From the sixth year of business onwards, VCs are characterized by CRRAs that are no higher than 1.91. Combination of rigorous theoretical and empirical evidence establishes that CRRAs less than or equal to 2.00 are evidence for risk seeking preferences. The CRRA for the representative risk bearing agent who aggregates preferences of risk averse and risk seeking agents is shown to aggregate to 3.59. This outcome, to wit, a higher CRRA (3.59) for an agent who aggregates risk averse and risk seeking preferences, in relation to the CRRA for the embedded representative risk averse agent (2.75) is formally and theoretically shown to be outcome that subsists in equilibrium. Totality of the formal theoretical and empirical evidence demonstrates interpretations of CRRAs that are higher than 2.75 as evidence for stock markets that consist in entirety of risk averse agents is not robust.

The intertemporal risk-Return relation, investor behavior, and technical trading profits: evidence from the G-7 countries

ABSTRACTThe intertemporal risk-return relation and investor behavior are both important pricing factors that jointly determine the expected market risk premium. Using the price adjustment process as a control variable, we find that the intertemporal risk-return relation is positive conditional on bad market news, but is non-positive conditional on good market news. This implies that good (bad) market news weakens (strengthens) the positive risk-return relation. The pattern in the distortion of the risk-return relation is consistent with short-term mispricing in which investors overvalue (undervalue) the stock market in reaction to good (bad) market news. We also show that ignoring the price adjustment process in the estimation of the risk-return relation leads to model misspecification and induces an upward (downward) bias in estimates of the relative risk aversion parameter conditional on good (bad) news. Our model of the asymmetric risk-return relation along with the price adjustment process is capable of generating the return dynamics that is attributable to technical trading profits. We suggest that the profitability of technical trading rules is not a violation of market efficiency, but a consequence of trading rules exploiting the asymmetric effect of price changes on the risk-return relation, along with the persistence property of price changes.

Intertemporal risk-return tradeoff in the short-run

We hypothesize that good (bad) market news causes overpricing (underpricing) in the short-term, thereby inducing a weak or negative (significantly positive) intertemporal risk-return tradeoff. We verify this asymmetry through the indirect relation of a weak or positive association between excess market returns and contemporaneous volatility innovations conditional on good news, and a significantly negative relation conditional on bad news. We also show that the inclusion of a price adjustment term is critical for reliable estimation of the intertemporal risk-return relation.

Risk-return trade-off for European stock markets

This paper adopts factor models with macro-finance predictors to test the intertemporal risk-return relation for 13 European stock markets from 1986 to 2012. We use country specific, euro area, and US macro-finance factors to determine the conditional volatility and conditional return. We find that the risk-return trade-off is generally negative. The Markov switching model documents that there is time-variation in this trade-off that is linked to the state of the economy, but not the business cycles. Quantile regressions show that the risk-return trade-off is stronger at the lowest quantile of the conditional return.

Is there a Positive Risk-Return Tradeoff? A Forward-Looking Approach to Measuring the Equity Premium

This article revisits the puzzling time-series relation between risk and return on the stock market portfolio. It replaces the standard ex post mean returns with forward-looking calculations of the equity risk premium derived from the classic Gordon stock valuation model. The article estimates the equity premium for several industrialised markets and finds that conditional market risk is significantly priced in the context of asset pricing theory both in the short- and long-run using various specifications for volatility. Findings herein lend credible support for the presence of a positive intertemporal risk-return relation and suggest that perhaps ex post realised returns are unjustifiably used to make ex ante inferences regarding expected returns and to motivate asset pricing tests.

Risk-Return Trade-Off for European Stock Markets

This paper adopts factor models with macro-finance predictors to test the intertemporal risk-return relation for 13 European stock markets from 1986 to 2012. We filter out country specific, euro area, and US macro-finance factors from the conditional volatility and return to determine the risk-return relationship. We find that the risk-return trade-off is generally negative. The Markov switching model documents that there is time-variation in this trade-off that is linked to the state of the economy, but not the business cycles. Quantile regressions show that the risk-return trade-off is stronger at the lowest quantile of the conditional return.

The intertemporal risk-return relation: A bivariate model approach

This paper examines the intertemporal risk-return relation using a more sensible empirical specification that is motivated by two concerns: the theoretical risk-return relation is an ex ante relation and the empirical method used to detect the relation should be reliable. We measure both the expected excess return and conditional variance jointly using the common information set based on a bivariate moving average representation of excess returns and variances. As a result, we can detect a significant positive relation between the expected excess return and the conditional variance. We also find that the positive relation is robust.

Characteristic-Based Covariances and Cross-Sectional Expected Returns

I suggest a characteristic-based covariance model that directly links the predetermined fi rm characteristics to time-varying covariance risk. Using a large cross section of individual stock-level data, I parsimoniously estimate both conditional expected returns and conditional covariances as functions of fi rm characteristics. I fi nd a strong and positive intertemporal risk-return relation on individual stocks. In comparison to the Fama-French three-factor model, the characteristic-based covariance model substantially reduces the pricing errors of characteristic-sorted portfolios on size, book-to-market, accruals, asset growth, investment-to-assets, return-on-assets, net stock issues, financial distress, and momentum. Portfolio tests similar to Daniel and Titman (1997) suggest that firm characteristics, mainly through the characteristic-based covariance structure of returns, appear to explain the cross section of average stock returns.

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.

The Role of Exchange Rates in Intertemporal Risk-Return Relations

In this paper, we investigate the role of currency denomination in intertemporal risk-return relations in international economies. 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. Our study shows that consumption risk sharing is incomplete and that exchange rate dynamics are informative about the pricing differences across different economies.

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

ABSTRACTWe 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.

Investigating the intertemporal risk–return relation in international stock markets with the component GARCH model

Daily data and component GARCH (CGARCH) models strongly support a positive risk–return relation, in contrast to previous international results. Long-run volatility appears to be important in determining the conditional equity premium, but the evidence might be spurious.

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.

Estimating the Intertemporal Capital Asset Pricing Model with Cross-Sectional Consistency

The intertemporal capital asset pricing model of Merton (1973) states that the expected excess return on an asset is proportional to the expected covariance of the excess return on this asset with the excess return on the market portfolio. The proportionality coefficient measures the average relative risk aversion of investors. When the investment opportunity is stochastic, the expected excess return is also proportional to the covariance of the excess return with the state variables that govern the state of the investment opportunity. The proportionality coefficients on these covariance terms measure the investors' average aversion to unfavorable shifts in these state variables. In this paper, we use GARCH-type models to estimate the conditional covariance of a wide array of industry and Fama-French size/book-to-market portfolios with the market portfolio and with the Fama-French size (SMB) and book-to-market (HML) risk factors. We then estimate the system of simultaneous equations that links the excess returns on these portfolios to the corresponding conditional covariances with the market portfolio and the common risk factors. We obtain a positive and highly significant estimate for the relative risk aversion coefficient. The coefficient is about three for the long sample from July 1926 to December 2002, and is around six for the more recent period from July 1963 to December 2002. Furthermore, the expected excess returns are negatively related to their conditional covariance with the Fama-French size risk factor, suggesting that an increase in the size factor predicts an unfavorable shift in the investment opportunity. However, we do not find any consistent loading on the covariance with the book-to-market risk factor. Our findings are robust to different ways of forming portfolios and estimating conditional covariances. Most of the existing literature estimates the intertemporal risk-return relation using one single series of the market portfolio return. We show that the estimates from a single return series have low statistical significance and large sample variation. Our key contribution here is to direct the attention of the literature to the cross-sectional consistency of the intertemporal asset pricing relation and the universal proportionality underlying the risk-return relation. By exploiting this universal relation, we obtain positive and highly significant estimates on the relative risk aversion coefficient. We also gain a better understanding on how different risk factors predict future movements in investment opportunities.