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43
Expected stock returns and volatility
 Journal of Financial Economics
, 1987
"... This paper examines the relation between stock returns and stock market volatility. We find evidence that the expected market risk premium (the expected return on a stock portfolio minus the Treasury bill yield) is positively related to the predictable volatility of stock returns. There is also evid ..."
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Cited by 337 (8 self)
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This paper examines the relation between stock returns and stock market volatility. We find evidence that the expected market risk premium (the expected return on a stock portfolio minus the Treasury bill yield) is positively related to the predictable volatility of stock returns. There is also evidence that unexpected stock market returns are negatively related to the unexpected change in the volatility of stock returns. This negative relation provides indirect evidence of a positive relation between expected risk premiums and volatility. 1.
Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk
 THE JOURNAL OF FINANCE • VOL. LVI
, 2001
"... This paper uses a disaggregated approach to study the volatility of common stocks at the market, industry, and firm levels. Over the period 1962–1997 there has been a noticeable increase in firmlevel volatility relative to market volatility. Accordingly, correlations among individual stocks and the ..."
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Cited by 270 (13 self)
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This paper uses a disaggregated approach to study the volatility of common stocks at the market, industry, and firm levels. Over the period 1962–1997 there has been a noticeable increase in firmlevel volatility relative to market volatility. Accordingly, correlations among individual stocks and the explanatory power of the market model for a typical stock have declined, whereas the number of stocks needed to achieve a given level of diversification has increased. All the volatility measures move together countercyclically and help to predict GDP growth. Market volatility tends to lead the other volatility series. Factors that may be responsible for these findings are suggested.
On estimating the expected return on the market  an exploratory investigation
 Journal of Financial Economics
, 1980
"... The expected market return is a number frequently required for the solution of many investment and corporate tinance problems, but by comparison with other tinancial variables, there has been little research on estimating this expected return. Current practice for estimating the expected market retu ..."
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Cited by 245 (1 self)
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The expected market return is a number frequently required for the solution of many investment and corporate tinance problems, but by comparison with other tinancial variables, there has been little research on estimating this expected return. Current practice for estimating the expected market return adds the historical average realized excess market returns to the current observed interest rate. While this model explicitly reflects the dependence of the market return on the interest rate, it fails to account for the effect of changes in the level of market risk. Three models of equilibrium expected market returns which reflect this dependence are analyzed in this paper. Estimation procedures which incorporate the prior restriction that equilibrium expected excess returns on the market must be positive are derived and applied to return data for the period 19261978. The principal conclusions from this exploratory investigation are: (1) in estimating models of the expected market return, the nonnegativity restriction of the expected excess return should be explicitly included as part of the specification; (2) estimators which use realized returns should be adjusted for heteroscedasticity. 1.
Stock Prices and Volume
, 1990
"... We undertake a comprehensive investigation of price and volume comovement using daily New York Stock Exchange data from 1928 to 1987. We adjust the data to take into account wellknown calendar effects and longrun trends. To describt tbe process, we use a seminonparametric estimate of the joint de ..."
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Cited by 109 (9 self)
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We undertake a comprehensive investigation of price and volume comovement using daily New York Stock Exchange data from 1928 to 1987. We adjust the data to take into account wellknown calendar effects and longrun trends. To describt tbe process, we use a seminonparametric estimate of the joint density of current price change and volume conditional on past price changes and volume. Four empirical regularities are found: 1) positive correlation between conditional volatility and volume, 2) large price movements are followed by high volume, 3) conditioning on lagged volume substantially attenuates the "leverage " effect, and 4) after conditioning on lagged volume, there is a positive risk/return relation.
Continuous Record Asymptotics for Rolling Sample Variance Estimators
 Econometrica
, 1996
"... It is widely known that conditional covariances of asset returns change over time. ..."
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Cited by 89 (0 self)
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It is widely known that conditional covariances of asset returns change over time.
There is a riskreturn tradeoff after all
, 2004
"... This paper studies the intertemporal relation between the conditional mean and the conditional variance of the aggregate stock market return. We introduce a new estimator that forecasts monthly variance with past daily squared returns, the mixed data sampling (or MIDAS) approach. Using MIDAS, we fin ..."
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Cited by 80 (15 self)
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This paper studies the intertemporal relation between the conditional mean and the conditional variance of the aggregate stock market return. We introduce a new estimator that forecasts monthly variance with past daily squared returns, the mixed data sampling (or MIDAS) approach. Using MIDAS, we find a significantly positive relation between risk and return in the stock market. This finding is robust in subsamples, to asymmetric specifications of the variance process and to controlling for variables associated with the business cycle. We compare the MIDAS results with tests of the intertemporal capital asset pricing model based on alternative conditional variance specifications and explain the conflicting results in the literature. Finally, we offer new insights about the dynamics of conditional variance.
Dynamic Derivative Strategies
, 2003
"... We study optimal investment strategies given investor access not only to bond and stock markets but also to the derivatives market. The problem is solved in closed form. Derivatives extend the risk and return tradeoffs associated with stochastic volatility and price jumps. As a means of exposure to ..."
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Cited by 33 (5 self)
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We study optimal investment strategies given investor access not only to bond and stock markets but also to the derivatives market. The problem is solved in closed form. Derivatives extend the risk and return tradeoffs associated with stochastic volatility and price jumps. As a means of exposure to volatility risk, derivatives enable nonmyopic investors to exploit the timevarying opportunity set; and as a means of exposure to jump risk, they enable investors to disentangle the simultaneous exposure to diffusive and jump risks in the stock market. Calibrating to the S&P 500 index and options markets, we find sizable portfolio improvement from derivatives investing.
Variation, jumps, market frictions and high frequency data in financial econometrics
, 2005
"... ..."
Inference for volatilitytype objects and implications for hedging. Mykland
 Statistics and Its Interface
, 2008
"... The paper studies inference for volatility type objects and its implications for the hedging of options. It considers the nonparametric estimation of volatilities and instantaneous covariations between diffusion type processes. This is then linked to options trading, where we show that our estimates ..."
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Cited by 12 (3 self)
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The paper studies inference for volatility type objects and its implications for the hedging of options. It considers the nonparametric estimation of volatilities and instantaneous covariations between diffusion type processes. This is then linked to options trading, where we show that our estimates can be used to trade options without reference to the specific model. The new options “delta ” becomes an additive modification of the (implied volatility) BlackScholes delta. The modification, in our example, is both substantial and statistically significant. In the inference problem, explicit expressions are found for asymptotic error distributions, and it is explained why one does not in this case encounter a biasvariance tradeoff, but rather a variancevariance tradeoff. Observation times can be irregular. Some key words and phrases: volatility estimation, statistical uncertainty, small interval asymptotics, mixing convergence, option hedging
Stochastic Volatility
, 2005
"... Stochastic volatility (SV) is the main concept used in the fields of financial economics and mathematical finance to deal with the endemic timevarying volatility and codependence found in financial markets. Such dependence has been known for a long time, early comments include Mandelbrot (1963) and ..."
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Cited by 12 (0 self)
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Stochastic volatility (SV) is the main concept used in the fields of financial economics and mathematical finance to deal with the endemic timevarying volatility and codependence found in financial markets. Such dependence has been known for a long time, early comments include Mandelbrot (1963) and Officer (1973). It was also clear to the founding fathers of modern continuous time finance that homogeneity was an unrealistic if convenient simplification, e.g. Black and Scholes (1972, p. 416) wrote “... there is evidence of nonstationarity in the variance. More work must be done to predict variances using the information available. ” Heterogeneity has deep implications for the theory and practice of financial economics and econometrics. In particular, asset pricing theory is dominated by the idea that higher rewards may be expected when we face higher risks, but these risks change through time in complicated ways. Some of the changes in the level of risk can be modelled stochastically, where the level of volatility and degree of codependence between assets is allowed to change over time. Such models allow us to explain, for example, empirically observed departures from BlackScholesMerton prices for options and understand why we should expect to see occasional dramatic moves in financial markets. The outline of this article is as follows. In section 2 I will trace the origins of SV and provide links with the basic models used today in the literature. In section 3 I will briefly discuss some of the innovations in the second generation of SV models. In section 4 I will briefly discuss the literature on conducting inference for SV models. In section 5 I will talk about the use of SV to price options. In section 6 I will consider the connection of SV with realised volatility. A extensive reviews of this literature is given in Shephard (2005). 2 The origin of SV models The origins of SV are messy, I will give five accounts, which attribute the subject to different sets of people.