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The Cross-Section of Volatility and Expected Returns
TL;DR: This paper examined the pricing of aggregate volatility risk in the cross-section of stock returns and found that stocks with high sensitivities to innovations in aggregate volatility have low average returns, and that stock with high idiosyncratic volatility relative to the Fama and French (1993) model have abysmally low return.
Abstract: We examine the pricing of aggregate volatility risk in the cross-section of stock returns Consistent with theory, we find that stocks with high sensitivities to innovations in aggregate volatility have low average returns In addition, we find that stocks with high idiosyncratic volatility relative to the Fama and French (1993) model have abysmally low average returns This phenomenon cannot be explained by exposure to aggregate volatility risk Size, book-to-market, momentum, and liquidity effects cannot account for either the low average returns earned by stocks with high exposure to systematic volatility risk or for the low average returns of stocks with high idiosyncratic volatility
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TL;DR: This paper examined whether a market structure within which lower ability agents exit (decrease equity positions), while higher ability agents enter the market in anticipation of an increase in market volatility can generate regime switches in risk aversion coefficients.
Abstract: This paper examines whether a market structure within which lower ability agents exit (decrease equity positions), while higher ability agents enter the market in anticipation of an increase in market volatility can generate regime switches in risk aversion coefficients. Using a theoretically motivated proxy for the representative agent's ability, and a switching regression model within which regime switches in market returns, market volatility, and an ability proxy are endogenously generated, I find I am able to generate regime switches in risk aversion coefficients. This results in evidence of two classes of investors that differ with respect to risk aversion coefficients; a negative correlation between the prices of the two sources of risk; and risk aversion coefficients that are low enough to rationalize equity premiums.
2 citations
TL;DR: In this paper, the authors explore how investors should take account of underlying factors driving their portfolio returns and propose a pragmatic and intuitive approach for identifying and measuring underlying factors in a portfolio via a heat map.
Abstract: The asset management industry has seen a strong development of factor-based investing. The central idea is that each asset can be seen as a bundle of underlying factor sensitivities. A factor-based investing approach provides better insight into the risk decomposition of the investment portfolio’s assets and potentially leads to better investment decision-making. In this paper we explore how investors should take account of underlying factors driving their portfolio returns. We show that underlying factors explain the majority of return variation among assets. We find there are times that a given factor sensitivity offers exceptionally high or low rewards in all assets exposed to it. These circumstances lead to an opportunity for market timing. We propose a pragmatic and intuitive approach for identifying and measuring underlying factors in a portfolio via a heat map. We argue that investors seeking to adopt a factor-based approach use it in conjunction with traditional asset allocation, rather than as a substitute. In addition, we provide suggestions on how to embed the factor-based approach within an existing investment process. Finally, a word about our relationship with ABN AMRO. The research project on factor-based investing is part of ABN AMRO Private Banking’s continuous process to challenge, and thereby to improve the investment process with new insights in the financial markets and investment approaches. Therefore we were given the task of writing this report.
2 citations
TL;DR: In this article, the explanatory power of equity multifactor models (where all the factors are excess returns) against ICAPM/macro models is compared, and it is shown that the performance of several multifactor model is probably overstated.
Abstract: I compare the explanatory power of equity multifactor models (where all the factors are excess returns) against ICAPM/macro models. I use a large cross-section of stocks and introduce a new cross-sectional R^2, based on the restriction that the risk price estimates are equal to the corresponding factor means. The equity factor models do not outperform significantly the ICAPM (and in some cases, the CAPM) in terms of explaining the broad cross-section of stock returns. This is especially true when the anomalies are not trivially related to the factors. This suggests that the performance of several multifactor models is probably overstated.
2 citations
TL;DR: This paper proposed an approach to extract option-implied equity premia, and empirically examined the information content of these risk premia for forecasting the stock market return, without specifying the functional form of the pricing kernel, and does not impose any restrictions on investors' preferences.
Abstract: This paper proposes a novel approach to extracting option-implied equity premia, and empirically examines the information content of these risk premia for forecasting the stock market return. Our approach does not require specifying the functional form of the pricing kernel, and does not impose any restrictions on investors' preferences. We only assume the existence of put and call options which complete the market, and show that the equity premium can be inferred from expected excess returns on a portfolio of options. An empirical investigation of SP (ii) the implied equity premium consistently outperforms variables commonly used in the forecasting literature both in- and out-of-sample; (iii) at the cross-sectional level, stocks that are more sensitive to the implied equity premium have higher returns on average.
2 citations
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TL;DR: This paper found that increases in implied market volatility (a proxy for market fear) have a significant impact on returns of bank stocks, above and beyond systematic risk proxied by the expected excess market return during a bad economic regime.
Abstract: We find that increases in implied market volatility (a proxy for market fear) have a significant impact on returns of bank stocks, above and beyond systematic risk proxied by the expected excess market return during a bad economic regime. Large bank returns are favorably affected by increases in implied market volatility during the crisis, while small banks are adversely affected by increases in implied market volatility. We attribute the different effects among the size-categorized bank portfolios to the perception that large banks are protected by too-big-to-fail policies. Within the sample of small banks, the adverse share price response to increased implied market volatility is more pronounced for banks that rely more heavily on non-traditional sources of funds, use a high proportion of loans in their assets, have a higher level of non-performing assets, and have a relatively low provision for loan losses. The adverse effect of negative innovations in implied market volatility on small bank returns during the crisis is primarily driven by exposure of their loan portfolio to weak economic conditions.
2 citations
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TL;DR: In this paper, the authors present some additional tests of the mean-variance formulation of the asset pricing model, which avoid some of the problems of earlier studies and provide additional insights into the nature of the structure of security returns.
Abstract: Considerable attention has recently been given to general equilibrium models of the pricing of capital assets Of these, perhaps the best known is the mean-variance formulation originally developed by Sharpe (1964) and Treynor (1961), and extended and clarified by Lintner (1965a; 1965b), Mossin (1966), Fama (1968a; 1968b), and Long (1972) In addition Treynor (1965), Sharpe (1966), and Jensen (1968; 1969) have developed portfolio evaluation models which are either based on this asset pricing model or bear a close relation to it In the development of the asset pricing model it is assumed that (1) all investors are single period risk-averse utility of terminal wealth maximizers and can choose among portfolios solely on the basis of mean and variance, (2) there are no taxes or transactions costs, (3) all investors have homogeneous views regarding the parameters of the joint probability distribution of all security returns, and (4) all investors can borrow and lend at a given riskless rate of interest The main result of the model is a statement of the relation between the expected risk premiums on individual assets and their "systematic risk" Our main purpose is to present some additional tests of this asset pricing model which avoid some of the problems of earlier studies and which, we believe, provide additional insights into the nature of the structure of security returns The evidence presented in Section II indicates the expected excess return on an asset is not strictly proportional to its B, and we believe that this evidence, coupled with that given in Section IV, is sufficiently strong to warrant rejection of the traditional form of the model given by (1) We then show in Section III how the cross-sectional tests are subject to measurement error bias, provide a solution to this problem through grouping procedures, and show how cross-sectional methods are relevant to testing the expanded two-factor form of the model We show in Section IV that the mean of the beta factor has had a positive trend over the period 1931-65 and was on the order of 10 to 13% per month in the two sample intervals we examined in the period 1948-65 This seems to have been significantly different from the average risk-free rate and indeed is roughly the same size as the average market return of 13 and 12% per month over the two sample intervals in this period This evidence seems to be sufficiently strong enough to warrant rejection of the traditional form of the model given by (1) In addition, the standard deviation of the beta factor over these two sample intervals was 20 and 22% per month, as compared with the standard deviation of the market factor of 36 and 38% per month Thus the beta factor seems to be an important determinant of security returns
2,899 citations
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TL;DR: In this paper, the generalized autoregressive conditionally heteroskedastic (GARCH) model of returns is modified to allow for volatility feedback effect, which amplifies large negative stock returns and dampens large positive returns, making stock returns negatively skewed and increasing the potential for large crashes.
Abstract: It is sometimes argued that an increase in stock market volatility raises required stock returns, and thus lowers stock prices. This paper modifies the generalized autoregressive conditionally heteroskedastic (GARCH) model of returns to allow for this volatility feedback effect. The resulting model is asymmetric, because volatility feedback amplifies large negative stock returns and dampens large positive returns, making stock returns negatively skewed and increasing the potential for large crashes. The model also implies that volatility feedback is more important when volatility is high. In U.S. monthly and daily data in the period 1926-88, the asymmetric model fits the data better than the standard GARCH model, accounting for almost half the skewness and excess kurtosis of standard monthly GARCH residuals. Estimated volatility discounts on the stock market range from 1% in normal times to 13% after the stock market crash of October 1987 and 25% in the early 1930's. However volatility feedback has little effect on the unconditional variance of stock returns.
1,793 citations
TL;DR: In this article, the authors examined a class of continuous-time models that incorporate jumps in returns and volatility, in addition to diffusive stochastic volatility, and developed a likelihood-based estimation strategy and provided estimates of model parameters, spot volatility, jump times and jump sizes using both S&P 500 and Nasdaq 100 index returns.
Abstract: This paper examines a class of continuous-time models that incorporate jumps in returns and volatility, in addition to diffusive stochastic volatility. We develop a likelihood-based estimation strategy and provide estimates of model parameters, spot volatility, jump times and jump sizes using both S&P 500 and Nasdaq 100 index returns. Estimates of jumps times, jump sizes and volatility are particularly useful for disentangling the dynamic effects of these factors during periods of market stress, such as those in 1987, 1997 and 1998. Using both formal and informal diagnostics, we find strong evidence for jumps in volatility, even after accounting for jumps in returns. We use implied volatility curves computed from option prices to judge the economic differences between the models. Finally, we evaluate the impact of estimation risk on option prices and find that the uncertainty in estimating the parameters and the spot volatility has important, though very different, effects on option prices.
1,040 citations
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TL;DR: In this article, a new way to generalize the insights of static asset pricing theory to a multi-period setting is proposed, which uses a loglinear approximation to the budget constraint to substitute out consumption from a standard intertemporal asset pricing model.
Abstract: This paper proposes a new way to generalize the insights of static asset pricing theory to a multi-period setting. The paper uses a loglinear approximation to the budget constraint to substitute out consumption from a standard intertemporal asset pricing model. In a homoskedastic lognormal selling, the consumption-wealth ratio is shown to depend on the elasticity of intertemporal substitution in consumption, while asset risk premia are determined by the coefficient of relative risk aversion. Risk premia are related to the covariances of asset returns with the market return and with news about the discounted value of all future market returns.
805 citations
TL;DR: This article investigated whether market-wide liquidity is a state variable important for asset pricing and found that expected stock returns are related cross-sectionally to the sensitivities of returns to fluctuations in aggregate liquidity.
Abstract: This study investigates whether market-wide liquidity is a state variable important for asset pricing. We find that expected stock returns are related cross-sectionally to the sensitivities of returns to fluctuations in aggregate liquidity. Our monthly liquidity measure, an average of individual-stock measures estimated with daily data, relies on the principle that order flow induces greater return reversals when liquidity is lower. Over a 34-year period, the average return on stocks with high sensitivities to liquidity exceeds that for stocks with low sensitivities by 7.5% annually, adjusted for exposures to the market return as well as size, value, and momentum factors.
789 citations