Essays On Volatility Risk Premia In Asset Pricing
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| Author | : Aoxiang Yang (Ph.D.) |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2022 |
| Genre | : |
| ISBN | : |
My dissertation is developed to address unresolved issues in the asset pricing literature, focusing on both risk premium levels and dynamics. Chapter 1 addresses short-horizon risk premium dynamics. In the data, stock market volatility weakly or even negatively predicts short-run equity and variance risk premia, challenging positive risk-return trade-offs at the heart of leading asset pricing models. I show that a puzzling negative volatility-risk premia relationship concentrates in scattered high-uncertainty states, which occur about 20\% of the time. While at other times, the relationship is strongly positive. I develop a micro-founded learning model in which due to learning frictions investors underreact to structural breaks in high-volatility periods and overreact to transitory variance shocks in normal times. The model can successfully explain the novel time-varying volatility-risk premia relationship at short and long horizons. The model can further account for many other data features, such as a robust positive correlation between equity and variance risk premium, the leverage effect, and negative observations of equity and variance risk premia at the onsets of recessions. Chapter 2, coauthored with Professor Bjorn Eraker, focuse on equilibrium derivatives pricing. It is motivated by the observation that leading asset pricing models typically can not explain the levels or dynamics of VIX options prices. We develop a tractable equilibrium pricing model to explain observed characteristics in equity returns, VIX futures, S\&P 500 options, and VIX options data based on affine jump-diffusive state dynamics and representative agents endowed with Duffie-Epstein recursive preferences. A specific model aimed at capturing VIX options prices and other asset market data is shown to successfully replicate the salient features of consumption, dividends, and asset market data, including the first two moments of VIX futures returns, the average implied volatilities in SPX and VIX options, and first and higher-order moments of VIX options returns. In the data, we document a time variation in the shape of VIX option implied volatility and a time-varying hedging relationship between VIX and SPX options which our model both captures. Our model also matches many other asset pricing moments such as equity premia, variance risk premia, risk-free interest rates, and short-horizon return predictability. To derive our specific model, we first develop a general framework for pricing assets under recursive Duffie-Epstein preferences with IES set to one under the assumption that state variables follow affine jump diffusions, as in \citet{DPS00}. Relative to the literature, our framework has a clear marginal contribution that it is an endowment-based equilibrium model with (i) clearly stated affine state variable dynamics and (ii) precisely characterized equilibrium value function, risk-free rate, prices of risks, and risk-neutral state dynamics. We prove our state-price density is a precise $IES\to1$ limit of that approximately solved in \citet{ErakShal08}. The recursive preference assumption implies that higher-order conditional moments of the economic fundamental, such as its growth volatility and volatility-of-volatility, are explicitly priced in equilibrium. Since VIX derivatives depend on these factors, this in turn implies that the former carry non-zero risk premia.
| Author | : Young Il Kim |
| Publisher | : |
| Total Pages | : 176 |
| Release | : 2008 |
| Genre | : Assets (Accounting) |
| ISBN | : |
Abstract: My dissertation addresses two main issues regarding asset returns: econometric modeling of asset returns in chapters 2 and 3 and puzzling features of the standard consumption-based asset pricing model (C-CAPM) in chapters 4 and 5. Chapter 2 develops a new theoretical derivation for the GARCH-skew-t model as a mixture distribution of normal and inverted-chi-square in order to represent the three important stylized facts of financial data: volatility clustering, skewness and thick-tails. The GARCH-skew-t is same as the GARCH-t model if the skewness parameter is shut-off. The GARCH-skew-t is applied to U.S. excess stock market returns, and the equity premium is computed based on the estimated model. It is shown that skewness and kurtosis can have significant effect on the equity premium and that with sufficiently negatively skewed distribution of the excess returns, a finite equity premium can be assured, contrary to the case of the Student t in which an infinite equity premium arises. Chapter 3 provides a new empirical guidance for modeling a skewed and thick-tailed error distribution along with GARCH effects based on the theoretical derivation for the GARCH-skew-t model and empirical findings on the Realized Volatility (RV) measure, constructed from the summation of higher frequency squared (demeaned) returns. Based on an 80-year sample of U.S. daily stock market returns, it is found that the distribution of monthly RV conditional on past returns is approximately the inverted-chi-square while monthly market returns, conditional on RV and past returns are normally distributed with RV in both mean and variance. These empirical findings serve as the building blocks underlying the GARCH-skew-t model. Thus, the findings provide a new empirical justification for the GARCH-skew-t modeling of equity returns. Moreover, the implied GARCH-skew-t model accurately represents the three important stylized facts for equity returns. Chapter 4 provides a possible solution to asset return puzzles such as high equity premium and low riskfree rate based on parameter uncertainty. It is shown that parameter uncertainty underlying the data generating process can lead to a negatively skewed and thick-tailed distribution that can explain most of the high equity premium and low riskfree rate even with the degree of risk aversion below 10 in the CRRA utility function. Chapter 5 investigates a possible link between stock market volatility and macroeconomic risk. This chapter studies why U.S. stock market volatility has not changed much during the "great moderation" era of the 1980s in contrast to the prediction made by the standard C-CAPM. A new model is developed such that aggregate consumption is decomposed into stock and non-stock source of income so that stock dividends are a small part of consumption. This new model predicts that the great moderation of macroeconomic risk must have originated from declining volatility of shocks to the relatively large non-stock factor of production while shocks to the relatively small stock assets have been persistently volatile during the moderation era. Furthermore, the model shows that the systematic risk of holding equity is positively associated with the stock share of total wealth.
| Author | : William N. Goetzmann |
| Publisher | : Oxford University Press |
| Total Pages | : 568 |
| Release | : 2006-11-16 |
| Genre | : Business & Economics |
| ISBN | : 0195148142 |
This book aims to create a strong understanding of the empirical basis for the equity risk premium. Through the research and anaylsis of two scholars who are experts in this field, this volume presents the key issues that are paramount to investors, including whether or not to use historical data as a method of equity investing, and can the equity premium reflect changes in fundamental values and cash flows of the market.
| Author | : Vincent Campasano |
| Publisher | : |
| Total Pages | : |
| Release | : 2018 |
| Genre | : |
| ISBN | : |
The first essay studies the dynamics of equity option implied volatility and shows that they depend both upon the option's time to maturity (horizon) and slope of the implied volatility term structure for the underlying asset (term struc ture). We propose a simple, illustrative framework which intuitively captures these dynamics. Guided by our framework, we examine a number of volatility trading strategies across horizon, and the extent to which profitability of trading strategies is due to an interaction between term structure and realized volatility. While profitable trading strategies based upon term structure exist for both long and short horizon options, this interaction requires that positions in long horizon options be very different than those required for short horizon options. Equity option returns depend upon both term structure and horizon, but for index options, implied volatility term structure slope negatively predicts returns. While the carry trade has been applied profitably across asset classes and to index v volatility, given this difference in index and equity implied volatility dynamics, I examine the carry trade in the equity volatility market in the second essay. I show that the carry trade in equity volatility produces significant returns, and unlike the returns to carry in other asset classes, is not exposed to liquidity or volatility risks and negatively loads on market risk. A long volatility carry portfolio, after transactions costs, remains significantly profitable and negatively loads on market risks, challenging traditional asset pricing theories. Overwriting an index position with call options creates a portfolio with fixed exposures to market and volatility risk premia. I allow for time-varying allocations to volatility and the market by conditioning on the slope of the implied volatility term structure. I show that a three asset portfolio holding a VIX futures position, the SandP 500 Index and cash triples the returns of the index and more than doubles the risk-adjusted returns of the covered call while maintaining a return volatility roughly equal to that of the SandP 500 Index.
| Author | : Christian Koeppel |
| Publisher | : |
| Total Pages | : |
| Release | : 2021 |
| Genre | : |
| ISBN | : |
WThis doctoral thesis focuses on the effects of investor sentiment on asset pricing and the challenges of portfolio optimization under parameter uncertainty. The first essay "Sentiment risk premia in the cross-section of global equity" applies a recently developed sentiment proxy to the construction of a new risk factor and provides a comprehensive understanding of its role in sentiment-augmented asset pricing models for international equity indices. We empirically demonstrate the existence of a statistically significant and economically relevant sentiment premium. Differentiating between developed and emerging markets we reveal different patterns of return reversals / persistence. Our results contribute to the explanation of global cross-sectional average excess returns, demonstrating superiority in terms of predictive power when compared to competing definitions of sentiment. The second essay "Does social media sentiment matter in the pricing of U.S. stocks?" finds that the inclusion of micro-grounded, social media-based sentiment significantly improves the performance of the five-factor model from Fama and French (2015, 2017). This holds for different industry and style portfolios such as size, value, profitability, and investment. Applying a robust GMM estimator, the sentiment risk premium provides the missing component in the behavioral asset pricing theory of Shefrin and Belotti (2008) and (partially) resolves the pricing puzzles of small extreme growth, small extreme investment stocks and small stocks that invest heavily despite low profitability. The third essay "Diversifying estimation errors: An efficient averaging rule for portfolio optimization" proposes a combination of established minimum-variance strategies to minimize the expected out-of-sample variance. The proposed averaging rule overcomes the strategy selection problem and diversifies estimation errors of the strategies included in our rule. Extensive simulations show that the contributions of estimation errors to the out-of-sample variances are uncorrelated between the considered strategies. We therefore conclude that averaging over multiple strategies offers sizable diversification benefits.
| Author | : Qi Shang |
| Publisher | : |
| Total Pages | : |
| Release | : 2012 |
| Genre | : |
| ISBN | : |
The thesis includes three papers: 1. Limited Arbitrage Analysis of CDS Basis Trading By modeling time-varying funding costs and demand pressure as the limits to arbitrage, the paper shows that assets with identical cash-flows have not only different expected returns, but also different expected returns in excess of funding costs. I solve the model in closed-form to show that the arbitrage on the CDS and corporate bond market is a risky arbitrage. The sign of the expected excess return of the arbitrage is decided by the sign and size of market frictions rather than the observed price discrepancy. The size and risk of the arbitrage excess return are increasing in market friction levels and assets' maturities. High levels of market frictions also destruct the positive predictability of credit spread term structure on credit spread changes. Results from the empirical section support the above-mentioned model predictions. 2. General Equilibrium Analysis of Stochastic Benchmarking This paper applies a closed-form continuous-time consumption-based general equilibrium model to analyze the equilibrium implications when some agents in the economy promise to beat a stochastic benchmark at an intermediate date. For very risky benchmark, these agents increase volatility and risk premium in the equilibrium. On the other hand, when they promise to beat less risky benchmark, they decrease volatility and risk premium in the equilibrium. In both cases, the degree of effect is state-dependent and stock price rises. 3. Institutional Asset Pricing with Heterogenous Belief (Co-authored) We propose an equilibrium asset pricing model in which investors with heterogeneous beliefs care about relative performance. We find that the relative performance concern leads agents to trade more similarly, which has two effects. First, similar trading directly decreases volatility. Second, similar trading decreases the impact of the dominant agents. When the economy is extremely good or bad, the second effect is dominant so that the relative performance concern enlarges the excess volatility caused by heterogeneous beliefs. When the first effect is dominant, which corresponds to a normal economy, the volatility is lower than without the relative performance concern. Moreover, this paper shows that the relative performance concern also influences investors' holdings, stock prices and risk premia.
| Author | : Philipp Karl Illeditsch |
| Publisher | : |
| Total Pages | : |
| Release | : 2010 |
| Genre | : |
| ISBN | : |
In the Ơ̐1rst essay, I decompose inƠ̐2ation risk into (i) a part that is correlated with real returns on the market portfolio and factors that determine investor0́9s preferences and investment opportunities and (ii) a residual part. I show that only the Ơ̐1rst part earns a risk premium. All nominal Treasury bonds, including the nominal money-market account, are equally exposed to the residual part except inƠ̐2ation-protected Treasury bonds, which provide a means to hedge it. Every investor should put 100% of his wealth in the market portfolio and inƠ̐2ation-protected Treasury bonds and hold a zero-investment portfolio of nominal Treasury bonds and the nominal money market account. In the second essay, I solve the dynamic asset allocation problem of Ơ̐1nite lived, constant relative risk averse investors who face inƠ̐2ation risk and can invest in cash, nominal bonds, equity, and inƠ̐2ation-protected bonds when the investment opportunityset is determined by the expected inƠ̐2ation rate. I estimate the model with nominal bond, inƠ̐2ation, and stock market data and show that if expected inƠ̐2ation increases, then investors should substitute inƠ̐2ation-protected bonds for stocks and they should borrow cash to buy long-term nominal bonds. In the lastessay, I discuss how heterogeneity in preferences among investors withexternal non-addictive habit forming preferences aƠ̐0ects the equilibrium nominal term structure of interest rates in a pure continuous time exchange economy and complete securities markets. Aggregate real consumption growth and inƠ̐2ation are exogenously speciƠ̐1ed and contain stochastic components thataƠ̐0ect their means andvolatilities. There are two classes of investors who have external habit forming preferences and diƠ̐0erent localcurvatures oftheir utility functions. The eƠ̐0ects of time varying risk aversion and diƠ̐0erent inƠ̐2ation regimes on the nominal short rate and the nominal market price of risk are explored, and simple formulas for nominal bonds, real bonds, and inƠ̐2ation risk premia that can be numerically evaluated using Monte Carlo simulation techniques are provided.
| Author | : Seunghan Lee |
| Publisher | : |
| Total Pages | : 99 |
| Release | : 2017 |
| Genre | : Cash flow |
| ISBN | : |
This dissertation studies the role of cash flow in explaining stock price variations and the determination of equity premium after correcting for the measurement error of cash flow growth. In Chapter 1, we incorporate price-total payout (dividends plus repurchases) ratio into the models of Binsbergen and Koijen (2010) and Campbell and Ammer (1993) to reassess the role of cash flow in stock price movement. We find that the existing results of a high persistence in expected returns and a strong dependence of stock price variation on discount rates are partly attributable to the use of price-dividend ratio with measurement error as a predictor of stock returns. The incorporation of price-total payout ratio enables the models i) to improve an in-sample goodness of fit for return and cash flow growth, ii) to produce a lower persistence of expected returns, which leads to a smaller shock to stock prices from the discount rate channel, iii) to show a higher contribution of cash flow channel to stock price movement in terms of variations in price-cash flow ratio and unexpected return. These results apply to medium and large cap portfolios as well as to aggregate market index. In Chapter 2, we explore the effects on stock market variation of other factors than stock repurchases that could account for the non-stationarity of price-dividend ratio by incorporating regime shifts in the mean of price-total payout ratio into the models of Binsbergen and Koijen (2010) and Campbell and Ammer (1993). Compared to the results of Chapter 1, we achieve i) an improvement in in-sample goodness of fit for return and cash flow growth, ii) a lower persistence and higher volatility of expected returns, iii) stronger role of cash flow channel in stock market variation, all of which show that not only stock repurchases but also other structural factors such as persistent decline in consumption volatility affecting the relationship between stock prices and cash flows should be taken into account when we attempt to investigate the sources of stock price variations. In Chapter 3, we incorporate price-total payout ratio and endogenously generated consumption volatility with regime shifts into the dynamic asset pricing model of Bansal, Kiku, Shaliastovich, and Yaron (2014) (hereafter, "BKSY model"), which stresses the role of a sizable positive risk premium from the macroeconomic volatility channel in explaining the equity premium by introducing the volatility risk into traditional consumption-based asset pricing model. Our extension of the BKSY model provides a different identification of the consumption volatility risk by including the effects of the economic agent's revision of expectation on the volatility states on each of three channels to determine the equity premium. From annual samples of 1930 to 2015, we find that our model shows a much smaller contribution of the consumption volatility risk to the total equity premium, most of which is now explained by the cash flow risk. This finding applies to cross-sectional portfolio returns as well as to aggregate market index return. Our model also indicates that the consumption volatility risk is not large enough to reverse a negative correlation between equity return and human capital return.
| Author | : Xiaofei Zhao |
| Publisher | : |
| Total Pages | : |
| Release | : 2013 |
| Genre | : |
| ISBN | : |
| Author | : Jie Cao |
| Publisher | : |
| Total Pages | : 232 |
| Release | : 2009 |
| Genre | : |
| ISBN | : |
In this dissertation, I explore the impact of idiosyncratic risk on asset returns. The first essay examines how idiosyncratic risk affects the cross-section of stock returns. I use an exponential GARCH model to forecast expected idiosyncratic volatility and employ a combination of the size effect, value premium, return momentum and short-term reversal to measure relative mispricing. I find that stock returns monotonically increase in idiosyncratic risk for relatively undervalued stocks and monotonically decrease in idiosyncratic risk for relatively overvalued stocks. This phenomenon is robust to various subsamples and industries, and cannot be explained by risk factors or firm characteristics. Further, transaction costs, short-sale constraints and information uncertainty cannot account for the role of idiosyncratic risk. Overall, these findings are consistent with the limits of arbitrage arguments and demonstrate the importance of idiosyncratic risk as an arbitrage cost. The second essay studies the cross-sectional determinants of delta-hedged stock option returns with an emphasis on the pricing of volatility risk. We find that the average delta-hedged option returns are significantly negative for most stocks, and they decrease monotonically with both total and idiosyncratic volatility of the underlying stock. Our results are robust and cannot be explained by the Fama-French factors, market volatility risk, jump risk, or the effect of past stock return and volatility-related option mispricing. Our results strongly support a negative market price of volatility risk specification that is proportional to the volatility level. Reflecting this volatility risk premium, writing covered calls on high volatility stocks on average earns about 2% more per month than selling covered calls on low volatility stocks. This spread is higher when it is more difficult to arbitrage between stock and option.
