C h a p t e r 1
TIME-VARYING IMPACT OF **INVESTOR** SENTIMENT
1.1 Introduction
Whether **investor** sentiment influences the market has been a long-standing question in the finance literature. From the Great Crash in 1929 to the Internet bubble, from the Nifty Fifty bubble to the 2008 financial crisis, each of these episodes is asso- ciated with dramatic changes in **asset** prices. Traditional finance theories—models in which investors have fully correct **beliefs** about the **asset** dynamics and therefore always force the **asset** prices to the rational present value of expected future cash flows—leave no room for **investor** sentiment and have considerable difficulty fitting these patterns. However, **investor** sentiment, which reflects excessive optimism and pessimism in **investor** **beliefs**, seems to play a central role in these phenomena. The large gap between the traditional models and the salient market episodes with dra- matic **asset** price movements has made researchers realize that belief-based **investor** sentiment plays an important role in **asset** **pricing** dynamics.

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E info@erim.eur.nl W www.erim.eur.nl
This dissertation consists of three **essays** on empirical **asset** **pricing**. In the first essay, I investigate whether common risk factors are priced across investment horizons. I show that only the market and size factors are priced, but only up to sixteen months. The results highlight the importance of horizon effects in the **pricing** of systematic risk. They also raise concerns about the ability of **asset** **pricing** models to price individual stocks. In the second essay, I estimate costs of equity capital for individual firms and industries using five models. I show that there is considerable disagreement about costs of equity capital across the models and that they are estimated with great errors. The models exhibit some forecasting power for future returns only when the estimation errors are small. My results raise questions about whether popular **asset** **pricing** models can be used for computing costs of equity capital. In the third essay, I show that firms differ greatly in the extent to which their stock prices are driven by cash flow news versus discount rate news. The differences in their relative importance are associated with differences in firm characteristics, risk exposures, and expected returns. I also show that the amount of return co-movement and the success of variables that predict the equity premium depend on the relative importance of the two components.

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c t j o
may be thought as uncorrelated, linear au- toregressive processes with a scale specific autoregressive parameter ρ j and scale specific shocks defined over the dilated time t − s j of each individual scale. Because j is measured in terms of quarters, each detail is associated with periodic fluctuations between 2 j−1 and 2 j quarters. The chosen lowest frequency component J = 5 strikes a compromise between identifiability and richness of the model. Figure 1.2 shows the adjusted R 2 as I increase the scales. After an initial drop at scales J = 2, the adjusted R 2 keeps increasing up to scales J = 5, after which it flat-lines, showing adding scales beyond the fifth brings little improvement to the model, while adding estimation issues. I therefore fix the number of scales to five. Bandi & Tamoni (2017) show that a large percentage of the **pricing** ability is associated with real consumption cycle periodicities of 2 to 8 years. Through business cycle fluctuations in the consumption components, the authors are able to generate directly business cycle fluctuations in the stochastic discount factor, a feature which was previously discussed by Alvarez & Jermann (2005) and Parker & Julliard (2005) as being empirically warranted and theoretically meaningful. For a more detailed discussion of the decomposi- tion, we address the interested reader to the Appendix.

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Using the observed **asset** prices data, we recover physical probabilities and risk adjustments for different preference parameters. Our empirical findings are in line with the evidence from the economic model. We find that the implied probability of a bad state is quite overstated without a sufficient preference for early resolution of uncertainty. Indeed, when the preferences collapse to expected utility, the implied probability of bad states is about 60%, compared to the its fixed value of 25%. This has a direct implication for the estimated risk compensation across states: the magnitude of the stochastic discount factor going to the bad state is more than two times smaller than going to the good state with expected utility, while the opposite is the case under early resolution of uncertainty. The optimal preference structure which minimizes the distance between the recovered and actual probabilities of the states in the data is very close to the one entertained in our calibrated model, and for risk aversion greater than one, suggests that the inter-temporal elasticity of substitution parameter is above one and that the agent has a a strong preference for early resolution of uncertainty. We verify that these key implications remain similar using various robustness checks on the number and location of the economic states and are quantitatively in line with the existing long-run risks literature (see e.g. Bansal and Yaron, 2004).

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relaxation of several of these constraints has the effect that optimal decisions are no longer linear in wealth. Consequently, in order to test the theory, one needs to integrate weighted decision rules over wealth using the distribution of wealth values for all investors.
One of the constraints I relax is an introduction of an option to declare a bankruptcy. When does a declaration of a bankruptcy improve the well-being of an **investor**? Does a possibility of such a declaration affect the investment and consumption decisions? I find that, as with any option, the option to declare the bankruptcy is valuable to the **investor** and may affect his investment behavior. It is reasonable to expect that the value of the option is higher if the wealth of the **investor** is relatively small, and the option’s value decreases with an increase in the investor’s wealth. Because this option is not tradable, the value of the option is different for different investors and depends upon the personal characteristics of the **investor** (such as risk-aversion, discount factor, and wealth). In the present article, I argue that the effect of such an option causes the distribution of wealth to have an effect on the consumption/investment behavior of average **investor**.

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3
and systemic importance. Moreover, in financial crisis periods there is a threat of bank runs, with the potential to increase the probability of bank failures leading to systemic risk. Therefore, understanding the sources of banks’ risk exposures is essential for bank regulators, investors, and bank customers. In this dissertation, we investigate the time-varying systematic risk exposures of banks in order to better understand the sources and the relative **pricing** of risk by taking advantage of this special nature of banks as compared to regular industrial firms. It is important for banks to understand the determinants of equity risk premise, since this premium not only affects their investment decision but also their financing decision. As is well known, the weighted average cost of capital (WACC) is a weighted average of the costs of debt and equity. The higher the equity risk premium, the higher the required rate of return on equity, and thus, the higher the WACC. The variation of risk premium is also of interest to regulators because it contains information about market perception of bank risk. Thus, if banks have increased their exposures to certain risks, regulators should consider actions, such as additional loss provisioning, additional capital infusion, as well as revising the required deposit insurance premium paid. Thus, this paper contributes to the **asset**-**pricing** literature by providing empirical evidence on the systematic risk factors that are relevant in **pricing** bank equities.

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it possible to hedge realised variation measures over arbitrary periods before option maturity while maintaining the benefit of exact hedging. I exploit this feature of the technology in order to investigate the difference in risk **pricing** between daytime and overnight trading. Investors holding positions in realised variation measures overnight are exposed to variance and higher order risk differently. While in day- time trading they can dynamically hedge or close the position altogether, overnight they face far more important constraints to trading, and much less efficient price dis- covery, if the market is open at all. The patterns that I find are striking. Long vari- ance positions 4 are profitable, on average, during daytime trading, but in night-time trades they entail losses. Evidence on aggregate variance risk premia for maturi- ties longer than two weeks showed that the premia were uniformly negative, which gave the variance swap the interpretation of an insurance contract. Not only is the insurance feature present exclusively in night-time trading, but also the daytime profits from long positions are greater than potential overnight losses: the aggregate variance risk premium over weekly horizons is positive. Where premia for jumps – big risk – are considered, similar patterns arise. Excess payoffs from long position in jump skewness and short in jump quarticity are significantly higher in overnight trades than in daytime trades. Additionally, the excess payoffs from such trades greatly increase after large stock price movements, even if subsequent big risks do not materialise. The effect of large innovations to the price of the index is thus clearly seen in a persistently elevated level of premia for big risk hedges.

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This paper adds to the literature by investigating the ability of all CPT components to explain option **pricing** anomalies and potentially characterize the observed negative volatil- ity premium in a general equilibrium setting. First, we propose an appropriate CPT setting and …nd equilibrium equity and option prices. Within this setting, we endow the representa- tive agent with a utility function that combines a traditional constant-relative-risk-aversion utility function with a PT-type value function. Moreover, the representative agents’ ex- pectations might be distorted according to the probability weighting scheme embedded in CPT. Then, we simulate the equilibrium conditions for two parameter sets. The …rst one or benchmark parametrization includes several parameters previously used in the literature while the second one isolates the speci…c impact of each component by switching o¤ the e¤ect of all others. Using the results from our simulations, we disentangle the speci…c role of all CPT parameters on the equilibrium price of zero-beta straddles. This methodology allows us to gather information about the equilibrium-implied price agents are willing to pay to hedge the risk of extreme events depending on the characteristics of their preference function. Using the same methodology, we also investigate the impact of all CPT compo- nents over the price of at-the-market (ATM hereafter) straddles. Finally, we explore the impact of CPT over the price of straddles in a time-varying framework. In order to do so, and following Barberis and Huang (2001), we extend our one-period setting to allow for the degree of loss aversion as well as the reference level for gains and losses to vary as a function of the recent performance of the representative agent’s portfolio.

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after entering the contract: changes in implied volatility a↵ect the daily mark-to-market, however at expiration realized volatility is the sole variable determining the return. Hence, volatility swaps make it possible to engage in volatility speculation while eliminating exposure to other factors.
The results provide strong evidence that HMI predicts the cross-section of FX volatility swap payo↵s. Returns cannot be explained by standard risk models like the Fama and French (1992) three factor model, the international capital **asset** **pricing** model (CAPM), a momentum factor, or a short-term mean reversion factor. Since volatility and option returns are highly non-linear, the common approach to adjust returns with a linear factor model might be inappropriate. Therefore, I examine returns to the strategy conditional on di↵erent market states by sorting equity market returns and carry trade returns into quartiles and analyze how returns to the strategy vary across these di↵erent environments. While it is beyond the scope of this study to determine whether returns to the strategy are compatible with the efficient market hypothesis, evidence suggests that it cannot be fully explained by standard risk factors.

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The estimates of expected returns from June 2004 to June 2006 are of particular interest.
During this period, the Federal Open Market Committee raised the policy rates 25 basis points for 17 consecutive meetings while the long-end of the yield curve remained relatively constant. The puzzling behaviour of long-rates has been labeled as a “conundrum” by the former Chairman Greenspan, and subsequent studies have attributed the phenomenon to declining risk premia. A comparison of the top and bottom panels in Figure 1.7 indicates that incorporating time-varying variance induces more a prominent reduction in risk premia during the conundrum period. Moreover, Figure 1.6 and Figure 1.7 show that negative one- year expected returns are associated with the conundrum period. The negative expected bond return, especially implied by M C , has an interesting implication for the design of structural **asset** **pricing** models. As shown in Martin (2015), any expected gross return R T

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Now we turn to examine the option prices across moneyness. As illustrated in Figure 2.7, while in the benchmark economy the implied volatility curve is rather flat, a sharp downward trend is exhibited in the VaR economy as the option type goes from the OTM puts to the OT- M calls. More importantly, the downward implied volatility curve steepens as the VaR agent dominates. This is consistent with the excess volatility that is observed in Figure 2.5; the intro- duction of the VaR constraint amplifies the volatility of the underlying **asset**, especially in the bad state, and therefore drives up the price of the OTM put. Another crucial ingredient that explains the smirk pattern is the jump component in the equilibrium **pricing** kernel as illustrat- ed in equation (2.5.2). When the economy becomes more restricted by the VaR constraint, the jump risk premium is pushed up. As mentioned previously, the price of OTM put options can effectively reflect the jump risk premium. In this sense, the BS implied volatility backed out from the deep OTM put increases relative to the ATM option. Consequently, we end up with a steep volatility curve, which is in line with the volatility smirk documented in the literature.

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not converge asymptotically to zero because the drift of the underlying fundamentals is allowed to switch according to a two-state Markov process.
The distinction between an incomplete information rational expectations model and a model incorporating behavioral biases might not always be so trivial. For instance, Anderson, Ghysels, and Juergens (2005) simply sidestep the potential behavioral as- pects of their framework, meaning whether the contribution of disagreement on as- set prices could also be interpreted as an overreaction of irrational agents. Brav and Heaton (2002) demonstrate that from a mathematical point the rational expectations incomplete information economy and an economy with irrational agents are hard to distinguish. Irrationality-induced anomalies cannot survive the presence of rational ar- bitrageurs unless there are limits to arbitrage that prevent the effectiveness of rational bets against mispricing. 12 Unquestionably, behavioral biases are appealing, 13 however, my motivation to remain in the class of rational **beliefs** is a practical one: The empirical quantification of these biases in **beliefs** or probability such as overconfidence or anchor- ing on a firm-specific level is difficult if not impossible. 14 I choose to remain in the class of rational **beliefs** and economic agents update their **beliefs** based on the available information using Bayes’ rule. The difference in their posteriors can arise either from a difference in agents’ priors or a difference in subjective parameters of the dynamics of cash flows or signals. In particular, I assume that the volatility of the signal growth rate is perceived differently by the two agents in my economy. In this way, belief dispersion does not converge to zero even asymptotically. I aim at investigating these properties both theoretically and empirically in two different projects: First, in the context of an equilibrium structural model of credit risk and second, in option markets for individual and index options.

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inal bonds and stocks, while 10-year nominal bonds and cash are shorted. The allocation to inflation-linked bonds is hardly affected. The long-short position in nominal bonds pays off in states of the economy where either expected inflation is high or real interest rates are low. In addition, when the **investor** anticipates the preference to annuitize wealth at retirement, the allocation to equities increases. An important determinant of the investment opportu- nity set at retirement is the level of the dividend yield. Low levels of the dividend yield correspond to low expected returns on variable annuities. Given the negative correlation be- tween innovations in equity returns and dividend yields, a long equity position in the period before retirement can hedge adverse changes of the dividend yield. Interestingly, the addi- tional hedging demands are already substantial during early stages of the investor’s life-cycle. Panel B of Figure 2.4 portrays the optimal hedging strategy for an individual implementing the optimal unconditional hedging strategy at retirement. The optimal hedging strategy of the optimal conditional and unconditional annuitization strategy are close. Next, Panel C displays the optimal hedging strategy when the **investor** allocates all wealth at retirement to inflation-linked annuities. The hedging portfolio is strikingly different from the one where the full annuity menu is at the individual’s disposal. First, neither inflation-linked nor stocks are present in the hedging strategy. When the **investor** allocates all capital at retirement to inflation-linked annuities, all that matters is the exposure to the real interest rate, which is managed by positions in the 3-year and 10-year nominal bond. Second, the allocation to both nominal bonds changes. Note that the hedging strategy has only significant weights as of, say, age 60. This is a consequence of the relatively low persistence of real interest rates in comparison with expected inflation and the dividend yield implied by our estimates. This suggests that hedging inflation-linked annuities, i.e., hedging real interest rate risk, is far less important than hedging the optimal (un)conditional annuitization strategy which (possibly) allocates wealth to all three annuity products. Finally, Panel D portrays the opti- mal hedging strategy if the **investor** allocates all wealth at retirement to nominal annuities. At early stages of the investor’s life-cycle, it turns out to be optimal to hold long 10-year nominal bonds, and short 3-year nominal bonds to hedge time-varying bond risk premia. Close to retirement, hedging real rate risk is more important and the hedging strategy is long in 3-year nominal bonds and shorts 10-year nominal bonds, as is the case for all other annuitization strategies.

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We illustrate how our method works in the context of three specific models, namely Mehra and Prescott (1985a), Cox, Ross, and Rubinstein (1979), and a simple non- Markovian economy. For each economy, we generate model-implied prices and seek to recover natural probabilities and preferences using our method. This provides an illustration of how our method works, its robustness, and its shortcomings. For Mehra and Prescott (1985a), we show that S > T so general recovery is impossible, but, when we restrict the class of utility functions, then we achieve recovery. For the binomial Cox-Ross-Rubinstein model (the discrete-time version of Black and Scholes (1973)), we show that recovery is impossible even under restrictive utility specifications because consumption growth is iid., which leads to a flat term structure, a **pricing** matrix of a lower rank, and a continuum of solutions for probabilities and preferences. While the former two models fall in the setting of Borovicka, Hansen, and Scheinkman (2016) (with a non-zero martingale component), we also show how recovery is possible in the non-Markovian setting, which falls outside the framework of Borovicka, Hansen, and Scheinkman (2016) and Ross (2015), illustrating the generality of our framework in terms of the allowed probabilities.

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In summary, we find that BAB and BAC are robust to controlling for a host of other fac- tors, have survived significant out-of-sample evidence – both through time and across **asset** classes and geographies – have lower turnover than many of the well-known idiosyncratic-risk measures, making them more implementable and realistic, and are supported by rigorous theory of leverage constraints with consistent evidence based on margin debt. Turning to the factors based on idiosyncratic risk, we note that these are more often defined based on a relatively short time period (high turnover) making them susceptible to microstructure noise and making it harder to believe that they capture the idea underlying the behavioral theory, 8 they are less robust to controlling for other factors and to using a lower turnover, and they are weaker globally. The strongest version appears to be our new SMAX factor, which is related to measures of sentiment. The low-risk e↵ect can be driven by more than

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fully understood. Therefore, Asparouhova et al. (2010) focus on the potential biases in the tests which examine whether liquidity is a priced risk factor. They suggest several methodological corrections for those biases which arise as a result of micro-structural noise, and show that the biases can be eliminated by a procedure where each return is weighted by the observed gross return on the same security in the prior period. Asparouhova et al. (2010) claim that sensitivity of expected stock returns to different measures of liquidity and the liquidity premium is biased towards finding a premium. They investigate this issue by using an array of illiquidity measures that are prevalent in the literature. Implementing the correction methods, the authors show that estimated premiums for illiquidity are significantly upward biased. They point out that those microstructure noises in security prices bias the results of empirical **asset** **pricing** specifications, and the microstructure noise attributable biases can be eliminated by running WLS regressions to estimate the return premiums that rely on stock returns as the dependent variable, and the prior-period gross return as the weighting variable. However, after correcting for the upward bias, they show that there still exists a strong evidence of a positive return premium for all of the measures used. Moreover, as a result of the simulation analysis, they document that upward biases in the estimated spread premiums can be reduced by excluding outlier securities. However, doing this has a negative effect in terms of statistical power such that the researcher may not be able to find the correct illiquidity premium.

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This chapter is novel in that it uses the state-**pricing** methodology to derive a volatility-index for the U.S. government bond market. Results presented here support the empirical application of state-**pricing** methodology in the construction of volatility indices. This is evidenced by the strong performance of GBVX in forecasting realized volatilities across the fixed income **asset** classes: the government bond, corporate bond portfolios and CMBS portfolios, and the fact that GBVX is an unbiased predictor for future realized volatility of its underlying **asset** while the recently available TYVIX index is a biased one. By comparing the forecasting abilities of GBVX and VIX in the fixed income markets, the current study shows that their information is non-overlapping and one is hardly a proxy for the other. Finally, this paper also demonstrates how the index can be effectively replicated by market makers, using a hedge portfolio comprising options on the 10-year Treasury note futures.

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I use a portfolio approach to analyze impacts of liquidity risk and liquidity level on stock returns, both separately and jointly. This is widely used in **asset** pric- ing literature; papers on liquidity and liquidity risk include Pástor/Stambaugh (2003) and Lou/Sadka (2011). I create liquidity variable as in Amihud (2002) and liquidity risk variable as liquidity betas in Acharya/Pedersen (2005); Pástor/Stam- baugh (2003); Watanabe/Watanabe (2008) and Sadka (2006). Then, by creating portfolios sorted on these variables, I investigate joint effects of liquidity level and liquidity risk. Portfolios based on Amihud’s liquidity measure and different types of liquidity risk are formed, when alphas of these portfolios are estimated for three **pricing** models and significance of alphas are used for making judgments about explanatory power of each indicator. I find that liquidity level has greater impact on common stock returns than liquidity risk does. Results are somewhat stronger for the early subsample, though they are also valid for more recent data. This finding is of particular importance for investors who might consider taking into account the liquidity level variables for portfolio allocation, **asset** **pricing** and risk management.

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