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We selectively survey, unify and extend the literature on realized volatility of financial asset returns. Rather than focusing exclusively on characterizing the properties of realized volatility, we progress by examining economically interesting functions of realized volatility, namely realized betas for equity portfolios, relating them both to their underlying realized variance and covariance parts and to underlying macroeconomic fundamentals.
This paper proposes a new approach for modeling investor fear after rare disasters. The key element is to take into account that investors’ information about fundamentals driving rare downward jumps in the dividend process is not perfect. Bayesian learning implies that beliefs about the likelihood of rare disasters drop to a much more pessimistic level once a disaster has occurred. Such a shift in beliefs can trigger massive declines in price-dividend ratios. Pessimistic beliefs persist for some time. Thus, belief dynamics are a source of apparent excess volatility relative to a rational expectations benchmark. Due to the low frequency of disasters, even an infinitely-lived investor will remain uncertain about the exact probability. Our analysis is conducted in continuous time and offers closed-form solutions for asset prices. We distinguish between rational and adaptive Bayesian learning. Rational learners account for the possibility of future changes in beliefs in determining their demand for risky assets, while adaptive learners take beliefs as given. Thus, risky assets tend to be lower-valued and price-dividend ratios vary less under adaptive versus rational learning for identical priors. Keywords: beliefs, Bayesian learning, controlled diffusions and jump processes, learning about jumps, adaptive learning, rational learning. JEL classification: D83, G11, C11, D91, E21, D81, C61
Traditional tests of the CAPM following the Fama / MacBeth (1973) procedure are tests of the joint hypotheses that there is a relationship between beta and realized return and that the market risk premium is positive. The conditional test procedure developed by Pettengill / Sundaram / Mathur (1995) allows to independently test the hypothesis of a relation between beta and realized returns. Monte Carlo simulations show that the conditional test reliably identifies this relation. In an empirical examination for the German stock market we find a significant relation between beta and return. Previous studies failed to identify this relationship probably because the average market risk premium in the sample period was close to zero. Our results provide a justification for the use of betas estimated from historical return data by portfolio managers.
The classical approaches to asset allocation give very different conclusions about how much foreign stocks a US investor should hold. US investors should either allocate a large portion of about 40% to foreign stocks (which is the result of mean/variance optimization and the international CAPM) or they should hold no foreign stocks at all (which is the conclusion of the domestic CAPM and mean/variance spanning tests). There is no way in between.
The idea of the Bayesian approach discussed in this article is to shrink the mean/variance efficient portfolio towards the market portfolio. The shrinkage effect is determined by the investor's prior belief in the efficiency of the market portfolio and by the degree of violation of the CAPM in the sample. Interestingly, this Bayesian approach leads to the same implications for asset allocation as the mean-variance/tracking error criterion. In both cases, the optimal portfolio is a combination of the market portfolio and the mean/variance efficient portfolio with the highest Sharpe ratio.
Applying both approaches to the subject of international diversification, we find that a substantial home bias is only justified when a US investor has a strong belief in the global mean/variance efficiency of the US market portfolio and when he has a high regret aversion of falling behind the US market portfolio. We also find that the current level of home bias can be justified whenever-regret aversion is significantly higher than risk aversion.
Finally, we compare the Bayesian approach of shrinking the mean/variance efficient portfolio towards the market portfolio to another Bayesian approach which shrinks the mean/variance efficient portfolio towards the minimum-variance portfolio. An empirical out-of-sample study shows that both Bayesian approaches lead to a clearly superior performance compared to the classical mean/variance efficient portfolio.
A large literature over several decades reveals both extensive concern with the question of time-varying betas and an emerging consensus that betas are in fact time-varying, leading to the prominence of the conditional CAPM. Set against that background, we assess the dynamics in realized betas, vis-à-vis the dynamics in the underlying realized market variance and individual equity covariances with the market. Working in the recently-popularized framework of realized volatility, we are led to a framework of nonlinear fractional cointegration: although realized variances and covariances are very highly persistent and well approximated as fractionally-integrated, realized betas, which are simple nonlinear functions of those realized variances and covariances, are less persistent and arguably best modeled as stationary I(0) processes. We conclude by drawing implications for asset pricing and portfolio management. JEL Klassifikation: C1, G1
Deviations from normality in financial return series have led to the development of alternative portfolio selection models. One such model is the downside risk model, whereby the investor maximizes his return given a downside risk constraint. In this paper we empirically observe the international equity allocation for the downside risk investor using 9 international markets’ returns over the last 34 years. The results are stable for various robustness checks. Investors may think globally, but instead act locally, due to greater downside risk. The results provide an alternative view of the home bias phenomenon, documented in international financial markets. JEL Classification: G11, G12, G15
Der Bestimmung risikoadäquater Diskontierungssätze kommt bei der Unternehmensbedeutung eine zentrale Bedeutung zu. Wird zu deren Bestimmung in der praktischen Anwendung das CAPM verwendet, gilt es dabei, risikolose Zinssätze und Risikoprämien zu bestimmen, für die erwartete Renditen des Marktportfeuilles und Beta-Faktoren als Maßgrößen für das systematische Risiko benötigt werden. Passend zu den zu bewertenden erwarteten Überschussgrößen sollten auch die zur Diskontierung verwendeten Renditeforderungen die im Bewertungszeitpunkt erwarteten künftigen Renditen vergleichbarer Anlagen widerspiegeln. Die weitaus meisten Beiträge zur Operationalisierung des CAPM leiten die Renditeforderungen jedoch aus historischen Kapitalmarktrenditen ab. Wir zeigen in diesem Beitrag auf, wie erwartete künftige Renditen aus beobachtbaren Größen, vor allen den Zinsstrukturkurven und den beobachtbaren Analystenprognosen, zukunftsorientiert abgeleitet werden können. Damit wird eine konzeptionell schlüssigere Bewertung der im Bewertungszeitpunkt erwarteten künftigen Überschüsse mit den zeitgleich erwarteten künftigen Renditen ermöglicht.