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Concept# Capital asset pricing model

Summary

In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio.
The model takes into account the asset's sensitivity to non-diversifiable risk (also known as systematic risk or market risk), often represented by the quantity beta (β) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset. CAPM assumes a particular form of utility functions (in which only first and second moments matter, that is risk is measured by variance, for example a quadratic utility) or alternatively asset returns whose probability distributions are completely described by the first two moments (for example, the normal distribution) and zero transaction costs (necessary for diversification to get rid of all idiosyncratic risk). Under these conditions, CAPM shows that the cost of equity c

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This thesis uses machine learning techniques and text data to investigate the relationships that arise between the Fed and financial markets, and their consequences for asset prices.The first chapter, entitled Market Expectations and the Impact of Unconventional Monetary Policy: An Application to Twitter Data, is an answer to (Greenlaw et al., 2018), who show, by looking at a large set of monetary policy announcements made between November 2008 and December 2017 - FOMC meetings, release of minutes and speeches of the Fed Chair - that long term yields tended to increase following these events. By doing so, the authors challenge common wisdom according to which the central bank intervention in the aftermath of the financial crisis lowered long term rates (Gagnon, 2016). Using machine learning and twitter data, this chapter develops a novel measure of market expectations of monetary policy, and shows that the increase in yields was simply due to a marginal adjustment of market expectations following announcements being less dovish than expected.The second chapter, entitled Informational Feedback Loop, Monetary Policy Decisions and Asset Prices Dynamics, investigates the consequences of a Fed that uses (1) its own private signal and (2) fed funds futures to take its monetary policy decision. Fed funds futures aggre- gate private information received by financial markets participants - traders - but they also depend on traders' expectations about the Fed's behavior, which makes futures endogenous in the central bank decision. The theoretical model shows that the surprise generated by monetary policy announcements and the subsequent adjustment in short term U.S. treasury yields depend on the precision of the signals received by each agent. When the signal received by traders is more precise than the central bank's, the latter relies more on fed funds futures to take its decision, and the surprise and adjustment of short term yields are smaller. By contrast, long term yields adjust only because the announcement provides traders with new information about the state of the economy, by revealing the central bank's private signal. Finally, when the Fed is averse to financial markets volatility, it tends to put some weight on fed funds futures even if they are not informative about the state of the economy. The empirical part of the paper provides some evidence supporting these channels, by using a topic and tone approach (Hansen and McMahon, 2016) to extract the precision of the signals received by the central bank and traders from FOMC minutes and tweets respectively.

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When investors have incomplete information, expected returns, as measured by an econometrician, deviate from those predicted by standard asset pricing models by including a term that is the product of the stock's idiosyncratic volatility and the investors' aggregated forecast errors. If investors are biased this term generates a relation between idiosyncratic volatility and expected stocks returns. Relying on forecast revisions from IBES, we construct a new variable that proxies for this term and show that it explains a significant part of the empirical relation between idiosyncratic volatility and stock returns. (C) 2012 Elsevier B.V. All rights reserved.

2012This thesis consists of three applications of machine learning techniques to empirical asset pricing.In the first part, which is co-authored work with Oksana Bashchenko, we develop a new method that detects jumps nonparametrically in financial time series and significantly outperforms the current benchmark on simulated data. We use a long short-term memory (LSTM) neural network that is trained on labelled data generated by a process that experiences both jumps and volatility bursts. As a result, the network learns how to disentangle the two. Then it is applied to out-of-sample simulated data and delivers results that considerably differ from the benchmark: we obtain fewer spurious detection and identify a larger number of true jumps. When applied to real data, our approach for jump screening allows to extract a more precise signal about future volatility.In the second part, which is co-authored work with Oksana Bashchenko, we develop a methodology for detecting asset bubbles using a neural network. We rely on the theory of local martingales in continuous-time and use a deep network to estimate the diffusion coefficient of the price process more accurately than the current estimator, obtaining an improved detection of bubbles. We show the outperformance of our algorithm over the existing statistical method in a laboratory created with simulated data. We then apply the network classification to real data and build a zero net exposure trading strategy that exploits the risky arbitrage emanating from the presence of bubbles in the US equity market from 2006 to 2008. The profitability of the strategy provides an estimation of the economical magnitude of bubbles as well as support for the theoretical assumptions relied on.In the third part, I propose a new tool to characterize the resolution of uncertainty around FOMC press conferences. It relies on the construction of a measure capturing the level of discussion complexity between the Fed Chair and reporters during the Q&A sessions. I show that complex discussions are associated with higher equity returns and a drop in realized volatility. The method creates an attention score by quantifying how much the Chair needs to rely on reading internal documents to be able to answer a question. This is accomplished by building a novel dataset of video images of the press conferences and leveraging recent deep learning algorithms from computer vision. This alternative data provides new information on nonverbal communication that cannot be extracted from the widely analyzed FOMC transcripts. This chapter can be seen as a proof of concept that certain videos contain valuable information for the study of financial markets.