Time, frequency, and common stock systematic risks.

摘要

This dissertation is comprised of three essays on systematic risk in financial markets. In particular, we focus on how the exposure and compensation for bearing such risk varies both with time and with frequency.;In the first essay, we develop a simple time-dependent factor pricing model. The time-dependent model has a number of implications, which we test empirically. Our contribution is an augmented Fama-MacBeth two-pass procedure which permits time-variation in both the estimated factor loadings in the first pass and in the estimated factor premia in the second pass by utilizing local linear regression. Local linearity induces time-dependence in the model parameters without imposing strong structural assumptions on the model itself. Our model permits a test of the factor pricing model at each point along the sample and further enables us to test at a given point in time whether an investor receives a premium for bearing the risk associated with a factor; by contrast, existing methods only offer such tests over the sampled interval rather than period-by-period. We find generally weak evidence of a factor pricing specification holding period-by-period, but find evidence that investors are generally compensated for bearing market risk, value risk, and momentum risk on a period-by-period basis.;In the second essay, we turn our focus from time to its complement, frequency. An implication of the canonical factor pricing framework is that factor loadings and factor premia are frequency-invariant. Since a large body of financial literature casts doubt on this assumption, our objective is to induce frequency-dependence into the factor pricing framework. Using wavelet analysis together with band spectrum regression, we extend the Fama-MacBeth procedure and allow factor loadings and premia to vary with frequency, which results in a linear decomposition of the typical factor premia into exhaustive and non-overlapping frequency bands. We design and implement a test for the frequency-invariance of the factor loadings and show that a frequency-dependent factor pricing model more capably characterizes the cross-section of expected returns than does its frequency-invariant counterpart. By ignoring differences in factor loadings and premia across the frequency spectrum, we describe how investors can be misled into making suboptimal investment decisions.;In the final essay, we move past the factor pricing paradigm and consider an alternative way of capturing systematic risk using vector autoregression (VAR). The output of an estimated VAR model on portfolio returns can be viewed as a Granger network, which is a directed graph with edges representing Granger causal relationships. Coupling this network-based approach with a methodology introduced in 2006 to extend the standard VAR-based tests of Granger non-causality to the frequency domain permits the formation of frequency-dependent Granger networks. We further discuss how time-dependence can be induced in these tests by invoking local linear modeling, thereby enabling us to form Granger networks that are localized in both time and frequency. By utilizing techniques from applied graph theory and network topology, such networks can be quantified in terms of the intensity of their interconnectivity using the concept of centrality. In highly centralized Granger networks as opposed to decentralized networks, new information tends to take substantially longer to fully incorporate into prices. Hence, in our context, such measures of centrality offer an indirect measurement of the degree to which new information is absorbed by financial markets. Using the returns on ten industry portfolios, we form empirically estimated time- and frequency-localized networks of these common stock portfolios. Plotting measures of the respective networks' connectivities (measured in a variety of ways) against time and frequency, a three-dimensional surface is formed, which we use to assess how this particular dimension of systematic risk evolved during the recent financial crisis.