How the Wealth Was Won: Factor Shares as Market Fundamentals
Daniel L Greenwald, MIT Sloan, Martin Lettau, Sydney C Ludvigson Link Video Video
Abstract
Why does the stock market rise and fall? From 1989 to 2017, the real per-capita value of corporate equity increased at a 7.5% annual rate. We estimate that 44% of this increase was attributable to a reallocation of rewards to shareholders in a decelerating economy, primarily at the expense of labor compensation. Economic growth accounted for just 25% of the increase, followed by a lower risk price (18%), and lower interest rates (14%). The period 1952 to 1988 experienced less than one third of the growth in market equity, but economic growth accounted for more than 100% of it.
The related work section of this paper is a good discussion of some of the different trade-offs of different methods within the context of economic modeling. On the one hand, VAR models are highly flexible but entirely statistical, thus lacking economic content outside of the rotation of the reduced form residuals to get the structural shocks. On the other hand, structural modeling is less flexible but add economic theory, aiding interpretation of various drivers and forces. While it’s not discussed directly in the paper, I would guess that an additional benefit of structural modeling is that it more easily let’s you work with non-stationary variables, which are difficult to deal with directly with purely statistical approaches for obvious reasons.
If I want to advance my ability to make economically meaningful claims within my essays, all roads seems to eventually lead to structural modeling.
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Our work also relates to the literature estimating log-affine SDFs in reduced form.12 These studies describe the evolution of the state variables and the SDF in purely statistical terms, for example using an estimated vector autoregression (VAR) for state dynamics. While less statistically flexible, our work features more economic structure, using separate and mutually uncorrelated fundamental components, as well as parametric restrictions on the SDF exposures obtained from theory, such as the leverage risk effect. This structure allows a much clearer interpretation of the drivers of asset prices. For example, unlike VAR-based models, which face the difficult task of transforming reduced-form residuals into identified structural shocks, our model allows us to directly read off the contribution of each latent state. We thus complement this literature by providing economic insight on the economic sources of market fluctuations, particularly the role of factor shares.
Has a kind of cool, natural definition of operating leverage nested within their model – whenever one line item grows faster than another in response to the same core impulse, you can think of that as operating leverage. As with debt, which causes returns to grow faster than the thing that is driving the returns, operating leverage means your outputs grow faster than your inputs. Here, the input is a change in the earnings share and the output is a change in payouts to shareholders as a proportion of output (revenue).
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Importantly, (3) implies that the volatility of cash flow growth is amplified relative to earnings share growth — a form of operating leverage. For example, if ω = 6%, then an increase in the earnings share St from 12% to 18% increases the cash flow share from 6% to 12%. As a result, proportional growth in the cash flow share (100%) is twice as large as in the earnings share (50%), a phenomenon that we call the leverage effect. We note that this leverage effect should hold on average even if the reinvestment share is not exactly constant, so long as investment at long horizons is proportional to output rather than earnings.
Interesting to think about variables having low frequency and high frequency components, where the main distinguishes characteristic is the persistence of the components. In a simple AR(1) autoregressive setup, this implies that the coefficient on the lag is higher for the low frequency component than the high frequency. In the most extreme case, the low frequency component could be model as a “permanent component” that evolves as a random walk (unit root) whereas the high frequency component could be modeled as a “transitory” white noise process. (Relevant to my work on The Universal Law of SaaS Growth, Backing into ARR)
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We choose a two-component mixture for each process to allow the model to flexibly capture both high and low frequency variation in the latent states. Since equity gives its owners access to profits for the lifetime of the firm, it is a heavily forward-looking asset that is much more influenced by persistent rather than transitory fluctuations. Our mixture specification allows the model to accurately capture both low frequency movements that have greater impact on equity prices, as well as higher frequency movements that have a smaller impact on equity prices but may nonetheless drive much of the variation in the observable series. Correspondingly, we refer to the components of each latent state vector as the high or low frequency component