Plausibility and empirical evidence suggest that the prices of equity factor portfolios are anchored by the macroeconomy in the long run. A new paper finds long-term equilibrium relations of factor prices and macro trends, such as activity, inflation, and market liquidity. This implies the predictability of factor performance going forward. When the price of a factor is greater than the long-term value implied by the macro trends, expected returns should be lower over the next period. The predictability seems to have been economically large in the past.

The below quotes are from the paper. Headings, cursive text, and text in brackets have been added.

This post ties in with this site’s summary on macro trends, particularly the section on why macro trends matter for investment management.

### The basic idea

“The price of classical equity factors…is anchored to the real economy in the long run. This long-run co-movement translates into short-run equity factors predictability…We __propose a cointegration framework that exploits long-run co-movement between macroeconomic trends and factor prices, and use it to predict the time-series variation in a given equity factor__… We show that factors beyond the aggregate market are predictable using macroeconomic variables.”

*N.B. Cointegration means that two independent non-stationary series form a linear combination that is stationary.*

“Looking at macroeconomic trends, long-run co-movement, and time-series predictability uncovers a novel link [between macroeconomic and asset returns] which is complementary to the one that looks at macroeconomic changes (innovations), short-run co-movement(betas) and cross-sectional predictability.”

“Our approach appeals to the __intuitive notion that financial assets should not overtake the real economy__. Accordingly, we propose a framework where the price level of a factor should comove with trends in economic fundamentals. Given that economic trends and factor prices are non-stationary variables, the validity of a given set of macroeconomic drivers to track asset prices is naturally investigated by assessing if there exists a stationary linear combination of them (i.e. if they are cointegrated).”

### How to test for ‘cointegration’

“We start by testing the presence of cointegration between macroeconomic trends related to real economic activity, inflation, and aggregate liquidity and the price of factors from leading asset pricing models.”

“In our empirical analysis, __we consider the factors featuring in two of the most prominent asset pricing models__: the five-factor model of Fama and French (2015) and the q-factor model of Hou, Xue, and Zhang (2015)… The q-factor model has its theoretical foundation in the neoclassical q-theory of investment and consists of four factors: the market excess return (MKT), a size factor (ME), an investment factor (IA), and a profitability factor (ROE). (view here http://global-q.org/factors.html) The Fama-French factor model adds to the market and size factors, a value-growth factor, a profitability factor (Robust-Minus-Weak, RMW), and an investment factor (Conservative-Minus-Aggressive, CMA).”

“__As macro factors we use the WTI crude oil returns, the traded liquidity factor, the potential output growth, and the Treasury term spread__…The central idea is to find a set of economic state variables that influence investors and asset prices in a systematic way through…their effect on nominal and real cash flows…We employ the WTI crude oil returns as a tradable proxy for inflation. To measure aggregate economic condition, we use potential output together with the term spread…The liquidity factor…is inversely related to aggregate volatility and provides a longer history relative to the VIX. Importantly, with the sole exception of potential output growth, our benchmark macroeconomic factors are available in real-time and not subject to revisions.”

“Our __sample period is 1968-2019.__ Throughout we use quarterly observations and, accordingly, we focus on (non-overlapping) 3-months holding-period excess return… We provide evidence of cointegration between the price of tradeable factors and macroeconomic drivers.”

### The evidence

“We find the presence of co-integration to be borne out by the data…The Johansen L-max test results establish __strong evidence of a single cointegrating relation__ among the macroeconomic drivers and each of the factors. Indeed, we may reject the null of no cointegration against the alternative of one cointegrating vector.”

“Macroeconomic trends related to economic activity, inflation and aggregate liquidity track the prices of factors featuring in leading asset pricing models…In other words, __factor prices share a common stochastic trend with key drivers of the macroeconomy__.”

“Importantly, the long-run relationship between factor prices and macroeconomic drivers has implications for short-run factor returns. Specifically, we show that __factor returns should be predictable by the deviations of the portfolio value from its long-term economic value with a negative sign__. The intuition is straightforward: when asset prices are higher (lower) than the long-run value implied by the macroeconomic drivers, expected returns are lower (higher) in the next period so that the long-run relationship is corrected.”

### Consequences for factor timing

“The long-run co-movement between factor prices and macro drivers has implications for the short-run predictability of factor returns: when the price of a factor is greater than the long-term value implied by the macro trends, expected returns should be lower over the next period.”

“The…coefficient [of] equilibrium correction term [i.e. the residual of the cointegrating relation] is economically and statistically significant, and negative: __a positive deviation of (log) prices for the characteristics-based factor from their long-term relation with the macro drivers in this period implies a lower expected return for the next period__, with an order of magnitude of about (minus) 0.1 per unit of deviation for the market, size, value, profitability, and the conservative-minus-aggressive factors.”

“We see that __the equilibrium correction term has significant forecasting power for future market excess __returns above and beyond standard predictors…Standard characteristics-based factors like High-Minus-Low (HML or value factor) are strongly predictable in- and out-of-sample, both at quarterly and annual frequencies.”

“Our result is [exemplified] in [the figure below]. Panel (a) shows that the price of [the value premium factor, i.e. investment in high book-to-market versus low book-to-market stocks] (blue line) mean reverts toward a macroeconomic trend (green line). In Panel (b), we employ the deviations of the factor prices from the macro trend to time the factor: the fitted value (green line) explains about one-fourth of the variability in value premium returns (blue line) at an annual frequency.”

### The economic value of factor timing

“We have provided strong evidence of predictability for individual factors. Next, we combine these forecasts to form an optimal factor timing portfolio, and study its benefits from an investor point of view.”

“The documented __predictability is economically large__ as confirmed by (1) variation in expected factors’ returns that is large relative to their unconditional level; and (2) significant economic gains from the perspective of a mean-variance investor.”

“We __report performance for four variations of the optimal timing portfolio: __(1) “Factor Timing” (FT); (2) “Factor Investing” (FI) sets all return forecasts to their unconditional mean; (3) “Market Timing” (MT) does the same [as Factor Timing] except for the market return; and (4) “Anomaly Timing” (AT) does the opposite: the market is forecasted by its unconditional mean, while anomalies receive dynamic forecasts.”

“The factor investing, market timing, factor timing, and anomaly timing portfolio all produce meaningful performance, with Sharpe ratios around 0.9 in sample. More importantly, __factor and anomaly timing improve out-of-sample performance relative to static factor investing__: timing yields Sharpe ratios of about 1 relative to the 0.87 attained with static investing.”

### Consequences for the stochastic discount factor

“Quantitatively, __the average variance of our estimated stochastic discount factor (SDF) increases from 0.80 (in the case of constant factor premiums) to 2.24 when taking into account the predictability__ of the factors induced by deviations of a portfolio value from its long-term economic value. Furthermore, changes in the means of the factors induces variation in the SDF, which is strongly heteroscedastic. The SDF fluctuations induced by factor timing are more pronounced than fluctuations in the SDF that accounts only for time variation in the market portfolio.”