Research DigestImproving growth predictability by incorporating time variations in state variables

In “Time-varying state variable risk premia in the ICAPM”, published in the Journal of Financial Economics, Paul Karehnke and his co-authors analyze the conditional asset pricing implications of the time variation in state variable risk.

Why study this

State variables, such as the t-bill rate and term spread, are useful to predict quarterly and annual consumption growth because they contain important information about the future state of the economy. But this forward-looking information varies over time, and so a state variable that conveys good news on average may also convey bad news, or none at all, over certain periods. This paper analyzes the conditional asset pricing implications of the variation over time in state variable risk.


  • The researchers document two channels by which state variable risk premia vary over time. Both are consistent with the conditional implications of an Intertemporal CAPM (ICAPM). 
  • Risk premia in the stock market for exposure to state variables that predict consumption growth are time-varying in a manner consistent with changes over time in this predictive relation.
  • This effect is magnified by time-variation in the conditional variance of the state variables. The intuition behind this is that investors want a larger compensation for a unit exposure to a state variable when there is more risk in absolute magnitude.
  • An important share of the variation in conditional variance is common to all state variables and associated with macro-uncertainty.
  • Portfolios of the benchmark factors, the Fama-French factors in particular, contain the same conditional expected return effects as the state variable risk premia.

The predictability we document is economically strong: state variable risk premia are significantly larger by about 6% annualized (or 0.4 in Sharpe ratio) whenever a state variable predicts consumption growth strongly relative to its own history.

Key insight

Risk premia for exposure to state variables are substantially time-varying.


Controlling for time-varying coefficients in the relation between the state variables and future consumption growth significantly improves consumption growth predictability relative to an unconditional model.

Final takeaway

“Given the [ICAPM-type] model’s success in explaining the conditional variation in state variable risk premia, our findings strengthen the case for time-varying, rational risk premia that drive the predictability of returns.”


Paul Karehnke - ESCP Business School Paul Karehnke Associate Professor of Finance at ESCP Business School
Pedro Barroso Pedro Barroso Associate Professor of Finance at Católica-Lisbon School of Business and Economics (Portugal)
Martijn Boons Martijn Boons Professor of Finance at Tilburg University (Netherlands)