# What is time-varying risk premium? Forecasting stock returns

I am trying to understand the concept 'Time-varying aggregate risk premium'.

Here is an extract from a Forecasting book, written by Rapach and Zhou,

"However, rational asset pricing theory posits that stock return predictability can result from exposure to time-varying aggregate risk, and to the extent that successful forecasting models consistently capture this time-varying aggregate risk premium, they will remain successful over time".

What is time-varying risk premium and why is it important in forecasting models?

• Thanks Alex C, how does this link to forecasting stock returns. You seem much more knowledgeable on the subject. I am trying to write a literature review, about why forecasting returns are important, my previous argument is forecasting models lose something when market agents use them. But them I am trying to find a counter argument to say why we still should research this. Thanks again. – user22485 Mar 15 '18 at 12:33

Another way of staying "time-varying risk-premium", is saying that the risk-premium is predictable. However, that the fact that the risk-premium is predictable does not means that you can make money out of this.

The best two references to understand this are:

The first tells you what economists mean by equity premium being time-varying or predictable. It basically implies that some variable (or state variable) predicts the equity premium. Cochrane argues that mathematically either dividend growth or returns must be predictable. He shows that the latter is true. Take a look at table (1):

The dividend-price ratio predicts the equity premium. When D/P is high the returns are high.

The second reference (Goyal), shows that equity premium is predictable in-sample but not out-of-sample. So you cannot trade on this predictability - which basically implies that you cannot forecast the ex-post return. Ex-ante we know that equity premium moves with some state variables in the economy (i.e. expected returns are high in recessions) but in practice this cannot be exploited economically.

Edit: Following the comments below here is another good reference by Cochrane. In particular in respect to the comment on whether how can risk-premium be predictable but not profitable to exploit, I make my words, Cochrane words:

Does this mean markets are “inefficient”? Is this an invitation to “buy low and sell high?” Not necessarily. Time varying risk premia are possible. Think like an economist, and think about market equilibrium, not trading opportunities. Prices must adjust to eliminate trading opportunities. People don’t buy stocks because they’re scared. Why at some times are they more scared than others?

• Correct me if I am wrong, so a forecasting model can help predict the time-varying risk premium, so even if I can't profit from the returns of trying to trade the forecasts, I can still try and predict the equity premium, which is useful (for risk management etc.) but not necessarily profitable? – user22485 Mar 15 '18 at 13:41
• Also, If I can predict them equity premium, how is this not profitable? – user22485 Mar 15 '18 at 13:46
• Yes. And knowing that risk premium is time-varying (as in high in bad times) helps build economic models. However, it is not profitable because you don't know the true state variables that rule the world. I have added an extra reference which might clarify what I mean. – phdstudent Mar 15 '18 at 13:47

Up until the work of Robert Shiller in about 1980, it was thought that the expected excess return on the market $(R_M−R_f)$ is constant and is an equilibrium risk premium. Shiller showed that this is not correct, so the next hypothesis was that the e.e.r. is not constant but changes with the state of the economy (though it remains >0 at all times). This is called the time-varying risk premium hypothesis. For example in the middle of a serious recession the risk premium is thought to be larger than usual, according to John Cochrane among others.

This new idea has changed the interpretation of the Efficient Market Hypothesis considerably. Under the "constant expected return" idea the EMH was interpreted as saying that aggregate stock prices are unforecastable. Under the "time varying expected return" idea this had to be revised to say that the market return could to some extent be forecast, but only due to the state of the economy, not to any insight into the future behavior of stocks. So the EMH was weakened considerably (IMHO). This partial foecastability continues to exist even if "everyone knows" the forecasting model, since it is due to macroeconomic factors not to superior private insight.