Cashflow Risk vs Discount Risk

The answer to your question could fill an entire asset pricing text book. Your question mixes theory and empirics.

A different way of looking at it is to look at the identity:

$$ 1 = E[M_t R_t]$$

To generate a sufficient risk premium either you need to have the covariance of the SDF with the the return to be sufficiently high.

Campbell and Cochrane basically change $M_t$ to generate a sufficiently volatile SDF.

Bansal and Yaron, use Epstein-Zin utility and change the standard cash-flow component of dividends. Lettau and Wachter similarly.

Empirically I think this blog post explains it super well: https://johnhcochrane.blogspot.com/2015/04/the-sources-of-stock-market-fluctuations.html

The cash flow news / discount rate news decomposition is given by

$$r_{t+1}-mathbb{E}_t[r_{t+1}]=(mathbb{E}_{t+1}-mathbb{E}_t)sum_{j=0}^{infty}rho^jDelta d_{t+1+j}-(mathbb{E}_{t+1}-mathbb{E}_t)sum_{j=1}^{infty}rho^jDelta r_{t+1+j},$$

where $r_{t}$ is log-return $d_{t}$ is log-dividend and $rho$ is a constant. This follows directly from the Campbell-Shiller decomposition.

Here the second term is discount rate news that determines shocks to the path of expected log-returns. This will be zero if expected stock returns are constant as in older finance theories. On the other hand, it is generally non-zero if returns are predictable. To see this assume we find $betaneq 0$ for some predictor $x_t$ so that

$$r_{t+1}=alpha +beta x_t+epsilon_{t+1}.$$

Then the discount rate news component is

$$(mathbb{E}_{t+1}-mathbb{E}_t)sum_{j=1}^{infty}betarho^jDelta x_{t+1+j}$$

For simplicity assume the predictor is AR(1) with persistence $lambda$.

$$(mathbb{E}_{t+1}-mathbb{E}_t)sum_{j=1}^{infty}betarho^jDelta x_{t+1+j}=(x_{t+1}-lambda x_t)frac{betalambdarho}{1-rholambda}.$$

Hence return predictability implies that return variation is partly driven by discount rate news. Modern asset pricing theories try to explain why certain variables $x_t$ can forecast returns. In the habit model the key predictor is consumption growth so higher consumption means lower expected returns. This can also explain why price-dividend ratios forecast returns. In the long run risk model there are two predictors: expected consumption growth and consumption volatility.

The cash flow news component does not create return predictability but creates variance in returns as a positive shock to future cash flows leads to higher returns.