What is Return to Consumption Asset In a paper I was reading, a budget constraint for the Euler equation for the consumption asset was described as:-

$$
W_{t+1} = (W_t - C_t) R_{c, t+1}
$$

Here $ R_{c, t+1}$ is the 'return to the consumption asset'. What does this mean?

Paper: Volatility, the Macroeconomics, and Asset Prices
On the previous page (introducing equation 2.2) the authors state that "consumption asset" means "wealth portfolio", so $R_{c,t+1}$ is the return to the wealth portfolio, which makes sense from the equation you quote.


  the log return to the consumption asset (wealth portfolio), $r_{c,t+1}$.