This paper shows that the correlation between discount rates on three major risky asset classes – equity, housing and corporate bonds – is approximately zero. I establish this new stylized fact – the time varying risk puzzle – by using new long-run data for 17 advanced economies. I confirm that asset valuations and macro-financial risk factors predict returns on individual asset classes, but I show that none of these variables have predictive power across asset classes. The absence of observed discount rate co-movement constitutes a major puzzle since all but a very select set of asset pricing models assume a joint pricing kernel and hence predict a high correlation of risk premia. My findings imply that time-varying discount rates are unlikely to be the key driver of asset price fluctuations. This puts into question prominent asset pricing models relating to time-varying risk aversion, disaster risk, and intermediary risk appetite. The absence of co-movement in the data is not fully attributable to asset-specific risk, investor heterogeneity or market segmentation. Instead, the data point to volatile expectations as the central source of asset price volatility, in line with behavioural models. The observed expectation volatility has real economic effects on a business cycle frequency. Elevated sentiment – or overoptimistic expectations – predict low future GDP growth, and sentiment reversals often mark the onset of financial crises.