This paper provides evidence on the degree of persistence of one of the key components of the CAPM, namely the market risk premium, as well as its volatility. The analysis applies fractional integration methods to data for the US, Germany and Japan, and for robustness purposes considers different time horizons (2, 5 and 10 years) and frequencies (monthly and weekly). The empirical findings in most cases imply that the market risk premium is a highly persistent variable which can be characterized as a random walk process, whilst its volatility is less persistent and exhibits stationary long-memory behaviour. There is also evidence that in the case of the US the degree of persistence has changed as a results of various events; this is confirmed by both endogenous break tests and the associated subsample estimates. Market participants should take this evidence into account when designing their investment strategies.