Multi‐scale inter‐temporal capital asset pricing model

This study investigates the multi‐scale inter‐temporal capital asset pricing model (ICAPM). We focus upon differences across timescales since they represent heterogeneities of investors in markets. This study employs a wavelet approach to decompose return data into multiple timescales. Furthermore, we impose a same risk‐aversion parameter constraint into all portfolios, which is proposed by Engle and Bali who show that the constraint provides a reasonable equity risk premium at a daily frequency. We observe positive relations between the expected returns on portfolios and the covariance of the market at a daily frequency, while these relations change as timescales increase. We find that a negative risk–return relation, which might be related to a correction process of overreaction at an approximately weekly frequency (2–16 days). The strongest positive relation is observed at an approximately monthly frequency (16–32 days). Monthly portfolio re‐balances are widely used and might impact stock market return patterns. The equity risk premium in the longer frequency ranges from 8.64 to 11.10%. Our results are robust after controlling for macroeconomic variables, market implied volatility and test portfolios. Moreover, we investigate size and value factors and reveal that the risk premia disappear in the longer frequency, which suggests that ICAPM is satisfied.