¹³We use the word ‘return’ always to mean the logarithm of the corresponding ‘factor’; and when not explicitly speciﬁed, we always take the expectation before taking the log; if we wanted to refer to $𝔼t[𝔯t+1]$ we would call it the expected log portfolio return rate (to distinguish it from the expected portfolio return factor, $log𝔼t[e𝔯t+1]$ ).