be the price of a security at time t
, including any cash dividends or interest
, and let pt − 1
be its price at t
− 1. Let RSt
be the simple return on the security from t
− 1 to t
Continuously compounded nominal return
The continuously compounded return is the value of RSt that satisfies
be the purchasing power of a dollar at time t
(the number of bundles of consumption that can be purchased for $1). Thus, πt
), where PLt
is the price level at t
(the dollar price of a bundle of consumption goods). The simple inflation rate ISt
The simple real return rst from t − 1 to t is
Continuously compounded real return
The continuously compounded inflation rate is the value of ICt that satisfies. Thus, the continuously compounded real return is the value of rct that satisfies.
Thus, the continuously compounded real return is just the continuously compounded nominal return minus the continuously compounded inflation rate.
Alternatively, the continuously compounded nominal return RCt is the real return rct plus the inflation rate ICt.