Week 2 Homework 1: A Little Model of Time-Varying Expected ReturnsHelp CenterWarning:The hard deadline has passed. You can attempt it, butyou will not get credit for it. You are welcome to try it as a learning exercise.Top of FormExpected returns vary over time. Here is a nice structure we use to represent this idea:xtrt+1=xt1+t=xt+t+1xtdenotes the expected return, andrt+1denotes the actual log return. (We usually run these in logs, I showed levels in class because it's easier.) Actual returns are expected returnsxtplus unpredictable noiset+1.t+1andt+1can be correlated -- good returns can be positively or negatively associated with good news about expected returns. In fact,t+1andt+1are negatively correlated -- when prices go up we have a good actual returnt+1>0but it's bad news for subsequent expected returnst+1