I. Module 2 Homework 1 [final]: A Little Model of Time-Varying Expected Returns
- Due No due date
- Points 18
- Questions 10
- Time Limit None
Instructions
Expected returns vary over time. Here is a nice structure we use to represent this idea:
denotes the expected return, and denotes the actual log return. (We usually run these in logs, I showed levels in class because it's easier.) Actual returns are expected returns plus unpredictable noise . and can be correlated -- good returns can be positively or negatively associated with good news about expected returns. In fact, and are negatively correlated -- when prices go up we have a good actual return but it's bad news for subsequent expected returns . In the lecture, I used , but we more generally think of expected returns as following a latent (we can't observe it directly) state variable of this form, and then prices reveal to us.
We use this sort of time series model widely in finance -- for example, all the term structure models are built this way. It's worth getting familiar with it.
When the problem calls for numerical values, use , , and the correlation between and shocks . These numbers are close to what we see in dividend-yield regressions, and the latter number reverse-engineers a very nice special case.