Week 4

Question 1

Mean reversion

Answer 1

An unexpected high return today reduces expected returns in the future, so that high short term returns tend to be offset by lower returns over the longer term.

Question 2

Why is there a negative correlation between expected and unexpected returns - Discount Rate Shocks for Bonds:

Answer 2

Discount Rate Shocks for Bonds: Suppose there’s a sudden positive shock to the discount rate, leading to higher expected returns on bonds. Investors, expecting higher returns, sell off existing bonds, driving their prices down. This reaction creates an unexpected negative return, showing a perfect negative correlation between expected and unexpected returns for bonds.

Question 3

[Diagram] Myopic solution

Answer 3

Myopic solution is the buy and hold strategy we started out with (i.i.d. stock returns). This is the flat green line that does not depend on the expected excess stock return (xt).

Question 4

[Diagram] Tactical asset allocation

Answer 4

Tactical asset allocation is for the myopic investor who now observes the conditional expected stock return (xt) and reacts accordingly. It increases linearly through the origin.

Question 5

[Diagram] Strategic asset allocation

Answer 5

Strategic asset allocation is the portfolio for the long term investor. This is slightly steeper than the tactical asset allocation line and is shifted upwards so that it has a positive intercept. Strategic shows horizon effects; investors with longer investment horizons tend to have a higher demand for stock investments. Hedge inflation to achieve growth.

Question 6

Sharpe ratio

Answer 6

Equity premium / SD

Question 7

Why is there a negative correlation between expected and unexpected returns - cash flow

Answer 7

Cash Flow Shocks for Stocks: Similarly, in the stock market, during recessions or economic downturns, when investors start anticipating higher returns, it’s often due to the expectation of improved future cash flows or earnings. However, the reality might not match these expectations immediately. The market might still experience negative returns due to ongoing economic challenges or other factors. This disparity between expected and actual returns leads to unexpected negative returns in stocks, correlating negatively with the initially anticipated positive returns.

Question 8

Explain why is there a negative correlation between expected and unexpected returns - define it in one sentence

Answer 8

Expected increase in returns accompanied with negative returns