Time Series of Returns - Price Dividend Flashcards
Interpreting regressing returns on lagged returns:
Stock: b = 0.04, t=0.33, R^2 = 0.002
T-Bill: b = 0.91, t=19.5 R^2 = 0.83
Excess: b = 0.04, t=0.39, R^2 = 0.00
The interpretation is the following. Firstly, b>0 indicates a momentum, i.e., past good returns mean higher future returns. If we had b<0 it indicates an overreaction or mean reversion.
Stock returns: Unpredictable based on past returns. b=0.04 means if returns go up 100% this year, you expect a rise of just 4% next year. This is the economic significance of a coefficient. The coefficient is statistically insignificant. The t-statistic of 0.33 is below the standard 2.0 critical value to be significant at the 5% level. The R^2, measuring the proportion of return variance that can be forecast one year ahead, is also miniscule at 0.002.
T-bills: The coefficient is large with a large t-statistic and R^2. In contrast to stock returns, T-bill returns have slow, predictable movements. If interest rates (and hence the one-year return on treasuries) were high last year, they are very likely to be high again this year. Most of the T-bill return is known ahead of time. It does not mean that T-bill markets are inefficient. Think of a trading strategy: If you know interest rates are high, so T-bill returns will be high next year, you’d have to borrow at the high rate to invest, which does not do you any good.
Excess Returns: If you know stock returns will be high next year, you can borrow money and invest in the market. The “right” way to run forecasting regressions is to try to forecast the excess return R_(t+1)^e=R_(t+1)^”stock” -R_(t+1)^”Tbill” , i.e., the return you can achieve by borrowing a dollar and investing. Exploiting this return takes no money out of pocket, only the willingness to bear risk. Studying excess returns separates willingness to consume less and save from the willingness to bear risk. Excess returns, just like stock returns, cannot be forecasted. The reason is that stock returns are so much more volatile than interest rates, that the “return” and “excess return” series look much the same. Still, excess returns is the right way to do it.
Present Value Identity
The price of a stock is the present value of all future dividends the stock will be. The discount-ed-cash-flow or present-value model relates (a) the price of a stock to its expected future cash flows (i.e., dividends), and (b) the price of a stock to variation in discount rates. Since dividends in all future periods enter the PV formula, a single period dividend or discount rate contributes little to the price, but persistent changes in dividends or discount rates have large effects.
Conclusion from P/D regression
Empirical findings on long-horizon returns are in line with time-varying expected returns following an AR(1) process with persistency. Persistent movements in expected returns have dramatic effects on stock prices, where the price much more volatile than under constant expected returns. Source of persistent variation in expected stock returns is unresolved.
EMH can only be tested in conjunction with model on equilibrium returns. The results are evidence against the joint hypothesis (the EMH holds and equilibrium stock returns are constant). The results do not preclude a model with time-varying equilibrium stock returns can fit the data.
