Lecture 2 Flashcards
(17 cards)
How can you predict expected returns methodologically?
- run regression of tomorrow’s returns on any variables we can see today
- e.g. r_t+1 = a + b x x_t + e
- if we find a big b or a large R^2, we might be able to make money
- This model implies: E (r_t+1) = a + b x x_t
Purpose: the return-prediction measures whether expected returns (risk premiums) vary over time
Explain the classic efficient markets view.
Classic efficient market view: stock prices are not predictable (the random walk view), so we should see that b = 0 and R^2 = 0 for any variable we regress on future returns
* Competition in stock markets should drive out any predictable movement in prices
* Informational efficiency is nothing more than the predicted effect of competition and free entry
What is the empirical evidence on excess returns’ predictability when using the simple regression model?
- insignificant coefficient and low R^2 for stocks
- Stock returns are not predictable
- the risk free rate is predictable
What are the empirical findings on return forecasting using dividend yield?
Method: longer horizons and new variables
Model: r_e = a + b x d/p + e
Findings: the return- forecasting coefficient is huge
Note: r_t+1 = (p_t+1 + d_t+1)/ p_t = p_t+1/p_t + d_t/p_t x d_t+1/d_t
(if there is no dividend or price growth, the coefficient should be 1)
What does low p_t/d_t imply?
- Expectation of low future returns
- Low ratio, means low returns, meaning prices will adjust in the future
Does variation in dividend/price ratio predict dividend growth? Give the regression equation and the empirical results.
- Variation in d_t/p_t does not predict dividend growth
- Note: r_t+1 = (p_t+1 + d_t+1)/ p_t = p_t+1/p_t + **d_t/p_t **x d_t+1/d_t
- (fat marked part does not predict)
- Model: r_t+1 = a + b x d_t/p_t + e
What is the “dog that did not bark” fallacy by Cochrane (2007)?
- if both returns and dividend growth are unforecastable, then the price dividend ratio is constant, which it is obviously not (it changes of about 15 % in expected returns between 1980 and 2008)
- E_t(r_t+1) = E_t (d_t+1/p_t) = d_t/p_t x E_t (d_t+1/d_t)
- dividend growth non-predictiability provides stronger evidence for return predictability than does return predictability itself
Does predictability mean that markets are “inefficient”?
No.
* Institutional finance: high risk aversion in bad economic times, time-varying risk premium
* Behavioral finance: irrational/ biased investors, people thing that future expected returnsa are constant and get expected cashflows wrong
* the type of return predictability we observe is over longer horizons, stocks have high expected returns in bad times and low expected returns in good times
What is the implication of return predictability on valuation and portfolios. Show by using a simple present value model.
- for corporate finance models, getting the expected returns/ cost of capital of a specific company is key
- remember: value of investment = expected cashflows/ (r_f + ß E_t (r_m - r_f))
- market excess return varies from 2% to 12%
- expected returns do not line up with CAPM ßs but rather multifactor betas
- capital budgeting is a “relative pricing” exercise
- Assumption: assume constant expected returns
Once more, explain the classic view versus the new fact regarding expected returns.
New view: if prices are low relative to dividends, they bounce back, good return
Classic view: Dividend price ratio predicts dividend growth, thus when price are low, dividends are predicted to tank as well
Define a simple AR (1) for dividends.
p_t = E_t(Sum ß^j d_t+j)
where ß = 1/(1+r)
AR: d_t+1 = p_d d_t + e_t+1
We should find that prices move one for one with dividends:
p_t = E_t (sum ß^j d_t+j) = (ß p_d)/ (1 - ß p_d) d_t
Write down a one period model for forecasting dividends by using a one-period asset.
- One period asset: r_t+1 / d_t+1 / p_t
- Take expectations and solve for price-dividend ratio: p_t / d_t = E_t (d_t+1/d_t) / E_t (r_t+1)
- Take logs: p_t - d_t = E_t ( Δ d_t+1) - E_t (r_t+1)
- Assumption: we do not assume constant expected returns
Define the Campbell-Shiller Formula
- Linearized dynamic present value formula
p_t - d_t = E_t ( sum p^(j-1) ( Δ d_t+j - r_t+j) where p = 1/ (1 + d/p) = 0.96
Present value identity for infinitely lived assets
Volatility: if E_t (r_t+1) and E_t ( Δ d_t+1) are constant, then p_t - d_t must be constant -> either r_t or Δ d_t are forecastable if d_t - p_t varies
Give the equation for a volatility decomposition test.
Var(dt - pt) ≈ Cov(dt - pt, Et[sum_{j=1}^∞ (rho)^(j-1) * rt+j])
- Cov(dt - pt, Et[sum_{j=1}^∞ (rho)^(j-1) * Δdt+j])
Define the Old View on Stocks Predictability
- Expected returns do not move much over time, stocks returns are unpredictable
- Prices move on news of cash flows
- CAPM: returns with high covariance with market returns are higher on average
- Beta derives from the covariance of firm and market cash-flows
Define the modern view on return predictability
- Expected returns E_t (r_t+1) move a lot over time and stocks are predictable
- Prices move on news of discount rate changes, p_t/d_t does not forecsat d_t
- The discount rate had to vary a lot over time p_t = E_t(discounted dividends)
- Betas derive from the covariance of firm and factor discount rates
Give some other findings on the predicability of stock returns.
Campbell and Shiller (1988)
▷ Variation in dividend yield is mostly driven by movements in discount rates, instead of movements in expected dividend growth.
Larrain and Yogo (2008)
▷ Net payout yield, the ratio of net payout to asset value, is mostly driven by movements in expected cash flow growth, instead of movements in discount rates.
There may be a problem with how dividends are measured, e.g., dividend & price with M&A.
▷ Not a black-and-white answer, the reality is often more complicated than a simple theory, and measurement is hard.
▷ The answer is probably in between the two extremes.
