Question

A famous predictive relationship for stock returns is based on the dividend yield (the amount, as a proportion of the stock price, that a firm returns to investors in the form of divi- dends). Figure 1.10 presents quarterly stock returns and divi- dend yields for an equal-weighted index of all stocks listed on the New York Stock Exchange, from 1980Q1 to 2011Q4, a total of 128 observations.

Give the ordinary least squares (OLS) formulas to esti- mate the parameters in the following model for the rela- tionship between stock returns (r) and dividend yields (d):
rₜ₊₁ = α + βdₜ +eₜ₊₁
Below are OLS estimates of the model in part (a).
rₜ₊₁ = -5.5417 + 18.7947 dₜ₊ₑₜ₊₁
(3.8931) (8.0611)
[-1.4235] [2.3316]
Below the estimated parameters are the standard errors are in parentheses (-), and t-statistics are in brackets [-].

Answer 1

Ordinary Least Squares (OLS) is a statistical method used to estimate the parameters of a linear regression model, often employed in financial analysis to predict stock returns based on dividend yields.

Step-by-step explanation:

The question is centered around the use of Ordinary Least Squares (OLS) estimation in the context of finance and stock market analysis. OLS is a method for estimating the unknown parameters in a linear regression model. The formula provided for stock returns 'r' based on dividend yields 'd' is an example of a linear relationship that can be analyzed using OLS.

In the model r₁₊₋₁ = α + βdₜ +e₁₊₋₋, the parameters α (alpha) and β (beta) are estimated using OLS and represent the intercept and slope of the regression line, respectively. The terms in parentheses and brackets below the estimated parameters represent standard errors and t-statistics, which are used to test the significance of the estimates. Based on the historical data, dividend yields are being used to predict the subsequent stock returns, taking into consideration the changes in dividend payout trends over time and their impact on stock performance.