The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors

A linearization of a rational expectations present value model for corporate stock prices produces a simple relation between the log dividend-price ratio and mathematical expectations of future log real dividend changes and future real discount rates. This relation can be tested using vector autoregressive methods. Three versions of the linearized model, differing in the measure of discount rates, are tested for U. S. time series 1871-1986: versions using real interest rate data, aggregate real consumption data, and return variance data. The results yield a metric to judge the relative importance of real dividend growth, measured real discount rates and unexplained factors in determining the dividend-price ratio.

Yield Spreads and Interest Rate Movements: A Bird's Eye View

The expectations theory of the term structure implies that the spread between a longer-term interest rate and a shorter-term interest rate forecasts two subsequent interest rate changes: the change in yield of the longer-term bond over the life of the shorter-term bond, and a weighted average of the changes in shorter-term rates over the life of the longer-term bond. For postwar U.S. data from Mcculloch [1987] and just about any combination of maturities between one month and ten years we find that the former relation is not borne out by the data, the latter roughly is. When the yield spread is high the yield on the longer-term bond tends to fall, contrary to the expectations theory; at the same time, the shorter-term interest rate tends to rise, just as the expectations theory requires. We discuss several possible interpretations of these findings. We argue that they are consistent with a model in which the spread is a multiple of the value implied by the expectations theory. This model could be generated by time-varying risk premia which are correlated with expected increases in short-term interest rates, or by a failure of rational expectations in our sample period.

Cointegration and Tests of Present Value Models

In a model where a variable Y[sub t] is proportional to the present value, with constant discount rate, of expected future values of a variable y[sub t] the "spread" S[sub t]= Y[sub t] - [theta sub t] will be stationary for some [theta] whether or not y[sub t]must be differenced to induce stationarity. Thus, Y[sub t] and y[sub t] are cointegrated. The model implies that S[sub t] is proportional to the optimal forecast of [delta Y{sub t+1}] and also to the optimal forecast of S*[sub t], the present value of future [delta y{sub t}]. We use vector autoregressive methods, and recent literature on cointegrated processes, to test the model. When Y[sub t] is the long-term interest rate and y[sub t] the short-term interest rate, we find in postwar U.S. data that S[sub t] behaves much like an optimal forecast of S*[sub t] even though as earlier research has shown it is negatively correlated with [delta Y{sub t+1}]. When Y[sub t] is a real stock price index and y[sub t] the corresponding real dividend, using annual U.S. data for 1871-1986 we obtain less encouraging results for the model, al-though the results are sensitive to the assumed discount rate.

Interpreting Cointegrated Models

Error-correction models for cointegrated economic variables are commonly interpreted as reflecting partial adjustment of one variable to another. We show that error-correction models may also arise because one variable forecasts another. Reduced-form estimates of error-correction models cannot be used to distinguish these interpretations. In an application, we show that the estimated coefficients in the Marsh-Merton [I9871 error-correction model of dividend behavior in the stock market are roughly implied by a near-rational expectations model wherein dividends are persistent and prices are disturbed by some persistent random noise. Their results thus do not demonstrate partial adjustment or "smoothing" by managers, but may reflect little more than the persistence of dividends and the noisiness of prices.

A Simple Account of the Behavior of Long-Term Interest Rates

Recent empirical research on the term structure of interest rates has shown that the long-term interest rate is well described by adistributed lag on short-term interest rates, but does not conform to the expectations theory of the term structure. It has been suggested that the long rate "overreacts" to the short rate. This paper presents aunified taxonomy of risk premia, or deviations from the expectations theory. This enables the hypothesis of overreaction to be formally stated. It is shown that, if anything, the long rate has underreacted to the short rate. However, the independent movement of the long rate is primarily responsible for the failure of the expectations theory.

A Scorecard for Indexed Government Debt

Within the last five years, Canada, Sweden and New Zealand have joined the ranks of the United Kingdom and other countries in issuing government bonds that are indexed to inflation. Some observers of the experience in these countries have argued that the United States should follow suit. This paper provides an overview of the issues surrounding debt indexation, and it tries to answer three empirical questions about indexed debt. First, how different would the returns on indexed bonds be from the returns on existing US debt instruments? Second, how would indexed bonds affect the government's average financing costs? Third, how might the Federal Reserve be able to use the information contained in the prices of indexed bonds to help formulate monetary policy? The paper concludes with a more speculative discussion of the possible consequences of increased use of indexed debt contracts by the private sector.

Valuation Ratios and the Long-run Stock Market Outlook: An Update

The use of price-earnings ratios and dividend-price ratios as forecasting variables for the stock market is examined using aggregate annual US data 1871 to 2000 and aggregate quarterly data for twelve countries since 1970. Various simple efficient-markets models of financial markets imply that these ratios should be useful in forecasting future dividend growth, future earnings growth, or future productivity growth. We conclude that, overall, the ratios do poorly in forecasting any of these. Rather, the ratios appear to be useful primarily in forecasting future stock price changes, contrary to the simple efficient-markets models. This paper is an update of our earlier paper (1998), to take account of the remarkable behavior of the stock market in the closing years of the twentieth century.Stock market, price-earnings ratio, forecasts, expectations, dividend-price ratio, efficient markets, Standard & Poor's 500, present value, productivity

Valuation Ratios and the Long-Run Stock Market Outlook: An Update

The use of price earnings ratios and dividend-price ratios as forecasting variables for the stock market is examined using aggregate annual US data 1871 to 2000 and aggregate quarterly data for twelve countries since 1970. Various simple efficient-markets models of financial markets imply that these ratios should be useful in forecasting future dividend growth, future earnings growth, or future productivity growth. We conclude that, overall, the ratios do poorly in forecasting any of these. Rather, the ratios appear to be useful primarily in forecasting future stock price changes, contrary to the simple efficient-markets models. This paper is an update of our earlier paper (1998), to take account of the remarkable behavior of the stock market in the closing years of the twentieth century.

Stock Prices, Earnings and Expected Dividends

This paper presents estimates indicating that, for aggregate U.S. stock market data 1871-1986, a long historical average of real earnings is a good predictor of the present value of future real dividends. This is true even when the information contained in stock prices is taken into account. We estimate that for each year the optimal forecast of the present value of future real dividends is roughly a weighted average of moving average earnings and current real price, with between 2/3 and 3/4 of the weight on the earnings measure. This means that simple present value models of stock prices can be strongly rejected. We use a vector autoregressive approach which enables us to compute the implications of this for the behavior of stock prices and returns. We estimate that log dividend-price ratios are more variable than, and virtually uncorrelated with, their theoretical counterparts given the present value models. Annual returns on stocks are quite highly correlated with their theoretical counterparts, but are two to four times as variable. Our approach also reveals the connection between recent papers showing forecastability of long-horizon returns on corporate stocks, and earlier literature claiming that stock prices are too volatile to be accounted for in terms of simple present value models. We show that excess volatility directly implies the forecastability of long-horizon returns.