Time-varying Return Volatility Research Articles

Lock-in of Extrapolative Expectations in an Asset Pricing Model

This paper examines an agent's choice of forecast method within a standard asset pricing model. To make a conditional forecast, a representative agent may choose one of the following: (1) a rational (or fundamentals-based) forecast that employs knowledge of the stochastic process governing dividends, (2) a constant forecast based on a simple long-run average of the forecast variable, or (3) a time-varying forecast that extrapolates from the last observation of the forecast variable. I show that a representative agent who is concerned about minimizing forecast errors may inadvertently become locked-in to an extrapolative forecast. In particular, the initial use of extrapolation alters the law of motion of the forecast variable so that the agent perceives no accuracy gain from switching to one of the alternative forecast methods. Under extrapolative expectations, the model can generate excess volatility of stock prices, time-varying volatility of returns, long-horizon predictability of returns, bubbles driven by optimism about the future, and sharp downward movements in stock prices that resemble market crashes. All of these features appear to be present in long-run U.S. stock market data.

LOCK-IN OF EXTRAPOLATIVE EXPECTATIONS IN AN ASSET PRICING MODEL

This paper examines an agent's choice of forecast method within a standard asset pricing model. A representative agent may choose: (1) a fundamentals-based forecast that employs knowledge of the dividend process, (2) a constant forecast that is based on a simple long-run average, or (3) a time-varying forecast that extrapolates from the last observation. I show that an agent who is concerned about minimizing forecast errors may inadvertently become “locked-in” to an extrapolative forecast. In particular, the initial use of extrapolation alters the law of motion of the forecast variable so that the agent perceives no accuracy gain from switching to one of the alternative forecast methods. The model can generate excess volatility of stock prices, time-varying volatility of returns, long-horizon predictability of returns, bubbles driven by optimism about the future, and sharp downward movements in stock prices that resemble market crashes.

Lock-in of Extrapolative Expectations in an Asset Pricing Model

This paper examines an agent's choice of forecast method within a standard asset pricing model. To make a conditional forecast, a representative agent may choose one of the following: (1) a rational (or fundamentals-based) forecast that employs knowledge of the stochastic process governing dividends, (2) a constant forecast based on a simple long-run average of the forecast variable, or (3) a time-varying forecast that extrapolates from the last observation of the forecast variable. I show that a representative agent who is concerned about minimizing forecast errors may inadvertently become locked-in to an extrapolative forecast. In particular, the initial use of extrapolation alters the law of motion of the forecast variable so that the agent perceives no accuracy gain from switching to one of the alternative forecast methods. Under extrapolative expectations, the model can generate excess volatility of stock prices, time-varying volatility of returns, long-horizon predictability of returns, bubbles driven by optimism about the future, and sharp downward movements in stock prices that resemble market crashes. All of these features appear to be present in long-run U.S. stock market data.

Measuring risk aversion from excess returns on a stock index

Measuring risk aversion from excess returns on a stock index presents two obstacles: 1. the time path of the stock-index variance needs to be modeled and estimated, and 2. other components of wealth must be accounted for. We distinguish two measures that relate the risk premium to variance: 1. the measure of risk aversion which, by the single-factor CAPM, would be the slope coefficient in the linear relation between the mean excess return and the variance of the overall risky portfolio of the representative investor, and 2. the slope coefficient in the linear relationship between the mean excess return on a stock index and its variance. Even when risk aversion is constant, the latter can vary significantly with the relative share of stocks in the risky wealth portfolio, and with the beta of unobserved wealth on stocks. We introduce a statistical model with ARCH disturbances and a time-varying parameter in the mean (TVP ARCH-M). The model decomposes the predictable component in stock returns into two parts: the time-varying price of volatility and the time-varying volatility of returns. The relative share of stocks and the beta of the excluded components of wealth on stocks are instrumented by macroeconomic variables. The ratio of corporate profit over national income and the inflation rate are found to be important forces in the dynamics of stock price volatility.