Long-Run Risks

Question 1

Bansal and Yaron 2004

Answer 1

• model consumption and dividend growth rates as containing (1) a small long-run predictable component, and (2) fluctuating economic uncertainty (consumption volatility).
• In our economy, financial markets dislike economic uncertainty and better long-run growth prospects raise equity prices.
• model can justify the equity premium, the risk-free rate, and the volatility of the market return, risk-free rate, and the price-dividend ratio. As in the data, dividend yields predict returns and the volatility of returns is time-varying.

Question 2

Bansal, Gallant and Tauchen 2009

Answer 2

• Empirically tests LRR vs Habit Formation model
• In one model, the long-run risks (LRR) model of Bansal and Yaron, low-frequency movements, and time-varying uncertainty in aggregate consumption growth are the key channels for understanding asset prices.
• In another, as typified by Campbell and Cochrane, habit formation, which generates time-varying risk aversion and consequently time variation in risk premia, is the key channel.
• Both models are found to fit the data equally well at conventional significance levels, and they can track quite closely a new measure of realized annual volatility.
• Further, scrutiny using a rich array of diagnostics suggests that the LRR model is preferred.
• “A unique dimension of the Bansal, Gallant, and Tauchen paper is that consumption and dividends in their model are cointegrated—this feature is typically missing in earlier work on asset market models”

Question 3

Bansal 2008

Answer 3

• Survey paper, gives nice intuitive explanation of seminal LR risk paper.
• Bansal and Yaron (2004) argue that investors care about the long-run growth prospects and the level of economic uncertainty.
• Changes in these fundamentals drive the risks and volatility in asset prices.
• They document that consumption and dividend growth rates contain a small long-run component. That is, current shocks to expected growth alter expectations about future economic growth not only for short horizons but also for the very long run.
• Agents care a lot about these long-run components as small revisions in them lead to large changes in asset prices.
• Any adverse movements in the long-run growth components lower asset prices and concomitantly the wealth and consumption of investors.
• This makes holding equity very risky for investors, making them demand a high equity risk compensation.

Question 4

Bansal, Dittmar and Kiku 2009

Answer 4

• argue that the cointegrating relation between dividends and consumption, a measure of long-run consumption risks, is a key determinant of risk premia at all investment horizons.
• As the investment horizon increases, transitory risks disappear, and the asset’s beta is dominated by long-run consumption risks.
• show that the return betas, derived from the cointegration-based VAR (EC-VAR) model, successfully account for the cross-sectional variation in equity returns at both short and long horizons; however, this is not the case when the cointegrating restriction is ignored.
• Our evidence highlights the importance of cointegration-based long-run consumption risks for financial markets.