Discount factor and conditional return volatility

Using Campbell's (1991) unexpected return decomposition, the implications of the Rational Valuation Formula are derived in terms of unconditional volatility of discount factors, given conditional return volatility and hence given the volatility of unexpected returns. This provides a bound on the discount rate volatility that any econometric specification must produce in order to be admissible. Using 130 years of monthly data on the S&P Composite Index, it is shown that one needs about 10% annualized expected return volatility to explain observed conditional return volatility. The study also shows that the static and Consumption CAPM and a GARM-M specification, broadly consistent with Merton's (1973) ICAPM, produce too little discount rate variability, under a standard assumption about the degree of persistence of returns.