Equity Premium Puzzle/ Risk Free Rate Puzzle/ Lucas Cost of Business Cycles

1. Equity Premium Puzzle

With standard time separable and constant relative risk averse preferences, the consumption based asset pricing model is not consistent with the differences in average return between stocks (equity return) and bonds (risk free return).

Equity return >> Risk Free Return

To be data consistent, the relative risk aversion (RRA) parameter must be very high.

According to the US data: the return on the S&P500 from 1889 to 1978 and the yield on government bonds,

Equity Return ー Bond (Risk Free) Return 〜 6%

http://www.econ.yale.edu/smith/econ510a/book9.pdf

2. Risk Free Rate Puzzle

When RRA parameter is high, the risk free rate must be also high. This is not consistent with the real data.

<Mehra Prescott Model 1985>
qt=(1+r)^(-1)=βE[1/(λ^γ)]

λ: Consumption growth rate, γ: Relative risk aversion parameter

When γ is high, the right hand is low (λ>1), and r must be high.


3. Lucas Cost of Business Cycles

Based on Mehra Prescott model, he found that business cycle costs are very low because agents would pay a very small amount to insure their consumption against the business cycle volatility.

In the Mehra Prescott model, there must be some problem in preference specification. Hence, it is not surprising that Business cycle risk is quite small.