Asset Pricing with Idiosyncratic Risk and Overlapping Generations

What is the effect of non-tradeable idiosyncratic risk on asset-market risk premiums? Constantinides and Duffie (1996) and Mankiw (1986) have shown that risk premiums will increase if the idiosyncratic shocks become more volatile during economic contractions. We add two important ingredients to this relationship: (i) the life cycle, and (ii) capital accumulation. We show that in a realistically calibrated life-cycle economy with production these ingredients mitigate the ability of idiosyncratic risk to account for the observed Sharpe ratio on U.S. equity. While the Constantinides-Duffie model can account for the U.S. value of 41% with a risk-aversion coefficient of 8, our model generates a Sharpe ratio of 33%, which is roughly half-way to the complete-markets value of 25%. Almost all of this reduction is due to capital accumulation. Life-cycle effects are important in our model — we demonstrate that idiosyncratic risk matters for asset pricing because it inhibits the intergenerational sharing of aggregate risk — but their net effect on the Sharpe ratio is small.