Finance

We analyze the risk characteristics and the valuation of assets in an economy in which the investment opportunity set is described by the real interest rate and the maximum Sharpe ratio. It is shown that, holding constant the beta of the underlying cash flow, the beta of a security is a function of the maturity of the cash flow. For parameter values estimated from U.S. data, the security beta is always increasing with the maturity of the underlying cash flow, while discount rates for risky cash flows can be increasing, decreasing or nonmonotone functions of the maturity of the cash flow. The variation in discount rates and present value factors that is due to variation in the real interest rate and the Sharpe ratio is shown to be large for long maturity cash flows, and the component of the volatility that is due to variation in the Sharpe ratio is more important than that due to variation in the real interest rate.