On the market price of risk

摘要

An important parameter describing the state of capital markets, investment opportunity sets, and asset pricing is the unobservable market risk price. The estimated risk price depends upon the selected asset set, the number of assets, the investment horizon, and the sample period. We document the large theoretical and empirical probability of an unacceptably negative sample estimate for the unbiased estimator of the squared risk price. We address admissibility and dominance under quadratic loss of alternative estimators, concluding that an optimized shrinkage estimator has the smallest expected quadratic loss compared with our alternative estimators. Using market data, we examine estimates for more inclusive investment opportunity sets and provide upper bounded estimates of the risk price and resultant unique Sharpe measure, to complement the existing literature's Sharpe measure bounds and equity premium estimates. Finally, we examine time series properties, behavior in the business cycle, and relation to some recently advocated economic factors.