The unbiasedness tests of implied volatility as a forecast of future realized volatility have found implied volatility to be a biased predictor. We explain this puzzle by recognizing that option prices contain a market risk premium not only on the asset itself, but also on its volatility. Hull...

We revisit the Roll (1977) critique regarding the unobservability of the market portfolio in the framework of the CAPM. It is equivalent to the unobservability of the pricing kernel (also known as the stochastic discount factor) in the language of the modern asset pricing theory. We advocate an...