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Unlike the realized past, the future always involves uncertainty. The uncertainty related to risk has a variety of implications that are not widely recognized. We will show analytically and demonstrate...

Academics have long debated the concept of time diversification, which questions whether time reduces the risk for stock investors or not. Prominent academics, led by Paul Samuelson, have shown (usually...

Consider a clairvoyant who can accurately predict two market parameters, Sharpe ratio and volatility, for the forthcoming 10-year period. Clairvoyant selects his stock allocation (leverage multiplier)...

Why would a skilled stock picker ever invest in more than a few of her best ideas? Isn’t diversification for those who don’t know what they are doing? It makes sense to think that a skilled stock picker...