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Why would anyone with a long enough time horizon invest in anything other than equities, given they have the highest expected return? The discussion has reignited following an article...

“In the short run, the market is a voting machine but in the long run, it is a weighing machine” is attributed to Benjamin Graham. Another industry giant, John Bogle, categorized total...

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...

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,...

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...

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...

Long-term investors measure growth rate, but eat compound wealth. The four determinants of terminal wealth ratio (randomly selected portfolio’s terminal wealth divided by benchmark...

We will show that the single best metric predicting drawdown risk is portfolio volatility normalized (divided) by Sharpe ratio i.e. fraction of full Kelly allocation. We first derive...

We will see how the diversification assessment framework provided by conventional finance theory is not applicable to what long-term investors really care about – compounded returns....

Expected return is at the center of financial analysis. But when you hear expected return, you can’t be sure if it is geometric expectation (time average) or arithmetic expectation...