Continuously rebalanced long-short trades are similar to highly levered trades in that their PNL profile depends not only on the final distribution of return, but also on the realized co-variance structure of the asset pair. It's easily possible for both orientations of a rebalanced long-short...

The looming Savings Crisis is usually attributed to people either not saving enough or making poor investment choices, but we believe there's another culprit. Many investors could benefit from a 'free lunch' of pooling their longevity risk with others, but due to market inefficiencies, they do...

We are often asked for our estimate of the long-term return of the equity market. Our framework currently indicates 5.3% above inflation for global equities, which we know strikes many investors as high. This is understandable, given that the most available and frequently cited valuation ratio...

In a world of low rates and high stock prices, it's natural many investors are looking for ways to earn a good return with limited exposure to equities. However, many candidate strategies have return distributions which are significantly different from the Normal and Log-normal distributions...

Early in the 1950s, academics and investors started proposing in earnest a variety of summary statistics to capture in a single number the quality of an investment. Sharpe Ratio became the most commonly used, and it's an important metric, but maximizing Sharpe Ratio doesn't always maximize...

In this short note, we show investors one way to calculate ideal investment sizing by using two rules of thumb based on a simple outline of individual risk aversion. We illustrate these two heuristics, which are not widely appreciated, with thought experiments involving coin flips and ketchup &...

For US investors, international equity exposure has never been so readily available at such a low cost. Nonetheless, surveys indicate US investors typically allocate 80–85% of their equity holdings to US equities, much higher than their proportion of global market value. In this note we...

In this note we present several thought experiments involving coin-flipping to illustrate the common tendency to over-weight past data in forecasting the future, particularly in the context of investment returns. We start by describing a survey we conducted of about 700 respondents involving the...

A sound policy for spending wealth over time is as important as a sensible investment policy. It's a complex problem for taxable individuals with finite, uncertain longevity. A good start is thinking about the simpler problem of how one would spend if immortal. This is exactly the real problem...