You're probably familiar, at least in passing, with the 'convexity' of long-term bonds - i.e. that yields dropping 1% produce a bigger price move than yields rising 1%. A significant amount of brainpower has gone into understanding all the ramifications of this convexity in the fixed income...

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...

We steer our financial course through life choosing how much to spend and how to invest what's left, periodically updating our choices as circumstances evolve. This is the essence of financial planning: specifying in advance a desired spending and investment policy conditional on relevant...

Benjamin Franklin's original maxim found in Poor Richard's Almanac was actually "A penny saved is two pence clear" rather than the more commonly known "A penny saved is a penny earned." We believe he was getting at the notion that one risk-free penny is worth two pennies of expected but...

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 &...