Do winners take all?
Capital concentration measures how the capital is distributed between stocks within an index. An increase means that more capital is allocated to larger cap stocks. A decrease indicates that capital is moving to smaller cap stocks. Our research has shown that the capital distribution among stocks is remarkably stable over the long term and tends to inevitably revert to median levels.

How similar are stock returns?
Correlation measures the market-weighted average pair-wise correlation of stocks in the index. It quantifies the degree of commonality between stocks’ returns, as a fraction of their volatility. As correlations rise, the underlying stocks’ returns tends to move in tandem with each other as the common component of return – the market – begins to dominate. As correlations decline, there is less commonality between stocks as a larger component of return among stocks may be explained by idiosyncratic components rather than the market component.

How different are stock returns?
Also known as cross-sectional volatility, this indicator measures whether stocks’ returns relative to their benchmark are converging (low dispersion) or diverging away (high dispersion). As dispersion increases, underlying stock or portfolio returns begin to diverge from the overall benchmark. We find that the market will eventually revert back to the long-term levels when return dispersion is substantially low or high, which is associated with strain on the market.

How easy is it to beat the market?
Market efficiency measures the level of index diversification versus the potential diversification available given the volatility and correlation characteristics of index constituents. Low market efficiency makes it possible for a skilled manager to achieve above-market outcomes with substantially lower equity risk through diversification. Conversely, high market efficiency means that reliably outperforming the index requires taking a similar level of equity risk.

How fat are the tails?
Skewness measures the asymmetry of index returns around the mean. Logarithmic returns tend to exhibit a left-skewed distribution, meaning the most extreme returns are below the mean, as investors tend to react more strongly to negative news. When there is irrational exuberance among investors, market returns tend to become less negatively or, even, positively skewed. Conversely, very low levels of skewness often coincide with the market shock itself, and eventually manifest into positive outcomes as markets stabilize.