Realized Semicovariances

VENI project

This year I had the honor of being awarded a VENI grant for a line of research revolving around realized semicovariances. The proposal consists of several projects based on two well-known observations. First, the correlation between stocks depends on whether their prices move upward or downward, and second, markets react differently to up and down movements of similar magnitude. These are not necessarily new ideas, and have been documented extensively in the past. Rather, based on preliminary analyses, it appears that the magnitude of these effects has been underestimated. Both asymmetries have been measured at relatively low frequencies, but reveal themselves more strongly at higher frequencies using intra-day observations of stock prices.

I introduce the concept of realized semicovariances: measures of co-dependence conditional on the sign of the stock returns. High-frequency data can be used to estimate these measures on a daily basis (or potentially even shorter timeframes). The semicovariances decompose the normal covariance into four terms, measuring the relative contribution of joint up- or down-, or mixed movements to the total covariance. Over long horizons the relative contributions of the various semicovariances even out, but at short horizons they show remarkably different dynamics.

The use of realized semicovariances in understanding financial markets will be investigated over several projects. For instance, I investigate how decomposing the covariance matrix helps in predicting future return volatility. Through observation of the relative contribution of the various semicovariances over time, it is possible to better anticipate changes in the risk inherent to portfolios. It turns out that the joint negative semicovariance is a better predictor of future total covariance—better even than the covariance itself. Indeed, the market’s mood is dominated by downside risk.

The semicovariances also play a natural role in understanding which stocks obtain high or low average returns. The standard Capital Asset Pricing Model states that stocks that have high covariance with the market risk factor obtain the highest returns. These stocks tend to lose money when the whole market is down, which makes them especially risky. Empirical evidence has been elusive, and standard asset pricing tests tend to fail at finding evidence of this market beta explaining cross-sectional differences in expected returns. Semibetas are naturally defined as an extension of the semicovariances. Based on the same intuition, one could argue that a stock that has high joint negative semibeta relative to the market is a truly risky stock and should carry a large risk premium. On the other hand, a stock that tends to go up in downtimes, as measured by a mixed semibeta, might even obtain a negative risk premium.

The VENI allows me additional research time and funds to investigate these and other projects over the next three years. For more details on this project, see my personal website, which at the time of writing contains a draft of the first research project.